{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Template fits\n",
    "\n",
    "In applications we are interested in separating a signal component from background components, we often fit parameteric models to data. Sometimes constructing a parametric model for some component is difficult. In that case, one fits a template instead which may be obtained from simulation or from a calibration sample in which a pure component can be isolated.\n",
    "\n",
    "The challenge then is to propagate the uncertainty of the template into the result. The template is now also estimated from a sample (be it simulated or a calibration sample), and the uncertainty associated to that can be substantial. We investigate different approaches for template fits, including the Barlow-Beeston and Barlow-Beeston-lite methods."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "from iminuit import Minuit\n",
    "from iminuit.cost import poisson_chi2, BarlowBeestonLite, ExtendedBinnedNLL\n",
    "import numpy as np\n",
    "from scipy.stats import norm, truncexpon\n",
    "from scipy.optimize import root_scalar, minimize\n",
    "import matplotlib.pyplot as plt\n",
    "from IPython.display import display\n",
    "from collections import defaultdict\n",
    "from joblib import Parallel, delayed"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As a toy example, we generate a mixture of two components: a normally distributed signal and exponentially distributed background."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "def generate(rng, nmc, truth, bins):\n",
    "    xe = np.linspace(0, 2, bins + 1)\n",
    "    b = np.diff(truncexpon(1, 0, 2).cdf(xe))\n",
    "    s = np.diff(norm(1, 0.1).cdf(xe))\n",
    "    n = rng.poisson(b * truth[0]) + rng.poisson(s * truth[1])\n",
    "    t = np.array([rng.poisson(b * nmc), rng.poisson(s * nmc)])\n",
    "    return xe, n, t\n",
    "\n",
    "rng = np.random.default_rng(1)\n",
    "truth = 750, 250\n",
    "xe, n, t = generate(rng, 100, truth, 15)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Data is visualized on the left-hand side. The templates are shown on the right-hand side. To show the effect of uncertainties in the template, this example intentially uses templates with poor statistical resolution."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 720x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(1, 2, figsize=(10, 4), sharex=True)\n",
    "ax[0].stairs(n, xe, fill=True, color=\"k\", alpha=0.5, label=\"data\")\n",
    "for i, ti in enumerate(t):\n",
    "    ax[1].stairs(ti, xe, fill=True, alpha=0.5, label=f\"template {i}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Bootstrapping template uncertainties\n",
    "\n",
    "Bootstrapping is a general purpose technique to include uncertainties backed up by bootstrap theory, so it can be applied to this problem.\n",
    "We perform a standard fit and pretend that the templates have no uncertainties. Then, we repeat this fit many times with templates that are fluctuated around the actual values assuming a Poisson distribution.\n",
    "\n",
    "There is no built-in cost function in iminuit for a template fit, so we write the cost function for this case."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table>\n",
       "    <tr>\n",
       "        <th colspan=\"5\" style=\"text-align:center\" title=\"Minimizer\"> Migrad </th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td colspan=\"2\" style=\"text-align:left\" title=\"Minimum value of function\"> FCN = 4.338e+04 (chi2/ndof = 3336.6) </td>\n",
       "        <td colspan=\"3\" style=\"text-align:center\" title=\"Total number of function and (optional) gradient evaluations\"> Nfcn = 110 </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td colspan=\"2\" style=\"text-align:left\" title=\"Estimated distance to minimum and goal\"> EDM = 3.77e-06 (Goal: 0.0002) </td>\n",
       "        <td colspan=\"3\" style=\"text-align:center\" title=\"Total run time of algorithms\"> time = 0.3 sec </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td colspan=\"2\" style=\"text-align:center;background-color:#92CCA6;color:black\"> Valid Minimum </td>\n",
       "        <td colspan=\"3\" style=\"text-align:center;background-color:#92CCA6;color:black\"> No Parameters at limit </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td colspan=\"2\" style=\"text-align:center;background-color:#92CCA6;color:black\"> Below EDM threshold (goal x 10) </td>\n",
       "        <td colspan=\"3\" style=\"text-align:center;background-color:#92CCA6;color:black\"> Below call limit </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"text-align:center;background-color:#92CCA6;color:black\"> Covariance </td>\n",
       "        <td style=\"text-align:center;background-color:#92CCA6;color:black\"> Hesse ok </td>\n",
       "        <td style=\"text-align:center;background-color:#92CCA6;color:black\" title=\"Is covariance matrix accurate?\"> Accurate </td>\n",
       "        <td style=\"text-align:center;background-color:#92CCA6;color:black\" title=\"Is covariance matrix positive definite?\"> Pos. def. </td>\n",
       "        <td style=\"text-align:center;background-color:#92CCA6;color:black\" title=\"Was positive definiteness enforced by Minuit?\"> Not forced </td>\n",
       "    </tr>\n",
       "</table><table>\n",
       "    <tr>\n",
       "        <td></td>\n",
       "        <th title=\"Variable name\"> Name </th>\n",
       "        <th title=\"Value of parameter\"> Value </th>\n",
       "        <th title=\"Hesse error\"> Hesse Error </th>\n",
       "        <th title=\"Minos lower error\"> Minos Error- </th>\n",
       "        <th title=\"Minos upper error\"> Minos Error+ </th>\n",
       "        <th title=\"Lower limit of the parameter\"> Limit- </th>\n",
       "        <th title=\"Upper limit of the parameter\"> Limit+ </th>\n",
       "        <th title=\"Is the parameter fixed in the fit\"> Fixed </th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th> 0 </th>\n",
       "        <td> x0 </td>\n",
       "        <td> 761 </td>\n",
       "        <td> 30 </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
       "        <td> 0 </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th> 1 </th>\n",
       "        <td> x1 </td>\n",
       "        <td> 193 </td>\n",
       "        <td> 19 </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
       "        <td> 0 </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
       "    </tr>\n",
       "</table><table>\n",
       "    <tr>\n",
       "        <td></td>\n",
       "        <th> x0 </th>\n",
       "        <th> x1 </th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th> x0 </th>\n",
       "        <td> 933 </td>\n",
       "        <td style=\"background-color:rgb(212,212,250);color:black\"> -172 <strong>(-0.294)</strong> </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th> x1 </th>\n",
       "        <td style=\"background-color:rgb(212,212,250);color:black\"> -172 <strong>(-0.294)</strong> </td>\n",
       "        <td> 365 </td>\n",
       "    </tr>\n",
       "</table>"
      ],
      "text/plain": [
       "┌─────────────────────────────────────────────────────────────────────────┐\n",
       "│                                Migrad                                   │\n",
       "├──────────────────────────────────┬──────────────────────────────────────┤\n",
       "│ FCN = 4.338e+04 (chi2/ndof = 3336.6)│              Nfcn = 110              │\n",
       "│ EDM = 3.77e-06 (Goal: 0.0002)    │            time = 0.3 sec            │\n",
       "├──────────────────────────────────┼──────────────────────────────────────┤\n",
       "│          Valid Minimum           │        No Parameters at limit        │\n",
       "├──────────────────────────────────┼──────────────────────────────────────┤\n",
       "│ Below EDM threshold (goal x 10)  │           Below call limit           │\n",
       "├───────────────┬──────────────────┼───────────┬─────────────┬────────────┤\n",
       "│  Covariance   │     Hesse ok     │ Accurate  │  Pos. def.  │ Not forced │\n",
       "└───────────────┴──────────────────┴───────────┴─────────────┴────────────┘\n",
       "┌───┬──────┬───────────┬───────────┬────────────┬────────────┬─────────┬─────────┬───────┐\n",
       "│   │ Name │   Value   │ Hesse Err │ Minos Err- │ Minos Err+ │ Limit-  │ Limit+  │ Fixed │\n",
       "├───┼──────┼───────────┼───────────┼────────────┼────────────┼─────────┼─────────┼───────┤\n",
       "│ 0 │ x0   │    761    │    30     │            │            │    0    │         │       │\n",
       "│ 1 │ x1   │    193    │    19     │            │            │    0    │         │       │\n",
       "└───┴──────┴───────────┴───────────┴────────────┴────────────┴─────────┴─────────┴───────┘\n",
       "┌────┬───────────┐\n",
       "│    │   x0   x1 │\n",
       "├────┼───────────┤\n",
       "│ x0 │  933 -172 │\n",
       "│ x1 │ -172  365 │\n",
       "└────┴───────────┘"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "def cost(yields):\n",
    "    mu = 0\n",
    "    for y, c in zip(yields, t):\n",
    "        mu += y * c / np.sum(c)\n",
    "    r = poisson_chi2(n, mu)\n",
    "    return r\n",
    "\n",
    "cost.errordef = Minuit.LEAST_SQUARES\n",
    "cost.ndata = np.prod(n.shape)\n",
    "\n",
    "starts = np.ones(2)\n",
    "m = Minuit(cost, starts)\n",
    "m.limits = (0, None)\n",
    "m.migrad()\n",
    "m.hesse()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The uncertainties reported by the fit correspond to the uncertainty in the data, but not the uncertainty in the templates. The chi2/ndof is also very large, since the uncertainties in the template are not considered in the fit.\n",
    "\n",
    "We bootstrap the templates 1000 times and compute the covariance of the fitted results."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "b = 1000\n",
    "rng = np.random.default_rng(1)\n",
    "pars = []\n",
    "for ib in range(b):\n",
    "    ti = rng.poisson(t)\n",
    "\n",
    "    def cost(yields):\n",
    "        mu = 0\n",
    "        for y, c in zip(yields, ti):\n",
    "            mu += y * c / np.sum(c)\n",
    "        r = poisson_chi2(n, mu)\n",
    "        return r\n",
    "    \n",
    "    mi = Minuit(cost, m.values[:])\n",
    "    mi.errordef = Minuit.LEAST_SQUARES\n",
    "    mi.limits = (0, None)\n",
    "    mi.strategy = 0\n",
    "    mi.migrad()\n",
    "    assert mi.valid\n",
    "    pars.append(mi.values[:])\n",
    "\n",
    "cov2 = np.cov(np.transpose(pars), ddof=1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We print the uncertainties from the different stages and the correlation between the two yields.\n",
    "\n",
    "To obtain the full error, we add the independent covariance matrices from the original fit and the bootstrap."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "fit\n",
      "  b 761 +- 31\n",
      "  s 193 +- 19\n",
      "  correlation -0.29\n",
      "bootstrap\n",
      "  b 761 +- 36\n",
      "  s 193 +- 35\n",
      "  correlation -0.96\n",
      "fit+bootstrap\n",
      "  b 761 +- 48\n",
      "  s 193 +- 39\n",
      "  correlation -0.73\n"
     ]
    }
   ],
   "source": [
    "cov1 = m.covariance\n",
    "\n",
    "for title, cov in zip((\"fit\", \"bootstrap\", \"fit+bootstrap\"), \n",
    "                      (cov1, cov2, cov1 + cov2)):\n",
    "    print(title)\n",
    "    for label, p, e in zip((\"b\", \"s\"), m.values, np.diag(cov) ** 0.5):\n",
    "        print(f\"  {label} {p:.0f} +- {e:.0f}\")\n",
    "    print(f\"  correlation {cov[0, 1] / np.prod(np.diag(cov)) ** 0.5:.2f}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The bootstrapped template errors are much larger than the fit errors in this case, since the sample used to generate the templates is much smaller than the data sample.\n",
    "\n",
    "The bootstrapped errors for both yields are nearly equal (they become exactly equal if the template sample is large) and the correlation is close to -1 (and becomes exactly -1 in large samples). This is expected, since the data sample is fixed in each iteration. Under these conditions, a change in the templates can only increase the yield of one component at an equal loss for the other component."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Template fit with nuisance parameters\n",
    "\n",
    "As described in [Barlow and Beeston, Comput.Phys.Commun. 77 (1993) 219-228](https://doi.org/10.1016/0010-4655(93)90005-W), the correct treatment from first principles is to write down the likelihood function for this case, in which the observed values and unknown parameters are clearly stated. The insight is that the true contents of the bins for the templates are unknown and we need to introduce a nuisance parameter for each bin entry in the template. The combined likelihood for the problem is then combines the estimation of the template yields with the estimation of unknown templates.\n",
    "\n",
    "This problem can be handled straight-forwardly with Minuit, but it leads to the introduction of a large number of nuisance parameters, one for each entry in each template. We again write a cost function for this case (here a class for convenience).\n",
    "\n",
    "As a technical detail, it is necessary to increase the call limit in Migrad for the fit to fully converge, since the limit set by Minuit's default heuristic is too tight for this application."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table>\n",
       "    <tr>\n",
       "        <th colspan=\"5\" style=\"text-align:center\" title=\"Minimizer\"> Migrad </th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td colspan=\"2\" style=\"text-align:left\" title=\"Minimum value of function\"> FCN = 18.27 (chi2/ndof = 1.4) </td>\n",
       "        <td colspan=\"3\" style=\"text-align:center\" title=\"Total number of function and (optional) gradient evaluations\"> Nfcn = 3464 </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td colspan=\"2\" style=\"text-align:left\" title=\"Estimated distance to minimum and goal\"> EDM = 6.02e-05 (Goal: 0.0002) </td>\n",
       "        <td colspan=\"3\" style=\"text-align:center\" title=\"Total run time of algorithms\"> time = 0.1 sec </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td colspan=\"2\" style=\"text-align:center;background-color:#92CCA6;color:black\"> Valid Minimum </td>\n",
       "        <td colspan=\"3\" style=\"text-align:center;background-color:#FFF79A;color:black\"> SOME Parameters at limit </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td colspan=\"2\" style=\"text-align:center;background-color:#92CCA6;color:black\"> Below EDM threshold (goal x 10) </td>\n",
       "        <td colspan=\"3\" style=\"text-align:center;background-color:#92CCA6;color:black\"> Below call limit </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"text-align:center;background-color:#92CCA6;color:black\"> Covariance </td>\n",
       "        <td style=\"text-align:center;background-color:#92CCA6;color:black\"> Hesse ok </td>\n",
       "        <td style=\"text-align:center;background-color:#92CCA6;color:black\" title=\"Is covariance matrix accurate?\"> Accurate </td>\n",
       "        <td style=\"text-align:center;background-color:#92CCA6;color:black\" title=\"Is covariance matrix positive definite?\"> Pos. def. </td>\n",
       "        <td style=\"text-align:center;background-color:#92CCA6;color:black\" title=\"Was positive definiteness enforced by Minuit?\"> Not forced </td>\n",
       "    </tr>\n",
       "</table><table>\n",
       "    <tr>\n",
       "        <td></td>\n",
       "        <th title=\"Variable name\"> Name </th>\n",
       "        <th title=\"Value of parameter\"> Value </th>\n",
       "        <th title=\"Hesse error\"> Hesse Error </th>\n",
       "        <th title=\"Minos lower error\"> Minos Error- </th>\n",
       "        <th title=\"Minos upper error\"> Minos Error+ </th>\n",
       "        <th title=\"Lower limit of the parameter\"> Limit- </th>\n",
       "        <th title=\"Upper limit of the parameter\"> Limit+ </th>\n",
       "        <th title=\"Is the parameter fixed in the fit\"> Fixed </th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th> 0 </th>\n",
       "        <td> x0 </td>\n",
       "        <td> 800 </td>\n",
       "        <td> 50 </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
       "        <td> 0 </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th> 1 </th>\n",
       "        <td> x1 </td>\n",
       "        <td> 190 </td>\n",
       "        <td> 40 </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
       "        <td> 0 </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th> 2 </th>\n",
       "        <td> x2 </td>\n",
       "        <td> 9.0 </td>\n",
       "        <td> 1.4 </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
       "        <td> 0 </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th> 3 </th>\n",
       "        <td> x3 </td>\n",
       "        <td> 8.5 </td>\n",
       "        <td> 1.3 </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
       "        <td> 0 </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th> 4 </th>\n",
       "        <td> x4 </td>\n",
       "        <td> 9.0 </td>\n",
       "        <td> 1.4 </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
       "        <td> 0 </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th> 5 </th>\n",
       "        <td> x5 </td>\n",
       "        <td> 7.4 </td>\n",
       "        <td> 1.2 </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
       "        <td> 0 </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th> 6 </th>\n",
       "        <td> x6 </td>\n",
       "        <td> 8.4 </td>\n",
       "        <td> 1.3 </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
       "        <td> 0 </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th> 7 </th>\n",
       "        <td> x7 </td>\n",
       "        <td> 6.4 </td>\n",
       "        <td> 1.1 </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
       "        <td> 0 </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th> 8 </th>\n",
       "        <td> x8 </td>\n",
       "        <td> 9.2 </td>\n",
       "        <td> 1.7 </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
       "        <td> 0 </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th> 9 </th>\n",
       "        <td> x9 </td>\n",
       "        <td> 4.8 </td>\n",
       "        <td> 2.3 </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
       "        <td> 0 </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th> 10 </th>\n",
       "        <td> x10 </td>\n",
       "        <td> 7.0 </td>\n",
       "        <td> 1.5 </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
       "        <td> 0 </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th> 11 </th>\n",
       "        <td> x11 </td>\n",
       "        <td> 5.5 </td>\n",
       "        <td> 1.0 </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
       "        <td> 0 </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th> 12 </th>\n",
       "        <td> x12 </td>\n",
       "        <td> 5.1 </td>\n",
       "        <td> 0.9 </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
       "        <td> 0 </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th> 13 </th>\n",
       "        <td> x13 </td>\n",
       "        <td> 4.6 </td>\n",
       "        <td> 0.9 </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
       "        <td> 0 </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th> 14 </th>\n",
       "        <td> x14 </td>\n",
       "        <td> 4.7 </td>\n",
       "        <td> 0.9 </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
       "        <td> 0 </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th> 15 </th>\n",
       "        <td> x15 </td>\n",
       "        <td> 4.3 </td>\n",
       "        <td> 0.8 </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
       "        <td> 0 </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th> 16 </th>\n",
       "        <td> x16 </td>\n",
       "        <td> 3.2 </td>\n",
       "        <td> 0.7 </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
       "        <td> 0 </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th> 17 </th>\n",
       "        <td> x17 </td>\n",
       "        <td> 0.0 </td>\n",
       "        <td> 0.4 </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
       "        <td> 0 </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th> 18 </th>\n",
       "        <td> x18 </td>\n",
       "        <td> 0.0 </td>\n",
       "        <td> 0.4 </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
       "        <td> 0 </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th> 19 </th>\n",
       "        <td> x19 </td>\n",
       "        <td> 0.0 </td>\n",
       "        <td> 0.4 </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
       "        <td> 0 </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th> 20 </th>\n",
       "        <td> x20 </td>\n",
       "        <td> 0.0 </td>\n",
       "        <td> 0.5 </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
       "        <td> 0 </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th> 21 </th>\n",
       "        <td> x21 </td>\n",
       "        <td> 0.0 </td>\n",
       "        <td> 0.4 </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
       "        <td> 0 </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th> 22 </th>\n",
       "        <td> x22 </td>\n",
       "        <td> 2.1 </td>\n",
       "        <td> 1.5 </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
       "        <td> 0 </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th> 23 </th>\n",
       "        <td> x23 </td>\n",
       "        <td> 19 </td>\n",
       "        <td> 4 </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
       "        <td> 0 </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th> 24 </th>\n",
       "        <td> x24 </td>\n",
       "        <td> 54 </td>\n",
       "        <td> 7 </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
       "        <td> 0 </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th> 25 </th>\n",
       "        <td> x25 </td>\n",
       "        <td> 23 </td>\n",
       "        <td> 4 </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
       "        <td> 0 </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th> 26 </th>\n",
       "        <td> x26 </td>\n",
       "        <td> 1.1 </td>\n",
       "        <td> 1.0 </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
       "        <td> 0 </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th> 27 </th>\n",
       "        <td> x27 </td>\n",
       "        <td> 0.0 </td>\n",
       "        <td> 0.4 </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
       "        <td> 0 </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th> 28 </th>\n",
       "        <td> x28 </td>\n",
       "        <td> 0.0 </td>\n",
       "        <td> 0.4 </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
       "        <td> 0 </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th> 29 </th>\n",
       "        <td> x29 </td>\n",
       "        <td> 0.0 </td>\n",
       "        <td> 0.4 </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
       "        <td> 0 </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th> 30 </th>\n",
       "        <td> x30 </td>\n",
       "        <td> 0.0 </td>\n",
       "        <td> 0.4 </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
       "        <td> 0 </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th> 31 </th>\n",
       "        <td> x31 </td>\n",
       "        <td> 0.0 </td>\n",
       "        <td> 0.5 </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
       "        <td> 0 </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
       "    </tr>\n",
       "</table><table>\n",
       "    <tr>\n",
       "        <td></td>\n",
       "        <th> x0 </th>\n",
       "        <th> x1 </th>\n",
       "        <th> x2 </th>\n",
       "        <th> x3 </th>\n",
       "        <th> x4 </th>\n",
       "        <th> x5 </th>\n",
       "        <th> x6 </th>\n",
       "        <th> x7 </th>\n",
       "        <th> x8 </th>\n",
       "        <th> x9 </th>\n",
       "        <th> x10 </th>\n",
       "        <th> x11 </th>\n",
       "        <th> x12 </th>\n",
       "        <th> x13 </th>\n",
       "        <th> x14 </th>\n",
       "        <th> x15 </th>\n",
       "        <th> x16 </th>\n",
       "        <th> x17 </th>\n",
       "        <th> x18 </th>\n",
       "        <th> x19 </th>\n",
       "        <th> x20 </th>\n",
       "        <th> x21 </th>\n",
       "        <th> x22 </th>\n",
       "        <th> x23 </th>\n",
       "        <th> x24 </th>\n",
       "        <th> x25 </th>\n",
       "        <th> x26 </th>\n",
       "        <th> x27 </th>\n",
       "        <th> x28 </th>\n",
       "        <th> x29 </th>\n",
       "        <th> x30 </th>\n",
       "        <th> x31 </th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th> x0 </th>\n",
       "        <td> 2.24e+03 </td>\n",
       "        <td style=\"background-color:rgb(152,152,250);color:black\"> -1.45e+03 <strong>(-0.756)</strong> </td>\n",
       "        <td style=\"background-color:rgb(221,221,250);color:black\"> -14.6 <strong>(-0.226)</strong> </td>\n",
       "        <td style=\"background-color:rgb(221,221,250);color:black\"> -13.8 <strong>(-0.222)</strong> </td>\n",
       "        <td style=\"background-color:rgb(221,221,250);color:black\"> -14.6 <strong>(-0.226)</strong> </td>\n",
       "        <td style=\"background-color:rgb(222,222,250);color:black\"> -12 <strong>(-0.214)</strong> </td>\n",
       "        <td style=\"background-color:rgb(221,221,250);color:black\"> -13.6 <strong>(-0.221)</strong> </td>\n",
       "        <td style=\"background-color:rgb(237,237,250);color:black\"> -5.25 <strong>(-0.100)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,207,207);color:black\"> 23.6 <strong>(0.289)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,153,153);color:black\"> 68.9 <strong>(0.644)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,202,202);color:black\"> 23.2 <strong>(0.320)</strong> </td>\n",
       "        <td style=\"background-color:rgb(233,233,250);color:black\"> -6.29 <strong>(-0.134)</strong> </td>\n",
       "        <td style=\"background-color:rgb(225,225,250);color:black\"> -8.3 <strong>(-0.191)</strong> </td>\n",
       "        <td style=\"background-color:rgb(226,226,250);color:black\"> -7.42 <strong>(-0.184)</strong> </td>\n",
       "        <td style=\"background-color:rgb(226,226,250);color:black\"> -7.59 <strong>(-0.185)</strong> </td>\n",
       "        <td style=\"background-color:rgb(227,227,250);color:black\"> -7.06 <strong>(-0.181)</strong> </td>\n",
       "        <td style=\"background-color:rgb(229,229,250);color:black\"> -5.12 <strong>(-0.161)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 3.17e-08 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -0 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -1.03e-06 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -2.7e-06 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -0 </td>\n",
       "        <td style=\"background-color:rgb(239,239,250);color:black\"> -5.71 <strong>(-0.081)</strong> </td>\n",
       "        <td style=\"background-color:rgb(233,233,250);color:black\"> -26.2 <strong>(-0.131)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,237,237);color:black\"> 29.7 <strong>(0.089)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,246,246);color:black\"> 5.32 <strong>(0.026)</strong> </td>\n",
       "        <td style=\"background-color:rgb(242,242,250);color:black\"> -3.16 <strong>(-0.062)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -0 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -0 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -0 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -0 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -2.53e-05 </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th> x1 </th>\n",
       "        <td style=\"background-color:rgb(152,152,250);color:black\"> -1.45e+03 <strong>(-0.756)</strong> </td>\n",
       "        <td> 1.64e+03 </td>\n",
       "        <td style=\"background-color:rgb(250,210,210);color:black\"> 14.6 <strong>(0.264)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,211,211);color:black\"> 13.8 <strong>(0.260)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,210,210);color:black\"> 14.6 <strong>(0.264)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,212,212);color:black\"> 12 <strong>(0.250)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,211,211);color:black\"> 13.6 <strong>(0.259)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,232,232);color:black\"> 5.25 <strong>(0.117)</strong> </td>\n",
       "        <td style=\"background-color:rgb(206,206,250);color:black\"> -23.6 <strong>(-0.338)</strong> </td>\n",
       "        <td style=\"background-color:rgb(152,152,250);color:black\"> -68.9 <strong>(-0.754)</strong> </td>\n",
       "        <td style=\"background-color:rgb(201,201,250);color:black\"> -23.2 <strong>(-0.375)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,226,226);color:black\"> 6.29 <strong>(0.157)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,216,216);color:black\"> 8.3 <strong>(0.223)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,218,218);color:black\"> 7.42 <strong>(0.215)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,217,217);color:black\"> 7.59 <strong>(0.217)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,218,218);color:black\"> 7.06 <strong>(0.212)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,222,222);color:black\"> 5.12 <strong>(0.188)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -3.07e-08 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 1.05e-06 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 2.68e-06 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0 </td>\n",
       "        <td style=\"background-color:rgb(250,236,236);color:black\"> 5.71 <strong>(0.095)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,227,227);color:black\"> 26.2 <strong>(0.153)</strong> </td>\n",
       "        <td style=\"background-color:rgb(236,236,250);color:black\"> -29.8 <strong>(-0.104)</strong> </td>\n",
       "        <td style=\"background-color:rgb(246,246,250);color:black\"> -5.32 <strong>(-0.030)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,239,239);color:black\"> 3.16 <strong>(0.073)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 2.53e-05 </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th> x2 </th>\n",
       "        <td style=\"background-color:rgb(221,221,250);color:black\"> -14.6 <strong>(-0.226)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,210,210);color:black\"> 14.6 <strong>(0.264)</strong> </td>\n",
       "        <td> 1.88 </td>\n",
       "        <td style=\"background-color:rgb(250,180,180);color:black\"> 0.842 <strong>(0.470)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,178,178);color:black\"> 0.895 <strong>(0.477)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,182,182);color:black\"> 0.734 <strong>(0.452)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,180,180);color:black\"> 0.831 <strong>(0.468)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,192,192);color:black\"> 0.584 <strong>(0.384)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,217,217);color:black\"> 0.525 <strong>(0.222)</strong> </td>\n",
       "        <td style=\"background-color:rgb(237,237,250);color:black\"> -0.302 <strong>(-0.098)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,225,225);color:black\"> 0.345 <strong>(0.165)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,192,192);color:black\"> 0.522 <strong>(0.384)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,189,189);color:black\"> 0.507 <strong>(0.403)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,192,192);color:black\"> 0.453 <strong>(0.389)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,191,191);color:black\"> 0.464 <strong>(0.392)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,193,193);color:black\"> 0.432 <strong>(0.382)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,199,199);color:black\"> 0.313 <strong>(0.340)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 2.22e-09 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 1.25e-08 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 2.6e-08 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0 </td>\n",
       "        <td style=\"background-color:rgb(250,246,246);color:black\"> 0.0578 <strong>(0.028)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,243,243);color:black\"> 0.264 <strong>(0.046)</strong> </td>\n",
       "        <td style=\"background-color:rgb(246,246,250);color:black\"> -0.3 <strong>(-0.031)</strong> </td>\n",
       "        <td style=\"background-color:rgb(249,249,250);color:black\"> -0.0537 <strong>(-0.009)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,247,247);color:black\"> 0.0319 <strong>(0.022)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 2.62e-07 </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th> x3 </th>\n",
       "        <td style=\"background-color:rgb(221,221,250);color:black\"> -13.8 <strong>(-0.222)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,211,211);color:black\"> 13.8 <strong>(0.260)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,180,180);color:black\"> 0.842 <strong>(0.470)</strong> </td>\n",
       "        <td> 1.71 </td>\n",
       "        <td style=\"background-color:rgb(250,180,180);color:black\"> 0.842 <strong>(0.470)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,183,183);color:black\"> 0.69 <strong>(0.445)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,181,181);color:black\"> 0.781 <strong>(0.460)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,193,193);color:black\"> 0.549 <strong>(0.378)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,217,217);color:black\"> 0.494 <strong>(0.218)</strong> </td>\n",
       "        <td style=\"background-color:rgb(238,238,250);color:black\"> -0.284 <strong>(-0.096)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,226,226);color:black\"> 0.324 <strong>(0.162)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,193,193);color:black\"> 0.491 <strong>(0.378)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,190,190);color:black\"> 0.477 <strong>(0.397)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,193,193);color:black\"> 0.426 <strong>(0.382)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,192,192);color:black\"> 0.436 <strong>(0.385)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,194,194);color:black\"> 0.406 <strong>(0.376)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,200,200);color:black\"> 0.294 <strong>(0.334)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -2.19e-10 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -0 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 1.19e-08 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 2.48e-08 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0 </td>\n",
       "        <td style=\"background-color:rgb(250,246,246);color:black\"> 0.0543 <strong>(0.028)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,243,243);color:black\"> 0.248 <strong>(0.045)</strong> </td>\n",
       "        <td style=\"background-color:rgb(246,246,250);color:black\"> -0.282 <strong>(-0.031)</strong> </td>\n",
       "        <td style=\"background-color:rgb(249,249,250);color:black\"> -0.0505 <strong>(-0.009)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,247,247);color:black\"> 0.03 <strong>(0.022)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 2.48e-07 </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th> x4 </th>\n",
       "        <td style=\"background-color:rgb(221,221,250);color:black\"> -14.6 <strong>(-0.226)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,210,210);color:black\"> 14.6 <strong>(0.264)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,178,178);color:black\"> 0.895 <strong>(0.477)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,180,180);color:black\"> 0.842 <strong>(0.470)</strong> </td>\n",
       "        <td> 1.88 </td>\n",
       "        <td style=\"background-color:rgb(250,182,182);color:black\"> 0.734 <strong>(0.452)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,180,180);color:black\"> 0.831 <strong>(0.468)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,192,192);color:black\"> 0.584 <strong>(0.384)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,217,217);color:black\"> 0.525 <strong>(0.222)</strong> </td>\n",
       "        <td style=\"background-color:rgb(237,237,250);color:black\"> -0.302 <strong>(-0.098)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,225,225);color:black\"> 0.345 <strong>(0.165)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,192,192);color:black\"> 0.522 <strong>(0.384)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,189,189);color:black\"> 0.507 <strong>(0.403)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,192,192);color:black\"> 0.453 <strong>(0.389)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,191,191);color:black\"> 0.464 <strong>(0.392)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,193,193);color:black\"> 0.432 <strong>(0.382)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,199,199);color:black\"> 0.313 <strong>(0.340)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -2.05e-10 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -6.69e-08 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 2.56e-08 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0 </td>\n",
       "        <td style=\"background-color:rgb(250,246,246);color:black\"> 0.0578 <strong>(0.028)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,243,243);color:black\"> 0.264 <strong>(0.046)</strong> </td>\n",
       "        <td style=\"background-color:rgb(246,246,250);color:black\"> -0.3 <strong>(-0.031)</strong> </td>\n",
       "        <td style=\"background-color:rgb(249,249,250);color:black\"> -0.0537 <strong>(-0.009)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,247,247);color:black\"> 0.0319 <strong>(0.022)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 2.63e-07 </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th> x5 </th>\n",
       "        <td style=\"background-color:rgb(222,222,250);color:black\"> -12 <strong>(-0.214)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,212,212);color:black\"> 12 <strong>(0.250)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,182,182);color:black\"> 0.734 <strong>(0.452)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,183,183);color:black\"> 0.69 <strong>(0.445)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,182,182);color:black\"> 0.734 <strong>(0.452)</strong> </td>\n",
       "        <td> 1.4 </td>\n",
       "        <td style=\"background-color:rgb(250,184,184);color:black\"> 0.681 <strong>(0.443)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,195,195);color:black\"> 0.478 <strong>(0.364)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,218,218);color:black\"> 0.431 <strong>(0.210)</strong> </td>\n",
       "        <td style=\"background-color:rgb(238,238,250);color:black\"> -0.248 <strong>(-0.092)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,227,227);color:black\"> 0.283 <strong>(0.156)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,195,195);color:black\"> 0.428 <strong>(0.364)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,193,193);color:black\"> 0.416 <strong>(0.382)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,195,195);color:black\"> 0.372 <strong>(0.368)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,194,194);color:black\"> 0.38 <strong>(0.371)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,196,196);color:black\"> 0.354 <strong>(0.362)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,202,202);color:black\"> 0.256 <strong>(0.322)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -1.25e-10 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 1.05e-08 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -1.65e-07 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0 </td>\n",
       "        <td style=\"background-color:rgb(250,246,246);color:black\"> 0.0473 <strong>(0.027)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,244,244);color:black\"> 0.216 <strong>(0.043)</strong> </td>\n",
       "        <td style=\"background-color:rgb(246,246,250);color:black\"> -0.246 <strong>(-0.029)</strong> </td>\n",
       "        <td style=\"background-color:rgb(249,249,250);color:black\"> -0.044 <strong>(-0.009)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,247,247);color:black\"> 0.0262 <strong>(0.021)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 2.14e-07 </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th> x6 </th>\n",
       "        <td style=\"background-color:rgb(221,221,250);color:black\"> -13.6 <strong>(-0.221)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,211,211);color:black\"> 13.6 <strong>(0.259)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,180,180);color:black\"> 0.831 <strong>(0.468)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,181,181);color:black\"> 0.781 <strong>(0.460)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,180,180);color:black\"> 0.831 <strong>(0.468)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,184,184);color:black\"> 0.681 <strong>(0.443)</strong> </td>\n",
       "        <td> 1.68 </td>\n",
       "        <td style=\"background-color:rgb(250,194,194);color:black\"> 0.541 <strong>(0.376)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,217,217);color:black\"> 0.487 <strong>(0.218)</strong> </td>\n",
       "        <td style=\"background-color:rgb(238,238,250);color:black\"> -0.28 <strong>(-0.096)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,226,226);color:black\"> 0.32 <strong>(0.162)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,194,194);color:black\"> 0.484 <strong>(0.377)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,191,191);color:black\"> 0.471 <strong>(0.396)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,193,193);color:black\"> 0.421 <strong>(0.381)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,192,192);color:black\"> 0.431 <strong>(0.384)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,194,194);color:black\"> 0.401 <strong>(0.375)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,200,200);color:black\"> 0.29 <strong>(0.333)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -2.24e-10 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 1.19e-08 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 2.37e-08 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -0 </td>\n",
       "        <td style=\"background-color:rgb(250,246,246);color:black\"> 0.0536 <strong>(0.028)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,243,243);color:black\"> 0.245 <strong>(0.045)</strong> </td>\n",
       "        <td style=\"background-color:rgb(246,246,250);color:black\"> -0.278 <strong>(-0.030)</strong> </td>\n",
       "        <td style=\"background-color:rgb(249,249,250);color:black\"> -0.0498 <strong>(-0.009)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,247,247);color:black\"> 0.0296 <strong>(0.021)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 2.43e-07 </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th> x7 </th>\n",
       "        <td style=\"background-color:rgb(237,237,250);color:black\"> -5.25 <strong>(-0.100)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,232,232);color:black\"> 5.25 <strong>(0.117)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,192,192);color:black\"> 0.584 <strong>(0.384)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,193,193);color:black\"> 0.549 <strong>(0.378)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,192,192);color:black\"> 0.584 <strong>(0.384)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,195,195);color:black\"> 0.478 <strong>(0.364)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,194,194);color:black\"> 0.541 <strong>(0.376)</strong> </td>\n",
       "        <td> 1.23 </td>\n",
       "        <td style=\"background-color:rgb(250,217,217);color:black\"> 0.421 <strong>(0.220)</strong> </td>\n",
       "        <td style=\"background-color:rgb(248,248,250);color:black\"> -0.0401 <strong>(-0.016)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,224,224);color:black\"> 0.295 <strong>(0.174)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,203,203);color:black\"> 0.346 <strong>(0.314)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,201,201);color:black\"> 0.331 <strong>(0.325)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,203,203);color:black\"> 0.295 <strong>(0.313)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,203,203);color:black\"> 0.302 <strong>(0.315)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,204,204);color:black\"> 0.281 <strong>(0.307)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,209,209);color:black\"> 0.204 <strong>(0.273)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -8.36e-11 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 8.66e-09 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 1.53e-08 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0 </td>\n",
       "        <td style=\"background-color:rgb(216,216,250);color:black\"> -0.424 <strong>(-0.258)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,243,243);color:black\"> 0.207 <strong>(0.044)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,248,248);color:black\"> 0.116 <strong>(0.015)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,247,247);color:black\"> 0.0813 <strong>(0.017)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,248,248);color:black\"> 0.0193 <strong>(0.016)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 1.4e-07 </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th> x8 </th>\n",
       "        <td style=\"background-color:rgb(250,207,207);color:black\"> 23.6 <strong>(0.289)</strong> </td>\n",
       "        <td style=\"background-color:rgb(206,206,250);color:black\"> -23.6 <strong>(-0.338)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,217,217);color:black\"> 0.525 <strong>(0.222)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,217,217);color:black\"> 0.494 <strong>(0.218)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,217,217);color:black\"> 0.525 <strong>(0.222)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,218,218);color:black\"> 0.431 <strong>(0.210)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,217,217);color:black\"> 0.487 <strong>(0.218)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,217,217);color:black\"> 0.421 <strong>(0.220)</strong> </td>\n",
       "        <td> 2.99 </td>\n",
       "        <td style=\"background-color:rgb(250,212,212);color:black\"> 0.999 <strong>(0.256)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,208,208);color:black\"> 0.732 <strong>(0.277)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,220,220);color:black\"> 0.348 <strong>(0.203)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,222,222);color:black\"> 0.298 <strong>(0.188)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,223,223);color:black\"> 0.266 <strong>(0.181)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,223,223);color:black\"> 0.272 <strong>(0.182)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,223,223);color:black\"> 0.253 <strong>(0.178)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,226,226);color:black\"> 0.184 <strong>(0.158)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 5.15e-11 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 4.54e-09 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 4.22e-10 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0 </td>\n",
       "        <td style=\"background-color:rgb(250,249,249);color:black\"> 0.0195 <strong>(0.008)</strong> </td>\n",
       "        <td style=\"background-color:rgb(196,196,250);color:black\"> -3.03 <strong>(-0.416)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,223,223);color:black\"> 2.16 <strong>(0.177)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,233,233);color:black\"> 0.842 <strong>(0.112)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,249,249);color:black\"> 0.00754 <strong>(0.004)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -7.68e-08 </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th> x9 </th>\n",
       "        <td style=\"background-color:rgb(250,153,153);color:black\"> 68.9 <strong>(0.644)</strong> </td>\n",
       "        <td style=\"background-color:rgb(152,152,250);color:black\"> -68.9 <strong>(-0.754)</strong> </td>\n",
       "        <td style=\"background-color:rgb(237,237,250);color:black\"> -0.302 <strong>(-0.098)</strong> </td>\n",
       "        <td style=\"background-color:rgb(238,238,250);color:black\"> -0.284 <strong>(-0.096)</strong> </td>\n",
       "        <td style=\"background-color:rgb(237,237,250);color:black\"> -0.302 <strong>(-0.098)</strong> </td>\n",
       "        <td style=\"background-color:rgb(238,238,250);color:black\"> -0.248 <strong>(-0.092)</strong> </td>\n",
       "        <td style=\"background-color:rgb(238,238,250);color:black\"> -0.28 <strong>(-0.096)</strong> </td>\n",
       "        <td style=\"background-color:rgb(248,248,250);color:black\"> -0.0401 <strong>(-0.016)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,212,212);color:black\"> 0.999 <strong>(0.256)</strong> </td>\n",
       "        <td> 5.1 </td>\n",
       "        <td style=\"background-color:rgb(250,209,209);color:black\"> 0.934 <strong>(0.271)</strong> </td>\n",
       "        <td style=\"background-color:rgb(245,245,250);color:black\"> -0.0941 <strong>(-0.042)</strong> </td>\n",
       "        <td style=\"background-color:rgb(239,239,250);color:black\"> -0.171 <strong>(-0.083)</strong> </td>\n",
       "        <td style=\"background-color:rgb(240,240,250);color:black\"> -0.153 <strong>(-0.079)</strong> </td>\n",
       "        <td style=\"background-color:rgb(240,240,250);color:black\"> -0.157 <strong>(-0.080)</strong> </td>\n",
       "        <td style=\"background-color:rgb(240,240,250);color:black\"> -0.146 <strong>(-0.078)</strong> </td>\n",
       "        <td style=\"background-color:rgb(241,241,250);color:black\"> -0.106 <strong>(-0.070)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 3.52e-10 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -8.49e-09 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -3.84e-08 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0 </td>\n",
       "        <td style=\"background-color:rgb(248,248,250);color:black\"> -0.048 <strong>(-0.014)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,243,243);color:black\"> 0.432 <strong>(0.045)</strong> </td>\n",
       "        <td style=\"background-color:rgb(233,233,250);color:black\"> -2.1 <strong>(-0.132)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,223,223);color:black\"> 1.75 <strong>(0.178)</strong> </td>\n",
       "        <td style=\"background-color:rgb(248,248,250);color:black\"> -0.0329 <strong>(-0.014)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -5.45e-07 </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th> x10 </th>\n",
       "        <td style=\"background-color:rgb(250,202,202);color:black\"> 23.2 <strong>(0.320)</strong> </td>\n",
       "        <td style=\"background-color:rgb(201,201,250);color:black\"> -23.2 <strong>(-0.375)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,225,225);color:black\"> 0.345 <strong>(0.165)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,226,226);color:black\"> 0.324 <strong>(0.162)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,225,225);color:black\"> 0.345 <strong>(0.165)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,227,227);color:black\"> 0.283 <strong>(0.156)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,226,226);color:black\"> 0.32 <strong>(0.162)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,224,224);color:black\"> 0.295 <strong>(0.174)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,208,208);color:black\"> 0.732 <strong>(0.277)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,209,209);color:black\"> 0.934 <strong>(0.271)</strong> </td>\n",
       "        <td> 2.33 </td>\n",
       "        <td style=\"background-color:rgb(250,226,226);color:black\"> 0.238 <strong>(0.157)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,229,229);color:black\"> 0.195 <strong>(0.139)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,230,230);color:black\"> 0.175 <strong>(0.134)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,230,230);color:black\"> 0.179 <strong>(0.135)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,230,230);color:black\"> 0.166 <strong>(0.132)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,232,232);color:black\"> 0.12 <strong>(0.117)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -6.84e-13 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 2.16e-09 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -3.23e-09 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0 </td>\n",
       "        <td style=\"background-color:rgb(250,249,249);color:black\"> 0.00938 <strong>(0.004)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,242,242);color:black\"> 0.336 <strong>(0.052)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,223,223);color:black\"> 1.97 <strong>(0.183)</strong> </td>\n",
       "        <td style=\"background-color:rgb(205,205,250);color:black\"> -2.32 <strong>(-0.349)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0.0023 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -1.04e-07 </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th> x11 </th>\n",
       "        <td style=\"background-color:rgb(233,233,250);color:black\"> -6.29 <strong>(-0.134)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,226,226);color:black\"> 6.29 <strong>(0.157)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,192,192);color:black\"> 0.522 <strong>(0.384)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,193,193);color:black\"> 0.491 <strong>(0.378)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,192,192);color:black\"> 0.522 <strong>(0.384)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,195,195);color:black\"> 0.428 <strong>(0.364)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,194,194);color:black\"> 0.484 <strong>(0.377)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,203,203);color:black\"> 0.346 <strong>(0.314)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,220,220);color:black\"> 0.348 <strong>(0.203)</strong> </td>\n",
       "        <td style=\"background-color:rgb(245,245,250);color:black\"> -0.0941 <strong>(-0.042)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,226,226);color:black\"> 0.238 <strong>(0.157)</strong> </td>\n",
       "        <td> 0.984 </td>\n",
       "        <td style=\"background-color:rgb(250,201,201);color:black\"> 0.296 <strong>(0.325)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,203,203);color:black\"> 0.264 <strong>(0.313)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,203,203);color:black\"> 0.271 <strong>(0.315)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,204,204);color:black\"> 0.252 <strong>(0.307)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,209,209);color:black\"> 0.182 <strong>(0.273)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -1.17e-10 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 7.06e-09 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 1.41e-08 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0 </td>\n",
       "        <td style=\"background-color:rgb(250,247,247);color:black\"> 0.0327 <strong>(0.022)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,244,244);color:black\"> 0.172 <strong>(0.041)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -0.0117 <strong>(-0.002)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,249,249);color:black\"> 0.0296 <strong>(0.007)</strong> </td>\n",
       "        <td style=\"background-color:rgb(223,223,250);color:black\"> -0.223 <strong>(-0.211)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 1.36e-07 </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th> x12 </th>\n",
       "        <td style=\"background-color:rgb(225,225,250);color:black\"> -8.3 <strong>(-0.191)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,216,216);color:black\"> 8.3 <strong>(0.223)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,189,189);color:black\"> 0.507 <strong>(0.403)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,190,190);color:black\"> 0.477 <strong>(0.397)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,189,189);color:black\"> 0.507 <strong>(0.403)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,193,193);color:black\"> 0.416 <strong>(0.382)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,191,191);color:black\"> 0.471 <strong>(0.396)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,201,201);color:black\"> 0.331 <strong>(0.325)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,222,222);color:black\"> 0.298 <strong>(0.188)</strong> </td>\n",
       "        <td style=\"background-color:rgb(239,239,250);color:black\"> -0.171 <strong>(-0.083)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,229,229);color:black\"> 0.195 <strong>(0.139)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,201,201);color:black\"> 0.296 <strong>(0.325)</strong> </td>\n",
       "        <td> 0.843 </td>\n",
       "        <td style=\"background-color:rgb(250,201,201);color:black\"> 0.257 <strong>(0.328)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,200,200);color:black\"> 0.263 <strong>(0.331)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,202,202);color:black\"> 0.245 <strong>(0.323)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,207,207);color:black\"> 0.177 <strong>(0.287)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -1.25e-10 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 7.48e-09 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 1.48e-08 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0 </td>\n",
       "        <td style=\"background-color:rgb(250,246,246);color:black\"> 0.0327 <strong>(0.024)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,244,244);color:black\"> 0.149 <strong>(0.039)</strong> </td>\n",
       "        <td style=\"background-color:rgb(247,247,250);color:black\"> -0.17 <strong>(-0.026)</strong> </td>\n",
       "        <td style=\"background-color:rgb(249,249,250);color:black\"> -0.0304 <strong>(-0.008)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,247,247);color:black\"> 0.0181 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -0 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 1.49e-07 </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th> x13 </th>\n",
       "        <td style=\"background-color:rgb(226,226,250);color:black\"> -7.42 <strong>(-0.184)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,218,218);color:black\"> 7.42 <strong>(0.215)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,192,192);color:black\"> 0.453 <strong>(0.389)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,193,193);color:black\"> 0.426 <strong>(0.382)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,192,192);color:black\"> 0.453 <strong>(0.389)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,195,195);color:black\"> 0.372 <strong>(0.368)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,193,193);color:black\"> 0.421 <strong>(0.381)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,203,203);color:black\"> 0.295 <strong>(0.313)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,223,223);color:black\"> 0.266 <strong>(0.181)</strong> </td>\n",
       "        <td style=\"background-color:rgb(240,240,250);color:black\"> -0.153 <strong>(-0.079)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,230,230);color:black\"> 0.175 <strong>(0.134)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,203,203);color:black\"> 0.264 <strong>(0.313)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,201,201);color:black\"> 0.257 <strong>(0.328)</strong> </td>\n",
       "        <td> 0.726 </td>\n",
       "        <td style=\"background-color:rgb(250,202,202);color:black\"> 0.235 <strong>(0.319)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,203,203);color:black\"> 0.219 <strong>(0.311)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,209,209);color:black\"> 0.158 <strong>(0.277)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -1.2e-10 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 6.52e-09 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 1.32e-08 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0 </td>\n",
       "        <td style=\"background-color:rgb(250,247,247);color:black\"> 0.0292 <strong>(0.023)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,244,244);color:black\"> 0.134 <strong>(0.037)</strong> </td>\n",
       "        <td style=\"background-color:rgb(247,247,250);color:black\"> -0.152 <strong>(-0.025)</strong> </td>\n",
       "        <td style=\"background-color:rgb(249,249,250);color:black\"> -0.0272 <strong>(-0.007)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,247,247);color:black\"> 0.0162 <strong>(0.018)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -0 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 1.33e-07 </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th> x14 </th>\n",
       "        <td style=\"background-color:rgb(226,226,250);color:black\"> -7.59 <strong>(-0.185)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,217,217);color:black\"> 7.59 <strong>(0.217)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,191,191);color:black\"> 0.464 <strong>(0.392)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,192,192);color:black\"> 0.436 <strong>(0.385)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,191,191);color:black\"> 0.464 <strong>(0.392)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,194,194);color:black\"> 0.38 <strong>(0.371)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,192,192);color:black\"> 0.431 <strong>(0.384)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,203,203);color:black\"> 0.302 <strong>(0.315)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,223,223);color:black\"> 0.272 <strong>(0.182)</strong> </td>\n",
       "        <td style=\"background-color:rgb(240,240,250);color:black\"> -0.157 <strong>(-0.080)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,230,230);color:black\"> 0.179 <strong>(0.135)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,203,203);color:black\"> 0.271 <strong>(0.315)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,200,200);color:black\"> 0.263 <strong>(0.331)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,202,202);color:black\"> 0.235 <strong>(0.319)</strong> </td>\n",
       "        <td> 0.749 </td>\n",
       "        <td style=\"background-color:rgb(250,203,203);color:black\"> 0.224 <strong>(0.313)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,208,208);color:black\"> 0.162 <strong>(0.279)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -1.1e-10 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 6.44e-09 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 1.36e-08 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0 </td>\n",
       "        <td style=\"background-color:rgb(250,246,246);color:black\"> 0.0299 <strong>(0.023)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,244,244);color:black\"> 0.137 <strong>(0.037)</strong> </td>\n",
       "        <td style=\"background-color:rgb(247,247,250);color:black\"> -0.155 <strong>(-0.025)</strong> </td>\n",
       "        <td style=\"background-color:rgb(249,249,250);color:black\"> -0.0278 <strong>(-0.007)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,247,247);color:black\"> 0.0165 <strong>(0.018)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -0 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 1.37e-07 </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th> x15 </th>\n",
       "        <td style=\"background-color:rgb(227,227,250);color:black\"> -7.06 <strong>(-0.181)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,218,218);color:black\"> 7.06 <strong>(0.212)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,193,193);color:black\"> 0.432 <strong>(0.382)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,194,194);color:black\"> 0.406 <strong>(0.376)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,193,193);color:black\"> 0.432 <strong>(0.382)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,196,196);color:black\"> 0.354 <strong>(0.362)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,194,194);color:black\"> 0.401 <strong>(0.375)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,204,204);color:black\"> 0.281 <strong>(0.307)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,223,223);color:black\"> 0.253 <strong>(0.178)</strong> </td>\n",
       "        <td style=\"background-color:rgb(240,240,250);color:black\"> -0.146 <strong>(-0.078)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,230,230);color:black\"> 0.166 <strong>(0.132)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,204,204);color:black\"> 0.252 <strong>(0.307)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,202,202);color:black\"> 0.245 <strong>(0.323)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,203,203);color:black\"> 0.219 <strong>(0.311)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,203,203);color:black\"> 0.224 <strong>(0.313)</strong> </td>\n",
       "        <td> 0.681 </td>\n",
       "        <td style=\"background-color:rgb(250,209,209);color:black\"> 0.151 <strong>(0.272)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -8.27e-11 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 6.34e-09 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 1.24e-08 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0 </td>\n",
       "        <td style=\"background-color:rgb(250,247,247);color:black\"> 0.0279 <strong>(0.023)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,245,245);color:black\"> 0.127 <strong>(0.037)</strong> </td>\n",
       "        <td style=\"background-color:rgb(247,247,250);color:black\"> -0.145 <strong>(-0.025)</strong> </td>\n",
       "        <td style=\"background-color:rgb(249,249,250);color:black\"> -0.0259 <strong>(-0.007)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,247,247);color:black\"> 0.0154 <strong>(0.017)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -0 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 1.26e-07 </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th> x16 </th>\n",
       "        <td style=\"background-color:rgb(229,229,250);color:black\"> -5.12 <strong>(-0.161)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,222,222);color:black\"> 5.12 <strong>(0.188)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,199,199);color:black\"> 0.313 <strong>(0.340)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,200,200);color:black\"> 0.294 <strong>(0.334)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,199,199);color:black\"> 0.313 <strong>(0.340)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,202,202);color:black\"> 0.256 <strong>(0.322)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,200,200);color:black\"> 0.29 <strong>(0.333)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,209,209);color:black\"> 0.204 <strong>(0.273)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,226,226);color:black\"> 0.184 <strong>(0.158)</strong> </td>\n",
       "        <td style=\"background-color:rgb(241,241,250);color:black\"> -0.106 <strong>(-0.070)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,232,232);color:black\"> 0.12 <strong>(0.117)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,209,209);color:black\"> 0.182 <strong>(0.273)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,207,207);color:black\"> 0.177 <strong>(0.287)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,209,209);color:black\"> 0.158 <strong>(0.277)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,208,208);color:black\"> 0.162 <strong>(0.279)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,209,209);color:black\"> 0.151 <strong>(0.272)</strong> </td>\n",
       "        <td> 0.452 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -7.37e-11 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 4.46e-09 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 8.72e-09 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0 </td>\n",
       "        <td style=\"background-color:rgb(250,247,247);color:black\"> 0.0202 </td>\n",
       "        <td style=\"background-color:rgb(250,245,245);color:black\"> 0.0921 <strong>(0.033)</strong> </td>\n",
       "        <td style=\"background-color:rgb(247,247,250);color:black\"> -0.105 <strong>(-0.022)</strong> </td>\n",
       "        <td style=\"background-color:rgb(249,249,250);color:black\"> -0.0188 <strong>(-0.006)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,248,248);color:black\"> 0.0111 <strong>(0.016)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -1.25e-06 </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th> x17 </th>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 3.17e-08 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -3.07e-08 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 2.22e-09 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -2.19e-10 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -2.05e-10 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -1.25e-10 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -2.24e-10 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -8.36e-11 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 5.15e-11 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 3.52e-10 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -6.84e-13 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -1.17e-10 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -1.25e-10 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -1.2e-10 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -1.1e-10 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -8.27e-11 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -7.37e-11 </td>\n",
       "        <td> 4.96e-09 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -0 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -6.59e-15 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 2.09e-14 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -0 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -1.21e-11 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -5.09e-11 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 8.9e-10 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 2.65e-10 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 7.3e-13 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -0 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -0 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -0 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -3.83e-14 </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th> x18 </th>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -0 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -0 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -0 </td>\n",
       "        <td> 0 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -0 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -0 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -0 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -0 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -0 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0 </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th> x19 </th>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -1.03e-06 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 1.05e-06 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 1.25e-08 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 1.19e-08 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -6.69e-08 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 1.05e-08 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 1.19e-08 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 8.66e-09 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 4.54e-09 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -8.49e-09 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 2.16e-09 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 7.06e-09 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 7.48e-09 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 6.52e-09 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 6.44e-09 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 6.34e-09 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 4.46e-09 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -6.59e-15 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0 </td>\n",
       "        <td> 5.45e-07 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 2.77e-13 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -9.96e-11 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 5.63e-10 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -2.33e-08 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -6.82e-09 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 1.04e-09 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 6.69e-13 </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th> x20 </th>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -2.7e-06 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 2.68e-06 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 2.6e-08 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 2.48e-08 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 2.56e-08 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -1.65e-07 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 2.37e-08 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 1.53e-08 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 4.22e-10 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -3.84e-08 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -3.23e-09 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 1.41e-08 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 1.48e-08 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 1.32e-08 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 1.36e-08 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 1.24e-08 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 8.72e-09 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 2.09e-14 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -0 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 2.77e-13 </td>\n",
       "        <td> 6.59e-07 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 9.44e-10 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 3.73e-10 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -6.51e-08 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -2.06e-08 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 1.05e-09 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -0 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -0 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -0 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 1.16e-12 </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th> x21 </th>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -0 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -0 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -0 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -0 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0 </td>\n",
       "        <td> 0 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -0 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -0 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -0 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -0 </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th> x22 </th>\n",
       "        <td style=\"background-color:rgb(239,239,250);color:black\"> -5.71 <strong>(-0.081)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,236,236);color:black\"> 5.71 <strong>(0.095)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,246,246);color:black\"> 0.0578 <strong>(0.028)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,246,246);color:black\"> 0.0543 <strong>(0.028)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,246,246);color:black\"> 0.0578 <strong>(0.028)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,246,246);color:black\"> 0.0473 <strong>(0.027)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,246,246);color:black\"> 0.0536 <strong>(0.028)</strong> </td>\n",
       "        <td style=\"background-color:rgb(216,216,250);color:black\"> -0.424 <strong>(-0.258)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,249,249);color:black\"> 0.0195 <strong>(0.008)</strong> </td>\n",
       "        <td style=\"background-color:rgb(248,248,250);color:black\"> -0.048 <strong>(-0.014)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,249,249);color:black\"> 0.00938 <strong>(0.004)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,247,247);color:black\"> 0.0327 <strong>(0.022)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,246,246);color:black\"> 0.0327 <strong>(0.024)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,247,247);color:black\"> 0.0292 <strong>(0.023)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,246,246);color:black\"> 0.0299 <strong>(0.023)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,247,247);color:black\"> 0.0279 <strong>(0.023)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,247,247);color:black\"> 0.0202 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -1.21e-11 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -9.96e-11 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 9.44e-10 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0 </td>\n",
       "        <td> 2.19 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0.0106 <strong>(0.002)</strong> </td>\n",
       "        <td style=\"background-color:rgb(249,249,250);color:black\"> -0.0762 <strong>(-0.007)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -0.0247 <strong>(-0.004)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0.00233 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 2.38e-08 </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th> x23 </th>\n",
       "        <td style=\"background-color:rgb(233,233,250);color:black\"> -26.2 <strong>(-0.131)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,227,227);color:black\"> 26.2 <strong>(0.153)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,243,243);color:black\"> 0.264 <strong>(0.046)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,243,243);color:black\"> 0.248 <strong>(0.045)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,243,243);color:black\"> 0.264 <strong>(0.046)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,244,244);color:black\"> 0.216 <strong>(0.043)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,243,243);color:black\"> 0.245 <strong>(0.045)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,243,243);color:black\"> 0.207 <strong>(0.044)</strong> </td>\n",
       "        <td style=\"background-color:rgb(196,196,250);color:black\"> -3.03 <strong>(-0.416)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,243,243);color:black\"> 0.432 <strong>(0.045)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,242,242);color:black\"> 0.336 <strong>(0.052)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,244,244);color:black\"> 0.172 <strong>(0.041)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,244,244);color:black\"> 0.149 <strong>(0.039)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,244,244);color:black\"> 0.134 <strong>(0.037)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,244,244);color:black\"> 0.137 <strong>(0.037)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,245,245);color:black\"> 0.127 <strong>(0.037)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,245,245);color:black\"> 0.0921 <strong>(0.033)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -5.09e-11 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 5.63e-10 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 3.73e-10 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0.0106 <strong>(0.002)</strong> </td>\n",
       "        <td> 17.8 </td>\n",
       "        <td style=\"background-color:rgb(250,245,245);color:black\"> 0.947 <strong>(0.032)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,247,247);color:black\"> 0.371 <strong>(0.020)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0.00445 <strong>(0.001)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -1.4e-08 </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th> x24 </th>\n",
       "        <td style=\"background-color:rgb(250,237,237);color:black\"> 29.7 <strong>(0.089)</strong> </td>\n",
       "        <td style=\"background-color:rgb(236,236,250);color:black\"> -29.8 <strong>(-0.104)</strong> </td>\n",
       "        <td style=\"background-color:rgb(246,246,250);color:black\"> -0.3 <strong>(-0.031)</strong> </td>\n",
       "        <td style=\"background-color:rgb(246,246,250);color:black\"> -0.282 <strong>(-0.031)</strong> </td>\n",
       "        <td style=\"background-color:rgb(246,246,250);color:black\"> -0.3 <strong>(-0.031)</strong> </td>\n",
       "        <td style=\"background-color:rgb(246,246,250);color:black\"> -0.246 <strong>(-0.029)</strong> </td>\n",
       "        <td style=\"background-color:rgb(246,246,250);color:black\"> -0.278 <strong>(-0.030)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,248,248);color:black\"> 0.116 <strong>(0.015)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,223,223);color:black\"> 2.16 <strong>(0.177)</strong> </td>\n",
       "        <td style=\"background-color:rgb(233,233,250);color:black\"> -2.1 <strong>(-0.132)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,223,223);color:black\"> 1.97 <strong>(0.183)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -0.0117 <strong>(-0.002)</strong> </td>\n",
       "        <td style=\"background-color:rgb(247,247,250);color:black\"> -0.17 <strong>(-0.026)</strong> </td>\n",
       "        <td style=\"background-color:rgb(247,247,250);color:black\"> -0.152 <strong>(-0.025)</strong> </td>\n",
       "        <td style=\"background-color:rgb(247,247,250);color:black\"> -0.155 <strong>(-0.025)</strong> </td>\n",
       "        <td style=\"background-color:rgb(247,247,250);color:black\"> -0.145 <strong>(-0.025)</strong> </td>\n",
       "        <td style=\"background-color:rgb(247,247,250);color:black\"> -0.105 <strong>(-0.022)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 8.9e-10 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -2.33e-08 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -6.51e-08 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0 </td>\n",
       "        <td style=\"background-color:rgb(249,249,250);color:black\"> -0.0762 <strong>(-0.007)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,245,245);color:black\"> 0.947 <strong>(0.032)</strong> </td>\n",
       "        <td> 49.8 </td>\n",
       "        <td style=\"background-color:rgb(250,233,233);color:black\"> 3.46 <strong>(0.113)</strong> </td>\n",
       "        <td style=\"background-color:rgb(249,249,250);color:black\"> -0.0548 <strong>(-0.007)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -9.78e-07 </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th> x25 </th>\n",
       "        <td style=\"background-color:rgb(250,246,246);color:black\"> 5.32 <strong>(0.026)</strong> </td>\n",
       "        <td style=\"background-color:rgb(246,246,250);color:black\"> -5.32 <strong>(-0.030)</strong> </td>\n",
       "        <td style=\"background-color:rgb(249,249,250);color:black\"> -0.0537 <strong>(-0.009)</strong> </td>\n",
       "        <td style=\"background-color:rgb(249,249,250);color:black\"> -0.0505 <strong>(-0.009)</strong> </td>\n",
       "        <td style=\"background-color:rgb(249,249,250);color:black\"> -0.0537 <strong>(-0.009)</strong> </td>\n",
       "        <td style=\"background-color:rgb(249,249,250);color:black\"> -0.044 <strong>(-0.009)</strong> </td>\n",
       "        <td style=\"background-color:rgb(249,249,250);color:black\"> -0.0498 <strong>(-0.009)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,247,247);color:black\"> 0.0813 <strong>(0.017)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,233,233);color:black\"> 0.842 <strong>(0.112)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,223,223);color:black\"> 1.75 <strong>(0.178)</strong> </td>\n",
       "        <td style=\"background-color:rgb(205,205,250);color:black\"> -2.32 <strong>(-0.349)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,249,249);color:black\"> 0.0296 <strong>(0.007)</strong> </td>\n",
       "        <td style=\"background-color:rgb(249,249,250);color:black\"> -0.0304 <strong>(-0.008)</strong> </td>\n",
       "        <td style=\"background-color:rgb(249,249,250);color:black\"> -0.0272 <strong>(-0.007)</strong> </td>\n",
       "        <td style=\"background-color:rgb(249,249,250);color:black\"> -0.0278 <strong>(-0.007)</strong> </td>\n",
       "        <td style=\"background-color:rgb(249,249,250);color:black\"> -0.0259 <strong>(-0.007)</strong> </td>\n",
       "        <td style=\"background-color:rgb(249,249,250);color:black\"> -0.0188 <strong>(-0.006)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 2.65e-10 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -6.82e-09 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -2.06e-08 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -0.0247 <strong>(-0.004)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,247,247);color:black\"> 0.371 <strong>(0.020)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,233,233);color:black\"> 3.46 <strong>(0.113)</strong> </td>\n",
       "        <td> 18.9 </td>\n",
       "        <td style=\"background-color:rgb(249,249,250);color:black\"> -0.0184 <strong>(-0.004)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -3.45e-07 </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th> x26 </th>\n",
       "        <td style=\"background-color:rgb(242,242,250);color:black\"> -3.16 <strong>(-0.062)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,239,239);color:black\"> 3.16 <strong>(0.073)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,247,247);color:black\"> 0.0319 <strong>(0.022)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,247,247);color:black\"> 0.03 <strong>(0.022)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,247,247);color:black\"> 0.0319 <strong>(0.022)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,247,247);color:black\"> 0.0262 <strong>(0.021)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,247,247);color:black\"> 0.0296 <strong>(0.021)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,248,248);color:black\"> 0.0193 <strong>(0.016)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,249,249);color:black\"> 0.00754 <strong>(0.004)</strong> </td>\n",
       "        <td style=\"background-color:rgb(248,248,250);color:black\"> -0.0329 <strong>(-0.014)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0.0023 </td>\n",
       "        <td style=\"background-color:rgb(223,223,250);color:black\"> -0.223 <strong>(-0.211)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,247,247);color:black\"> 0.0181 </td>\n",
       "        <td style=\"background-color:rgb(250,247,247);color:black\"> 0.0162 <strong>(0.018)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,247,247);color:black\"> 0.0165 <strong>(0.018)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,247,247);color:black\"> 0.0154 <strong>(0.017)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,248,248);color:black\"> 0.0111 <strong>(0.016)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 7.3e-13 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 1.04e-09 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 1.05e-09 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0.00233 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0.00445 <strong>(0.001)</strong> </td>\n",
       "        <td style=\"background-color:rgb(249,249,250);color:black\"> -0.0548 <strong>(-0.007)</strong> </td>\n",
       "        <td style=\"background-color:rgb(249,249,250);color:black\"> -0.0184 <strong>(-0.004)</strong> </td>\n",
       "        <td> 1.14 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -0 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 1.56e-08 </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th> x27 </th>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -0 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -0 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -0 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -0 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -0 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0 </td>\n",
       "        <td> 0 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -0 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -0 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0 </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th> x28 </th>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -0 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -0 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -0 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -0 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0 </td>\n",
       "        <td> 0 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -0 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -0 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0 </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th> x29 </th>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -0 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -0 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -0 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -0 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -0 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -0 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -0 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -0 </td>\n",
       "        <td> 0 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -0 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -0 </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th> x30 </th>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -0 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -0 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -0 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -0 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -0 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -0 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -0 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -0 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -0 </td>\n",
       "        <td> 0 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -0 </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th> x31 </th>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -2.53e-05 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 2.53e-05 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 2.62e-07 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 2.48e-07 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 2.63e-07 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 2.14e-07 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 2.43e-07 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 1.4e-07 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -7.68e-08 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -5.45e-07 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -1.04e-07 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 1.36e-07 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 1.49e-07 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 1.33e-07 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 1.37e-07 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 1.26e-07 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -1.25e-06 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -3.83e-14 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 6.69e-13 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 1.16e-12 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -0 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 2.38e-08 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -1.4e-08 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -9.78e-07 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -3.45e-07 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 1.56e-08 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -0 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -0 </td>\n",
       "        <td> 5.19e-06 </td>\n",
       "    </tr>\n",
       "</table>"
      ],
      "text/plain": [
       "┌─────────────────────────────────────────────────────────────────────────┐\n",
       "│                                Migrad                                   │\n",
       "├──────────────────────────────────┬──────────────────────────────────────┤\n",
       "│ FCN = 18.27 (chi2/ndof = 1.4)    │             Nfcn = 3464              │\n",
       "│ EDM = 6.02e-05 (Goal: 0.0002)    │            time = 0.1 sec            │\n",
       "├──────────────────────────────────┼──────────────────────────────────────┤\n",
       "│          Valid Minimum           │       SOME Parameters at limit       │\n",
       "├──────────────────────────────────┼──────────────────────────────────────┤\n",
       "│ Below EDM threshold (goal x 10)  │           Below call limit           │\n",
       "├───────────────┬──────────────────┼───────────┬─────────────┬────────────┤\n",
       "│  Covariance   │     Hesse ok     │ Accurate  │  Pos. def.  │ Not forced │\n",
       "└───────────────┴──────────────────┴───────────┴─────────────┴────────────┘\n",
       "┌───┬──────┬───────────┬───────────┬────────────┬────────────┬─────────┬─────────┬───────┐\n",
       "│   │ Name │   Value   │ Hesse Err │ Minos Err- │ Minos Err+ │ Limit-  │ Limit+  │ Fixed │\n",
       "├───┼──────┼───────────┼───────────┼────────────┼────────────┼─────────┼─────────┼───────┤\n",
       "│ 0 │ x0   │    800    │    50     │            │            │    0    │         │       │\n",
       "│ 1 │ x1   │    190    │    40     │            │            │    0    │         │       │\n",
       "│ 2 │ x2   │    9.0    │    1.4    │            │            │    0    │         │       │\n",
       "│ 3 │ x3   │    8.5    │    1.3    │            │            │    0    │         │       │\n",
       "│ 4 │ x4   │    9.0    │    1.4    │            │            │    0    │         │       │\n",
       "│ 5 │ x5   │    7.4    │    1.2    │            │            │    0    │         │       │\n",
       "│ 6 │ x6   │    8.4    │    1.3    │            │            │    0    │         │       │\n",
       "│ 7 │ x7   │    6.4    │    1.1    │            │            │    0    │         │       │\n",
       "│ 8 │ x8   │    9.2    │    1.7    │            │            │    0    │         │       │\n",
       "│ 9 │ x9   │    4.8    │    2.3    │            │            │    0    │         │       │\n",
       "│ 10│ x10  │    7.0    │    1.5    │            │            │    0    │         │       │\n",
       "│ 11│ x11  │    5.5    │    1.0    │            │            │    0    │         │       │\n",
       "│ 12│ x12  │    5.1    │    0.9    │            │            │    0    │         │       │\n",
       "│ 13│ x13  │    4.6    │    0.9    │            │            │    0    │         │       │\n",
       "│ 14│ x14  │    4.7    │    0.9    │            │            │    0    │         │       │\n",
       "│ 15│ x15  │    4.3    │    0.8    │            │            │    0    │         │       │\n",
       "│ 16│ x16  │    3.2    │    0.7    │            │            │    0    │         │       │\n",
       "│ 17│ x17  │    0.0    │    0.4    │            │            │    0    │         │       │\n",
       "│ 18│ x18  │    0.0    │    0.4    │            │            │    0    │         │       │\n",
       "│ 19│ x19  │    0.0    │    0.4    │            │            │    0    │         │       │\n",
       "│ 20│ x20  │    0.0    │    0.5    │            │            │    0    │         │       │\n",
       "│ 21│ x21  │    0.0    │    0.4    │            │            │    0    │         │       │\n",
       "│ 22│ x22  │    2.1    │    1.5    │            │            │    0    │         │       │\n",
       "│ 23│ x23  │    19     │     4     │            │            │    0    │         │       │\n",
       "│ 24│ x24  │    54     │     7     │            │            │    0    │         │       │\n",
       "│ 25│ x25  │    23     │     4     │            │            │    0    │         │       │\n",
       "│ 26│ x26  │    1.1    │    1.0    │            │            │    0    │         │       │\n",
       "│ 27│ x27  │    0.0    │    0.4    │            │            │    0    │         │       │\n",
       "│ 28│ x28  │    0.0    │    0.4    │            │            │    0    │         │       │\n",
       "│ 29│ x29  │    0.0    │    0.4    │            │            │    0    │         │       │\n",
       "│ 30│ x30  │    0.0    │    0.4    │            │            │    0    │         │       │\n",
       "│ 31│ x31  │    0.0    │    0.5    │            │            │    0    │         │       │\n",
       "└───┴──────┴───────────┴───────────┴────────────┴────────────┴─────────┴─────────┴───────┘\n",
       "┌─────┬─────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────┐\n",
       "│     │        x0        x1        x2        x3        x4        x5        x6        x7        x8        x9       x10       x11       x12       x13       x14       x15       x16       x17       x18       x19       x20       x21       x22       x23       x24       x25       x26       x27       x28       x29       x30       x31 │\n",
       "├─────┼─────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────┤\n",
       "│  x0 │  2.24e+03 -1.45e+03     -14.6     -13.8     -14.6       -12     -13.6     -5.25      23.6      68.9      23.2     -6.29      -8.3     -7.42     -7.59     -7.06     -5.12  3.17e-08        -0 -1.03e-06  -2.7e-06        -0     -5.71     -26.2      29.7      5.32     -3.16        -0        -0        -0        -0 -2.53e-05 │\n",
       "│  x1 │ -1.45e+03  1.64e+03      14.6      13.8      14.6        12      13.6      5.25     -23.6     -68.9     -23.2      6.29       8.3      7.42      7.59      7.06      5.12 -3.07e-08         0  1.05e-06  2.68e-06         0      5.71      26.2     -29.8     -5.32      3.16         0         0         0         0  2.53e-05 │\n",
       "│  x2 │     -14.6      14.6      1.88     0.842     0.895     0.734     0.831     0.584     0.525    -0.302     0.345     0.522     0.507     0.453     0.464     0.432     0.313  2.22e-09         0  1.25e-08   2.6e-08         0    0.0578     0.264      -0.3   -0.0537    0.0319         0         0         0         0  2.62e-07 │\n",
       "│  x3 │     -13.8      13.8     0.842      1.71     0.842      0.69     0.781     0.549     0.494    -0.284     0.324     0.491     0.477     0.426     0.436     0.406     0.294 -2.19e-10        -0  1.19e-08  2.48e-08         0    0.0543     0.248    -0.282   -0.0505      0.03         0         0         0         0  2.48e-07 │\n",
       "│  x4 │     -14.6      14.6     0.895     0.842      1.88     0.734     0.831     0.584     0.525    -0.302     0.345     0.522     0.507     0.453     0.464     0.432     0.313 -2.05e-10         0 -6.69e-08  2.56e-08         0    0.0578     0.264      -0.3   -0.0537    0.0319         0         0         0         0  2.63e-07 │\n",
       "│  x5 │       -12        12     0.734      0.69     0.734       1.4     0.681     0.478     0.431    -0.248     0.283     0.428     0.416     0.372      0.38     0.354     0.256 -1.25e-10         0  1.05e-08 -1.65e-07         0    0.0473     0.216    -0.246    -0.044    0.0262         0         0         0         0  2.14e-07 │\n",
       "│  x6 │     -13.6      13.6     0.831     0.781     0.831     0.681      1.68     0.541     0.487     -0.28      0.32     0.484     0.471     0.421     0.431     0.401      0.29 -2.24e-10         0  1.19e-08  2.37e-08        -0    0.0536     0.245    -0.278   -0.0498    0.0296         0         0         0         0  2.43e-07 │\n",
       "│  x7 │     -5.25      5.25     0.584     0.549     0.584     0.478     0.541      1.23     0.421   -0.0401     0.295     0.346     0.331     0.295     0.302     0.281     0.204 -8.36e-11         0  8.66e-09  1.53e-08         0    -0.424     0.207     0.116    0.0813    0.0193         0         0         0         0   1.4e-07 │\n",
       "│  x8 │      23.6     -23.6     0.525     0.494     0.525     0.431     0.487     0.421      2.99     0.999     0.732     0.348     0.298     0.266     0.272     0.253     0.184  5.15e-11         0  4.54e-09  4.22e-10         0    0.0195     -3.03      2.16     0.842   0.00754         0         0         0         0 -7.68e-08 │\n",
       "│  x9 │      68.9     -68.9    -0.302    -0.284    -0.302    -0.248     -0.28   -0.0401     0.999       5.1     0.934   -0.0941    -0.171    -0.153    -0.157    -0.146    -0.106  3.52e-10         0 -8.49e-09 -3.84e-08         0    -0.048     0.432      -2.1      1.75   -0.0329         0         0         0         0 -5.45e-07 │\n",
       "│ x10 │      23.2     -23.2     0.345     0.324     0.345     0.283      0.32     0.295     0.732     0.934      2.33     0.238     0.195     0.175     0.179     0.166      0.12 -6.84e-13         0  2.16e-09 -3.23e-09         0   0.00938     0.336      1.97     -2.32    0.0023         0         0         0         0 -1.04e-07 │\n",
       "│ x11 │     -6.29      6.29     0.522     0.491     0.522     0.428     0.484     0.346     0.348   -0.0941     0.238     0.984     0.296     0.264     0.271     0.252     0.182 -1.17e-10         0  7.06e-09  1.41e-08         0    0.0327     0.172   -0.0117    0.0296    -0.223         0         0         0         0  1.36e-07 │\n",
       "│ x12 │      -8.3       8.3     0.507     0.477     0.507     0.416     0.471     0.331     0.298    -0.171     0.195     0.296     0.843     0.257     0.263     0.245     0.177 -1.25e-10         0  7.48e-09  1.48e-08         0    0.0327     0.149     -0.17   -0.0304    0.0181        -0         0         0         0  1.49e-07 │\n",
       "│ x13 │     -7.42      7.42     0.453     0.426     0.453     0.372     0.421     0.295     0.266    -0.153     0.175     0.264     0.257     0.726     0.235     0.219     0.158  -1.2e-10         0  6.52e-09  1.32e-08         0    0.0292     0.134    -0.152   -0.0272    0.0162         0        -0         0         0  1.33e-07 │\n",
       "│ x14 │     -7.59      7.59     0.464     0.436     0.464      0.38     0.431     0.302     0.272    -0.157     0.179     0.271     0.263     0.235     0.749     0.224     0.162  -1.1e-10         0  6.44e-09  1.36e-08         0    0.0299     0.137    -0.155   -0.0278    0.0165         0         0        -0         0  1.37e-07 │\n",
       "│ x15 │     -7.06      7.06     0.432     0.406     0.432     0.354     0.401     0.281     0.253    -0.146     0.166     0.252     0.245     0.219     0.224     0.681     0.151 -8.27e-11         0  6.34e-09  1.24e-08         0    0.0279     0.127    -0.145   -0.0259    0.0154         0         0         0        -0  1.26e-07 │\n",
       "│ x16 │     -5.12      5.12     0.313     0.294     0.313     0.256      0.29     0.204     0.184    -0.106      0.12     0.182     0.177     0.158     0.162     0.151     0.452 -7.37e-11         0  4.46e-09  8.72e-09         0    0.0202    0.0921    -0.105   -0.0188    0.0111         0         0         0         0 -1.25e-06 │\n",
       "│ x17 │  3.17e-08 -3.07e-08  2.22e-09 -2.19e-10 -2.05e-10 -1.25e-10 -2.24e-10 -8.36e-11  5.15e-11  3.52e-10 -6.84e-13 -1.17e-10 -1.25e-10  -1.2e-10  -1.1e-10 -8.27e-11 -7.37e-11  4.96e-09        -0 -6.59e-15  2.09e-14        -0 -1.21e-11 -5.09e-11   8.9e-10  2.65e-10   7.3e-13        -0        -0         0        -0 -3.83e-14 │\n",
       "│ x18 │        -0         0         0        -0         0         0         0         0         0         0         0         0         0         0         0         0         0        -0         0         0        -0        -0         0         0         0         0         0         0        -0        -0        -0         0 │\n",
       "│ x19 │ -1.03e-06  1.05e-06  1.25e-08  1.19e-08 -6.69e-08  1.05e-08  1.19e-08  8.66e-09  4.54e-09 -8.49e-09  2.16e-09  7.06e-09  7.48e-09  6.52e-09  6.44e-09  6.34e-09  4.46e-09 -6.59e-15         0  5.45e-07  2.77e-13         0 -9.96e-11  5.63e-10 -2.33e-08 -6.82e-09  1.04e-09         0         0         0         0  6.69e-13 │\n",
       "│ x20 │  -2.7e-06  2.68e-06   2.6e-08  2.48e-08  2.56e-08 -1.65e-07  2.37e-08  1.53e-08  4.22e-10 -3.84e-08 -3.23e-09  1.41e-08  1.48e-08  1.32e-08  1.36e-08  1.24e-08  8.72e-09  2.09e-14        -0  2.77e-13  6.59e-07         0  9.44e-10  3.73e-10 -6.51e-08 -2.06e-08  1.05e-09        -0         0        -0        -0  1.16e-12 │\n",
       "│ x21 │        -0         0         0         0         0         0        -0         0         0         0         0         0         0         0         0         0         0        -0        -0         0         0         0         0         0         0         0         0        -0         0        -0        -0        -0 │\n",
       "│ x22 │     -5.71      5.71    0.0578    0.0543    0.0578    0.0473    0.0536    -0.424    0.0195    -0.048   0.00938    0.0327    0.0327    0.0292    0.0299    0.0279    0.0202 -1.21e-11         0 -9.96e-11  9.44e-10         0      2.19    0.0106   -0.0762   -0.0247   0.00233         0         0         0         0  2.38e-08 │\n",
       "│ x23 │     -26.2      26.2     0.264     0.248     0.264     0.216     0.245     0.207     -3.03     0.432     0.336     0.172     0.149     0.134     0.137     0.127    0.0921 -5.09e-11         0  5.63e-10  3.73e-10         0    0.0106      17.8     0.947     0.371   0.00445         0         0         0         0  -1.4e-08 │\n",
       "│ x24 │      29.7     -29.8      -0.3    -0.282      -0.3    -0.246    -0.278     0.116      2.16      -2.1      1.97   -0.0117     -0.17    -0.152    -0.155    -0.145    -0.105   8.9e-10         0 -2.33e-08 -6.51e-08         0   -0.0762     0.947      49.8      3.46   -0.0548         0         0         0         0 -9.78e-07 │\n",
       "│ x25 │      5.32     -5.32   -0.0537   -0.0505   -0.0537    -0.044   -0.0498    0.0813     0.842      1.75     -2.32    0.0296   -0.0304   -0.0272   -0.0278   -0.0259   -0.0188  2.65e-10         0 -6.82e-09 -2.06e-08         0   -0.0247     0.371      3.46      18.9   -0.0184         0         0         0         0 -3.45e-07 │\n",
       "│ x26 │     -3.16      3.16    0.0319      0.03    0.0319    0.0262    0.0296    0.0193   0.00754   -0.0329    0.0023    -0.223    0.0181    0.0162    0.0165    0.0154    0.0111   7.3e-13         0  1.04e-09  1.05e-09         0   0.00233   0.00445   -0.0548   -0.0184      1.14         0         0        -0         0  1.56e-08 │\n",
       "│ x27 │        -0         0         0         0         0         0         0         0         0         0         0         0        -0         0         0         0         0        -0         0         0        -0        -0         0         0         0         0         0         0         0        -0        -0         0 │\n",
       "│ x28 │        -0         0         0         0         0         0         0         0         0         0         0         0         0        -0         0         0         0        -0        -0         0         0         0         0         0         0         0         0         0         0        -0        -0         0 │\n",
       "│ x29 │        -0         0         0         0         0         0         0         0         0         0         0         0         0         0        -0         0         0         0        -0         0        -0        -0         0         0         0         0        -0        -0        -0         0        -0        -0 │\n",
       "│ x30 │        -0         0         0         0         0         0         0         0         0         0         0         0         0         0         0        -0         0        -0        -0         0        -0        -0         0         0         0         0         0        -0        -0        -0         0        -0 │\n",
       "│ x31 │ -2.53e-05  2.53e-05  2.62e-07  2.48e-07  2.63e-07  2.14e-07  2.43e-07   1.4e-07 -7.68e-08 -5.45e-07 -1.04e-07  1.36e-07  1.49e-07  1.33e-07  1.37e-07  1.26e-07 -1.25e-06 -3.83e-14         0  6.69e-13  1.16e-12        -0  2.38e-08  -1.4e-08 -9.78e-07 -3.45e-07  1.56e-08         0         0        -0        -0  5.19e-06 │\n",
       "└─────┴─────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────┘"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "class BB:\n",
    "    def __init__(self, n, t):\n",
    "        self.data = n, t\n",
    "\n",
    "    def __call__(self, par):\n",
    "        n, t = self.data\n",
    "        bins = len(n)\n",
    "        yields = par[:2]\n",
    "        nuisances = par[2:]\n",
    "        b = nuisances[:bins]\n",
    "        s = nuisances[bins:]\n",
    "        mu = 0\n",
    "        for y, c in zip(yields, (b, s)):\n",
    "            mu += y * c / np.sum(c)\n",
    "        r = poisson_chi2(n, mu) + poisson_chi2(t[0], b) + poisson_chi2(t[1], s)\n",
    "        return r\n",
    "\n",
    "    @property\n",
    "    def ndata(self):\n",
    "        n, t = self.data\n",
    "        return np.prod(n.shape) + np.prod(t.shape)\n",
    "\n",
    "m1 = Minuit(BB(n, t), np.concatenate([truth, t[0], t[1]]))\n",
    "m1.limits = (0, None)\n",
    "m1.migrad(ncall=100000)\n",
    "m1.hesse()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The result of this fit is comparable to the bootstrap method for this example, but the chi2/ndof is now reasonable and the uncertainties are correct without further work. This method should perform better than the bootstrap method, if the count per bin in the templates is small.\n",
    "\n",
    "Another advantage is of this technique is that one can profile over the likelihood to obtain a 2D confidence regions, which is not possible with the bootstrap technique."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "m1.draw_mncontour(\"x0\", \"x1\");"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Before moving on, we briefly explore a possible refinement of the previous method, which is to hide the nuisance parameters from Minuit with a nested fit. It turns out that this technique is not an improvement, but it is useful to show that explicitly.\n",
    "\n",
    "The idea is to construct an outer cost function, which only has the yields as parameters. Inside the outer cost function, the best nuisance parameters are found for the current yields with an inner cost function. Technically, this is achieved by calling a minimizer on the inner cost function at every call to the outer cost function.\n",
    "\n",
    "Technical detail: It is important here to adjust Minuit's expectation of how accurate the cost function is computed. Usually, Minuit performs its internal calculations under the assumption that the cost function is accurate to machine precision. This is usually not the case when a minimizer is used internally to optimize the inner function. We perform the internal minimization with SciPy, which allows us to set the tolerance. We set it here to 1e-8, which is sufficient for this problem and saves a bit of time on the internal minimisation. We then instruct Minuit to expect only this precision."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table>\n",
       "    <tr>\n",
       "        <th colspan=\"5\" style=\"text-align:center\" title=\"Minimizer\"> Migrad </th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td colspan=\"2\" style=\"text-align:left\" title=\"Minimum value of function\"> FCN = 18.27 (chi2/ndof = 1.4) </td>\n",
       "        <td colspan=\"3\" style=\"text-align:center\" title=\"Total number of function and (optional) gradient evaluations\"> Nfcn = 60 </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td colspan=\"2\" style=\"text-align:left\" title=\"Estimated distance to minimum and goal\"> EDM = 1.23e-08 (Goal: 0.0002) </td>\n",
       "        <td colspan=\"3\" style=\"text-align:center\" title=\"Total run time of algorithms\"> time = 7.8 sec </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td colspan=\"2\" style=\"text-align:center;background-color:#92CCA6;color:black\"> Valid Minimum </td>\n",
       "        <td colspan=\"3\" style=\"text-align:center;background-color:#92CCA6;color:black\"> No Parameters at limit </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td colspan=\"2\" style=\"text-align:center;background-color:#92CCA6;color:black\"> Below EDM threshold (goal x 10) </td>\n",
       "        <td colspan=\"3\" style=\"text-align:center;background-color:#92CCA6;color:black\"> Below call limit </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"text-align:center;background-color:#92CCA6;color:black\"> Covariance </td>\n",
       "        <td style=\"text-align:center;background-color:#92CCA6;color:black\"> Hesse ok </td>\n",
       "        <td style=\"text-align:center;background-color:#92CCA6;color:black\" title=\"Is covariance matrix accurate?\"> Accurate </td>\n",
       "        <td style=\"text-align:center;background-color:#92CCA6;color:black\" title=\"Is covariance matrix positive definite?\"> Pos. def. </td>\n",
       "        <td style=\"text-align:center;background-color:#92CCA6;color:black\" title=\"Was positive definiteness enforced by Minuit?\"> Not forced </td>\n",
       "    </tr>\n",
       "</table><table>\n",
       "    <tr>\n",
       "        <td></td>\n",
       "        <th title=\"Variable name\"> Name </th>\n",
       "        <th title=\"Value of parameter\"> Value </th>\n",
       "        <th title=\"Hesse error\"> Hesse Error </th>\n",
       "        <th title=\"Minos lower error\"> Minos Error- </th>\n",
       "        <th title=\"Minos upper error\"> Minos Error+ </th>\n",
       "        <th title=\"Lower limit of the parameter\"> Limit- </th>\n",
       "        <th title=\"Upper limit of the parameter\"> Limit+ </th>\n",
       "        <th title=\"Is the parameter fixed in the fit\"> Fixed </th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th> 0 </th>\n",
       "        <td> x0 </td>\n",
       "        <td> 800 </td>\n",
       "        <td> 50 </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
       "        <td> 0 </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th> 1 </th>\n",
       "        <td> x1 </td>\n",
       "        <td> 190 </td>\n",
       "        <td> 40 </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
       "        <td> 0 </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
       "    </tr>\n",
       "</table><table>\n",
       "    <tr>\n",
       "        <td></td>\n",
       "        <th> x0 </th>\n",
       "        <th> x1 </th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th> x0 </th>\n",
       "        <td> 2.22e+03 </td>\n",
       "        <td style=\"background-color:rgb(152,152,250);color:black\"> -1.43e+03 <strong>(-0.754)</strong> </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th> x1 </th>\n",
       "        <td style=\"background-color:rgb(152,152,250);color:black\"> -1.43e+03 <strong>(-0.754)</strong> </td>\n",
       "        <td> 1.62e+03 </td>\n",
       "    </tr>\n",
       "</table>"
      ],
      "text/plain": [
       "┌─────────────────────────────────────────────────────────────────────────┐\n",
       "│                                Migrad                                   │\n",
       "├──────────────────────────────────┬──────────────────────────────────────┤\n",
       "│ FCN = 18.27 (chi2/ndof = 1.4)    │              Nfcn = 60               │\n",
       "│ EDM = 1.23e-08 (Goal: 0.0002)    │            time = 7.8 sec            │\n",
       "├──────────────────────────────────┼──────────────────────────────────────┤\n",
       "│          Valid Minimum           │        No Parameters at limit        │\n",
       "├──────────────────────────────────┼──────────────────────────────────────┤\n",
       "│ Below EDM threshold (goal x 10)  │           Below call limit           │\n",
       "├───────────────┬──────────────────┼───────────┬─────────────┬────────────┤\n",
       "│  Covariance   │     Hesse ok     │ Accurate  │  Pos. def.  │ Not forced │\n",
       "└───────────────┴──────────────────┴───────────┴─────────────┴────────────┘\n",
       "┌───┬──────┬───────────┬───────────┬────────────┬────────────┬─────────┬─────────┬───────┐\n",
       "│   │ Name │   Value   │ Hesse Err │ Minos Err- │ Minos Err+ │ Limit-  │ Limit+  │ Fixed │\n",
       "├───┼──────┼───────────┼───────────┼────────────┼────────────┼─────────┼─────────┼───────┤\n",
       "│ 0 │ x0   │    800    │    50     │            │            │    0    │         │       │\n",
       "│ 1 │ x1   │    190    │    40     │            │            │    0    │         │       │\n",
       "└───┴──────┴───────────┴───────────┴────────────┴────────────┴─────────┴─────────┴───────┘\n",
       "┌────┬─────────────────────┐\n",
       "│    │        x0        x1 │\n",
       "├────┼─────────────────────┤\n",
       "│ x0 │  2.22e+03 -1.43e+03 │\n",
       "│ x1 │ -1.43e+03  1.62e+03 │\n",
       "└────┴─────────────────────┘"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "precision = 1e-8\n",
    "\n",
    "def cost(yields):\n",
    "    bins = len(n)\n",
    "\n",
    "    def inner(nuisance):\n",
    "        b = nuisance[:bins]\n",
    "        s = nuisance[bins:]\n",
    "        mu = 0\n",
    "        for y, c in zip(yields, (b, s)):\n",
    "            mu += y * c / np.sum(c)\n",
    "        r = poisson_chi2(n, mu) + poisson_chi2(t[0], b) + poisson_chi2(t[1], s)\n",
    "        return r\n",
    "\n",
    "    bounds = np.zeros((2 * bins, 2))\n",
    "    bounds[:, 1] = np.inf\n",
    "    r = minimize(inner, np.ravel(t), bounds=bounds, tol=precision)\n",
    "    assert r.success\n",
    "    return r.fun\n",
    "\n",
    "cost.errordef = Minuit.LEAST_SQUARES\n",
    "cost.ndata = np.prod(n.shape)\n",
    "\n",
    "m2 = Minuit(cost, truth)\n",
    "m2.precision = precision\n",
    "m2.limits = (0, None)\n",
    "m2.migrad()\n",
    "m2.hesse()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We obtain the exact same result as expected, but the runtime is much longer (more than a factor 10), which disfavors this technique compared to the straight-forward fit. The minimization is not as efficient, because Minuit cannot exploit correlations between the internal and the external parameters that allow it to converge it faster when it sees all parameters at once."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Barlow-Beeston-lite\n",
    "\n",
    "The implementation described by [Barlow and Beeston, Comput.Phys.Commun. 77 (1993) 219-228](https://doi.org/10.1016/0010-4655(93)90005-W) solves the problem similarly to the nested fit described above, but the solution to the inner problem is found with a more efficient algorithm. Unfortunately, their approach still requires numerically solving a non-linear equation per bin. The finite accuracy of the non-linear solver introduces discontinuities in the log-likelihood that confuse Minuit, as noted by [Conway, PHYSTAT 2011, https://arxiv.org/abs/1103.0354](https://doi.org/10.48550/arXiv.1103.0354). To address this, Conway proposes a simplified treatment where the uncertainty in the template is described by a multiplicative factor constrained by a Gaussian. With this simplification, the optimal nuisance parameters can be found by bin-by-bin by solving a quadratic equation which has only one allowed solution that can be found analytically. Conway's method and an improved approximate method derived in [Dembinski, https://arxiv.org/abs/2206.12346](https://doi.org/10.48550/arXiv.2206.12346) are implemented in the built-in BarlowBeestonLite cost function."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table>\n",
       "    <tr>\n",
       "        <th colspan=\"5\" style=\"text-align:center\" title=\"Minimizer\"> Migrad </th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td colspan=\"2\" style=\"text-align:left\" title=\"Minimum value of function\"> FCN = 11.52 (chi2/ndof = 0.9) </td>\n",
       "        <td colspan=\"3\" style=\"text-align:center\" title=\"Total number of function and (optional) gradient evaluations\"> Nfcn = 48 </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td colspan=\"2\" style=\"text-align:left\" title=\"Estimated distance to minimum and goal\"> EDM = 6.05e-05 (Goal: 0.0002) </td>\n",
       "        <td colspan=\"3\" style=\"text-align:center\" title=\"Total run time of algorithms\">  </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td colspan=\"2\" style=\"text-align:center;background-color:#92CCA6;color:black\"> Valid Minimum </td>\n",
       "        <td colspan=\"3\" style=\"text-align:center;background-color:#92CCA6;color:black\"> No Parameters at limit </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td colspan=\"2\" style=\"text-align:center;background-color:#92CCA6;color:black\"> Below EDM threshold (goal x 10) </td>\n",
       "        <td colspan=\"3\" style=\"text-align:center;background-color:#92CCA6;color:black\"> Below call limit </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"text-align:center;background-color:#92CCA6;color:black\"> Covariance </td>\n",
       "        <td style=\"text-align:center;background-color:#92CCA6;color:black\"> Hesse ok </td>\n",
       "        <td style=\"text-align:center;background-color:#92CCA6;color:black\" title=\"Is covariance matrix accurate?\"> Accurate </td>\n",
       "        <td style=\"text-align:center;background-color:#92CCA6;color:black\" title=\"Is covariance matrix positive definite?\"> Pos. def. </td>\n",
       "        <td style=\"text-align:center;background-color:#92CCA6;color:black\" title=\"Was positive definiteness enforced by Minuit?\"> Not forced </td>\n",
       "    </tr>\n",
       "</table><table>\n",
       "    <tr>\n",
       "        <td></td>\n",
       "        <th title=\"Variable name\"> Name </th>\n",
       "        <th title=\"Value of parameter\"> Value </th>\n",
       "        <th title=\"Hesse error\"> Hesse Error </th>\n",
       "        <th title=\"Minos lower error\"> Minos Error- </th>\n",
       "        <th title=\"Minos upper error\"> Minos Error+ </th>\n",
       "        <th title=\"Lower limit of the parameter\"> Limit- </th>\n",
       "        <th title=\"Upper limit of the parameter\"> Limit+ </th>\n",
       "        <th title=\"Is the parameter fixed in the fit\"> Fixed </th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th> 0 </th>\n",
       "        <td> x0 </td>\n",
       "        <td> 0.86e3 </td>\n",
       "        <td> 0.11e3 </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
       "        <td> 0 </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th> 1 </th>\n",
       "        <td> x1 </td>\n",
       "        <td> 190 </td>\n",
       "        <td> 40 </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
       "        <td> 0 </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
       "    </tr>\n",
       "</table><table>\n",
       "    <tr>\n",
       "        <td></td>\n",
       "        <th> x0 </th>\n",
       "        <th> x1 </th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th> x0 </th>\n",
       "        <td> 1.16e+04 </td>\n",
       "        <td style=\"background-color:rgb(207,207,250);color:black\"> -1.56e+03 <strong>(-0.330)</strong> </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th> x1 </th>\n",
       "        <td style=\"background-color:rgb(207,207,250);color:black\"> -1.56e+03 <strong>(-0.330)</strong> </td>\n",
       "        <td> 1.94e+03 </td>\n",
       "    </tr>\n",
       "</table>"
      ],
      "text/plain": [
       "┌─────────────────────────────────────────────────────────────────────────┐\n",
       "│                                Migrad                                   │\n",
       "├──────────────────────────────────┬──────────────────────────────────────┤\n",
       "│ FCN = 11.52 (chi2/ndof = 0.9)    │              Nfcn = 48               │\n",
       "│ EDM = 6.05e-05 (Goal: 0.0002)    │                                      │\n",
       "├──────────────────────────────────┼──────────────────────────────────────┤\n",
       "│          Valid Minimum           │        No Parameters at limit        │\n",
       "├──────────────────────────────────┼──────────────────────────────────────┤\n",
       "│ Below EDM threshold (goal x 10)  │           Below call limit           │\n",
       "├───────────────┬──────────────────┼───────────┬─────────────┬────────────┤\n",
       "│  Covariance   │     Hesse ok     │ Accurate  │  Pos. def.  │ Not forced │\n",
       "└───────────────┴──────────────────┴───────────┴─────────────┴────────────┘\n",
       "┌───┬──────┬───────────┬───────────┬────────────┬────────────┬─────────┬─────────┬───────┐\n",
       "│   │ Name │   Value   │ Hesse Err │ Minos Err- │ Minos Err+ │ Limit-  │ Limit+  │ Fixed │\n",
       "├───┼──────┼───────────┼───────────┼────────────┼────────────┼─────────┼─────────┼───────┤\n",
       "│ 0 │ x0   │  0.86e3   │  0.11e3   │            │            │    0    │         │       │\n",
       "│ 1 │ x1   │    190    │    40     │            │            │    0    │         │       │\n",
       "└───┴──────┴───────────┴───────────┴────────────┴────────────┴─────────┴─────────┴───────┘\n",
       "┌────┬─────────────────────┐\n",
       "│    │        x0        x1 │\n",
       "├────┼─────────────────────┤\n",
       "│ x0 │  1.16e+04 -1.56e+03 │\n",
       "│ x1 │ -1.56e+03  1.94e+03 │\n",
       "└────┴─────────────────────┘"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "c = BarlowBeestonLite(n, xe, t, method=\"jsc\") # Conway\n",
    "m3 = Minuit(c, *truth)\n",
    "m3.limits = (0, None)\n",
    "m3.migrad()\n",
    "m3.hesse()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table>\n",
       "    <tr>\n",
       "        <th colspan=\"5\" style=\"text-align:center\" title=\"Minimizer\"> Migrad </th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td colspan=\"2\" style=\"text-align:left\" title=\"Minimum value of function\"> FCN = 11.42 (chi2/ndof = 0.9) </td>\n",
       "        <td colspan=\"3\" style=\"text-align:center\" title=\"Total number of function and (optional) gradient evaluations\"> Nfcn = 47 </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td colspan=\"2\" style=\"text-align:left\" title=\"Estimated distance to minimum and goal\"> EDM = 1.85e-06 (Goal: 0.0002) </td>\n",
       "        <td colspan=\"3\" style=\"text-align:center\" title=\"Total run time of algorithms\">  </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td colspan=\"2\" style=\"text-align:center;background-color:#92CCA6;color:black\"> Valid Minimum </td>\n",
       "        <td colspan=\"3\" style=\"text-align:center;background-color:#92CCA6;color:black\"> No Parameters at limit </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td colspan=\"2\" style=\"text-align:center;background-color:#92CCA6;color:black\"> Below EDM threshold (goal x 10) </td>\n",
       "        <td colspan=\"3\" style=\"text-align:center;background-color:#92CCA6;color:black\"> Below call limit </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"text-align:center;background-color:#92CCA6;color:black\"> Covariance </td>\n",
       "        <td style=\"text-align:center;background-color:#92CCA6;color:black\"> Hesse ok </td>\n",
       "        <td style=\"text-align:center;background-color:#92CCA6;color:black\" title=\"Is covariance matrix accurate?\"> Accurate </td>\n",
       "        <td style=\"text-align:center;background-color:#92CCA6;color:black\" title=\"Is covariance matrix positive definite?\"> Pos. def. </td>\n",
       "        <td style=\"text-align:center;background-color:#92CCA6;color:black\" title=\"Was positive definiteness enforced by Minuit?\"> Not forced </td>\n",
       "    </tr>\n",
       "</table><table>\n",
       "    <tr>\n",
       "        <td></td>\n",
       "        <th title=\"Variable name\"> Name </th>\n",
       "        <th title=\"Value of parameter\"> Value </th>\n",
       "        <th title=\"Hesse error\"> Hesse Error </th>\n",
       "        <th title=\"Minos lower error\"> Minos Error- </th>\n",
       "        <th title=\"Minos upper error\"> Minos Error+ </th>\n",
       "        <th title=\"Lower limit of the parameter\"> Limit- </th>\n",
       "        <th title=\"Upper limit of the parameter\"> Limit+ </th>\n",
       "        <th title=\"Is the parameter fixed in the fit\"> Fixed </th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th> 0 </th>\n",
       "        <td> x0 </td>\n",
       "        <td> 760 </td>\n",
       "        <td> 90 </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
       "        <td> 0 </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th> 1 </th>\n",
       "        <td> x1 </td>\n",
       "        <td> 190 </td>\n",
       "        <td> 40 </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
       "        <td> 0 </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
       "    </tr>\n",
       "</table><table>\n",
       "    <tr>\n",
       "        <td></td>\n",
       "        <th> x0 </th>\n",
       "        <th> x1 </th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th> x0 </th>\n",
       "        <td> 8.08e+03 </td>\n",
       "        <td style=\"background-color:rgb(207,207,250);color:black\"> -1.26e+03 <strong>(-0.329)</strong> </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th> x1 </th>\n",
       "        <td style=\"background-color:rgb(207,207,250);color:black\"> -1.26e+03 <strong>(-0.329)</strong> </td>\n",
       "        <td> 1.81e+03 </td>\n",
       "    </tr>\n",
       "</table>"
      ],
      "text/plain": [
       "┌─────────────────────────────────────────────────────────────────────────┐\n",
       "│                                Migrad                                   │\n",
       "├──────────────────────────────────┬──────────────────────────────────────┤\n",
       "│ FCN = 11.42 (chi2/ndof = 0.9)    │              Nfcn = 47               │\n",
       "│ EDM = 1.85e-06 (Goal: 0.0002)    │                                      │\n",
       "├──────────────────────────────────┼──────────────────────────────────────┤\n",
       "│          Valid Minimum           │        No Parameters at limit        │\n",
       "├──────────────────────────────────┼──────────────────────────────────────┤\n",
       "│ Below EDM threshold (goal x 10)  │           Below call limit           │\n",
       "├───────────────┬──────────────────┼───────────┬─────────────┬────────────┤\n",
       "│  Covariance   │     Hesse ok     │ Accurate  │  Pos. def.  │ Not forced │\n",
       "└───────────────┴──────────────────┴───────────┴─────────────┴────────────┘\n",
       "┌───┬──────┬───────────┬───────────┬────────────┬────────────┬─────────┬─────────┬───────┐\n",
       "│   │ Name │   Value   │ Hesse Err │ Minos Err- │ Minos Err+ │ Limit-  │ Limit+  │ Fixed │\n",
       "├───┼──────┼───────────┼───────────┼────────────┼────────────┼─────────┼─────────┼───────┤\n",
       "│ 0 │ x0   │    760    │    90     │            │            │    0    │         │       │\n",
       "│ 1 │ x1   │    190    │    40     │            │            │    0    │         │       │\n",
       "└───┴──────┴───────────┴───────────┴────────────┴────────────┴─────────┴─────────┴───────┘\n",
       "┌────┬─────────────────────┐\n",
       "│    │        x0        x1 │\n",
       "├────┼─────────────────────┤\n",
       "│ x0 │  8.08e+03 -1.26e+03 │\n",
       "│ x1 │ -1.26e+03  1.81e+03 │\n",
       "└────┴─────────────────────┘"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "c = BarlowBeestonLite(n, xe, t, method=\"hpd\") # Dembinski\n",
    "m4 = Minuit(c, *truth)\n",
    "m4.limits = (0, None)\n",
    "m4.migrad()\n",
    "m4.hesse()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "full fit\n",
      "  x0 796 +- 47\n",
      "  x1 187 +- 40\n",
      "  correlation -0.76\n",
      "BBL-JSC\n",
      "  x0 858 +- 108\n",
      "  x1 185 +- 44\n",
      "  correlation -0.33\n",
      "BBL-HPD\n",
      "  x0 762 +- 90\n",
      "  x1 194 +- 43\n",
      "  correlation -0.33\n"
     ]
    }
   ],
   "source": [
    "for title, m in zip((\"full fit\", \"BBL-JSC\", \"BBL-HPD\"), (m1, m3, m4)):\n",
    "    print(title)\n",
    "    cov = m.covariance\n",
    "    for label, p, e in zip((\"x0\", \"x1\"), m.values, np.diag(cov) ** 0.5):\n",
    "        print(f\"  {label} {p:.0f} +- {e:.0f}\")\n",
    "    print(f\"  correlation {cov[0, 1] / (cov[0, 0] * cov[1, 1]) ** 0.5:.2f}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The best yields found by the Barlow-Beeston-Lite (BBL) method differ from those found with the Barlow-Beeston (BB) method, because the two likelihoods are rather different. In this particular case, the uncertainty for the signal estimated by the BBL is larger. The difference shows up in particular in the 68 % confidence regions."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "c1 = m1.mncontour(\"x0\", \"x1\")\n",
    "c3 = m3.mncontour(\"x0\", \"x1\")\n",
    "c4 = m4.mncontour(\"x0\", \"x1\")\n",
    "c1 = np.append(c1, [c1[0]], axis=0)\n",
    "c3 = np.append(c3, [c3[0]], axis=0)\n",
    "c4 = np.append(c4, [c4[0]], axis=0)\n",
    "plt.plot(c1[:,0], c1[:, 1], label=\"BB\")\n",
    "plt.plot(c3[:,0], c3[:, 1], label=\"BBL(JSC)\")\n",
    "plt.plot(c4[:,0], c4[:, 1], label=\"BBL(HPD)\")\n",
    "plt.legend();"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The results obtained with the different Barlow-Beeston methods are similar but not identical."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Bias of the estimate and the estimated variance\n",
    "\n",
    "A single toy experiment cannot be used to judge the performance of these methods. We need to study the properties of these fits applied to sets of toy experiments, which allow us to measure the bias of the estimate itself and the bias of its variance estimate, which should reflect the true variance.\n",
    "\n",
    "We run three sets of experiments, with increasing number of events sampled for the templates. We expect that all methods converge as the sample used to compute the templates grows, since this reduces their relative uncertainties. To judge the estimates, we compute the pull distribution of the estimated signal yield, where the pull is defined as\n",
    "$$\n",
    "z = (\\hat s  - s)/ \\hat V_s^{1/2},\n",
    "$$\n",
    "with true signal yield $s$, estimate $\\hat s$, and the estimated variance $\\hat V_s$ of $\\hat s$. The performance of the method is indicated by the degree of agreement of the mean of $z$ with 0 and the standard deviation with 1. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "[Parallel(n_jobs=-1)]: Using backend LokyBackend with 8 concurrent workers.\n",
      "[Parallel(n_jobs=-1)]: Done  34 tasks      | elapsed:   10.7s\n",
      "[Parallel(n_jobs=-1)]: Done  50 out of  50 | elapsed:   11.0s finished\n",
      "[Parallel(n_jobs=-1)]: Using backend LokyBackend with 8 concurrent workers.\n",
      "[Parallel(n_jobs=-1)]: Done  50 out of  50 | elapsed:    1.0s finished\n",
      "[Parallel(n_jobs=-1)]: Using backend LokyBackend with 8 concurrent workers.\n",
      "[Parallel(n_jobs=-1)]: Done  50 out of  50 | elapsed:    0.8s finished\n"
     ]
    }
   ],
   "source": [
    "@delayed\n",
    "def compute(seed, truth, nmc):\n",
    "    rng = np.random.default_rng(seed)\n",
    "    xe, n, t = generate(rng, nmc, truth, 15)\n",
    "    accept = True\n",
    "    result = []\n",
    "    ma = False\n",
    "    for ti in t:\n",
    "        ma |= ti > 0\n",
    "    m_bb = Minuit(BB(n[ma], t[:, ma]), np.concatenate([truth, *t[:, ma]]))\n",
    "    m_bbl = Minuit(BarlowBeestonLite(n, xe, t, method=\"jsc\"), *truth)\n",
    "    m_bbl2 = Minuit(BarlowBeestonLite(n, xe, t, method=\"hpd\"), *truth)\n",
    "    for m in (m_bb, m_bbl, m_bbl2):\n",
    "        m.limits = (0, None)\n",
    "        # try hard to converge and get correct error estimates\n",
    "        for iter in range(10):\n",
    "            m.strategy = 0\n",
    "            m.migrad(ncall=1000000, iterate=1)\n",
    "            m.hesse()\n",
    "            if m.valid and m.accurate:\n",
    "                break\n",
    "        if not m.valid or not m.accurate: # should never happen\n",
    "            print(cost.__name__)\n",
    "            display(m)\n",
    "        accept &= m.valid\n",
    "        result.append((m.values[0], m.values[1], m.covariance[0, 0], m.covariance[1, 1]))\n",
    "    if accept:\n",
    "        return result\n",
    "    return None\n",
    "\n",
    "results = {}\n",
    "for nmc in (200, 1000, 10000):\n",
    "    r = Parallel(-1, verbose=1)(compute(s, truth, nmc) for s in range(50))\n",
    "    r = [_ for _ in r if _ is not None]\n",
    "    results[nmc] = np.array(r)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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4cODIdixs8ODBPnv2bHd3v+WWW3zKlCllzjtjxgwfO3ZssWk9evTwlStX+uHDh71///7+j3/8I+Y2nnnmGXd3nz59ul999dXuHjqe559/fmS+e+65x8ePH19q+Xnz5vktt9wS1/4cPHjQW7Vq5Vu3bvUDBw54165dfcOGDaXm2717tx86dMjd3e+77z5/4IEH3N19zpw5npWV5QcPHvSCggK/+OKLfeHChXFtu7rF+lsAVnsZeVUJXY45NZ3QTzjhBM/IyPCMjAzv2rWrv/TSS+7u/vHHH3tycnJkemZmpr/99ttV3l52drZnZ2f70qVLvV69epFtZ2Rk+M6dO3316tW+bdu2Km+nyEcffeQ9evTwNm3a+ODBg33//v3u7r5gwYJIknN3b9GihTdq1Mjr16/vKSkpvnHjRnd3X7VqlXfu3Nlbt27tY8eO9cOHD5faRm5urvfr18/T09M9KyvLd+zYEWnr0qWL5+fnu7s74J07d47s74IFC9zdfezYsZVKqv/4xz88LS3NW7du7b/97W8j0x944IHIOl944QVv27atp6Wl+ahRoyL7XVhY6GPGjPEOHTp4x44dY37A1JTKJvQKHxJdXfTEIinLpk2bau1FKanYY489RoMGDRg9enTM9gMHDnDRRRexfPnySFfN8SrW34KZrXH3zFjz62eLInJU3XbbbdSrV6/M9u3btzN58uTjPpkfCR0xETmqkpOTueGGG8psT0tLIy0t7ShGFBw6QxcRCQgldBGRgFBCFxEJCCV0OfYtmZTYoQJHUm1x6dKlXHnllTHXN3jwYLZu3QpAy5Yt2bNnDwC/+93v6Ny5M127dqVbt26R29UPHjzIhAkTSEtLo3v37vTu3Tty12W/fv0SXqwrkVTJsWYrOSqhi5SQyGqLGzdu5NChQ7Ru3brY9JUrV/LSSy/x3nvvsX79el5//fVIPZIHHniAXbt2sWHDBt577z3mz5/P3r17Abjhhhv485//HPe+qJJjcUGv5KiELlKOqlZbnDVrFgMHDiw1fdeuXTRp0iTy870mTZrQvHlz9u3bx7Rp03j88ccjbc2aNWPIkCFAqNzA7NmzK4xblRyPz0qOcSV0M+tvZpvNLMfMJpQxzxAzyzazjWb2XGLDFDl6iqotdujQgdGjR/PAAw9E2oqqLbZp04ZHH32Uu+66q9x1rVixgnPOOafU9EsvvZQdO3bQrl07fvazn0XO2nJycjjrrLM49dRTY66vUaNGHDhwgLy8vFJtBQUFvPDCC1x22WUMGjSIhg0bsnLlSq644gqaN2/OunXrWLduHTfffDPXXHNNpJLjyy+/zL59+7jwwgsZPHgwr7zyCocPHwZCdWKiPwiih6+//rrY9o92JcfNmzfzl7/8hYEDBzJhwgRWr15dqpLjunXrmD59Oi1atChWyfHNN98EQnViYu3beeedF4mpZCXHWDEVVXIEyqzkeMYZZ3DZZZdV601zFf4O3cySgCnAJUAusMrMFrp7dtQ8acC9wPnu/pWZnV5dAYtUt0RWW4xVXRDglFNOYc2aNbz55pssWbKEoUOHMnnyZLp3715hfEWVCBs3blxsuio5qpJjPDcW9QRy3H0rgJnNAQYC0R1JNwNT3P0rAHf/ItGBitSEqlZbLFldMFpSUhJ9+vShT58+pKenM3PmTIYMGcL27dvJz88v8yw9uhJhNFVyVCXHeLpcUoAdUeO54WnR2gHtzGyFmb1tZv1jrcjMxpjZajNbXdX+OpGj4YMPPuDQoUOlzoYBli9fTps2bcpdvmPHjuTk5JSavnnzZrZs2RIZX7duHS1atODkk09m1KhR3HnnnZFfiOzevZsXXngBCPVTf/bZZ7Rs2bLUOnv16sX06dNZu3Yt7du3Z9SoUZx77rm89957HDx4kGuvvZY//OEPtGv374dkv/baa3Tt2pX777+fvn37kp2dzR//+Ec6d+4MEDlDjzVEJ3MI9Rf37duXefPmATBz5syY1w/KcsYZZ3Dqqafy9ttv4+6R7pSS+vTpw3PPhXp1n3322UhyLHmsJ0yYQNeuXRk2bFix5T/88MNIgi86Qy85FP2yqUePHmzZsoWPP/6YgoIC5syZw4ABA0rFtGfPnkg31aRJkxg5ciQAZ511FsuWLaOwsJCDBw+ybNmy6q1TVFbVrqIBGAw8FTV+A/CnEvO8BPwdOBFoRegDoGF561W1RSlLbay2uGTJEk9OTvaUlJTI8NZbb/lf/vIX//Wvfx1Zd0pKiufn5/vq1au9d+/e3rFjR09PT/errrrKd+/e7e7uBw4c8F/84hfepk0b79y5s/fs2dNfeeUVdw9VOiwqRRsPVXKs3ZUcE14+F+gNvBo1fi9wb4l5/h8wImr8n0CP8tarhC5lqemEnkj79u3zXr16eWFhoX/xxRfevHnzKq3vjjvu8Ndffz1B0QXPo48+6tOmTSuzff/+/d6rVy8/ePDgUYzqyFU2ocfT5bIKSDOzVmZWFxgGLCwxz3ygD4CZNSHUBbO1ct8VRILnpJNO4qGHHmLWrFlccMEFTJpU8Y1N5enSpQtZWVkJii54jvdKjnHVQzezHwN/BJKAp939d2b2MKFPioVmZsB/A/2BQ8Dv3L3cH3qqHrqURfXQRUIqWw89ro8pd18ELCoxbWLUawfuCg8iIlIDdKeoiEhAKKGLiASEErqISEAE81KvBMqf18VfXTAeP+v2s4SuT+RYoTN0kRKOVj30kss988wzNG3alG7dutGpUyemTZtWbPrZZ59NWloal112WSQmCJVufeONNxJ/IBLkwIEDDB06lLZt29KrVy+2bdsWc76RI0dy+umnF7tNH+DLL7/kkksuIS0tjUsuuaTSJX+///57LrroIg4dOhSzvaCggAsvvJDCwsK41xlP3feCggJGjBhBeno6GRkZLF26NNI2e/Zs0tPT6dq1K/379y/2f6IqlNBFSjga9dDLMnToUNatW8fSpUu57777+PzzzyPT165dy5YtW5gwYQJXX301mzZtAuD2228v88ELZfnyyy/LbPvuu+84ePBgpdZXnunTp9OoUSNycnIYP348v/rVr2LOd9NNN8UsdDZ58mSysrLYsmULWVlZld7Xp59+mquvvpqkpKSY7XXr1iUrK4u5c+fGvc546r4XfSC///77LF68mLvvvpvDhw9TWFjInXfeyZIlS1i/fj1du3blT3/6U6X2qSxK6CLlqK566BU5/fTTadOmDZ988kmptr59+zJmzBimTp0KQIsWLcjLy+Ozzz4rd535+fk8+eST9OzZM/JwiVg1wz/88EPatWvHPffcE/nQqIoFCxYwfPhwIPRt5Z///GfMp/ZceOGF/OAHPyh3+bJqrOfn5zNw4EA6derEySefjJnRv3+opFT0ezBx4sTI/qakpESKqw0aNIhZs2bFtT8eZ9336Brpp59+Og0bNmT16tWRuzq/++473J38/HyaN28e17Yroj50kRKK6qHv37+fXbt2FevOKKqHvnfvXvbt2xd5bFxZVqxYwXXXXVdsWt++fSNni99++y0dOnQotdzWrVvZunUrbdu2jfmEnO7du/Pkk08WG1+xYgXXXHNNqXmXL1/OU089FWl/9tlnIwW6Fi0K3V6yZs0aRowYwaBBgzjttNNYv349c+fOZfTo0ZgZo0aNYsiQIdSvXx+ACy64IPIUpWiPPPII/fr1KzYtuqZ4nTp1OO2008jLy6NJkyZlH7gon3/+OWeccQYAP/zhDyPfWqI9/vjjNGvWjAULFrB169bIQyYKCgrYunVrpJjZww8/zMMPP8zXX3/NBRdcEHkEXpcuXVi1ahUAe/fuLbMa4nPPPRdJzhXVfc/IyGDhwoVcd9117NixgzVr1rBjxw569uzJE088QXp6OvXr1yctLY0pU6bEdSwqooQuUkJ110NfsmRJJJktXbq02KPY5s6dy/Lly6lXrx5PPvlkzDNWoNQZbnSN72h33HEHf/3rX5kyZQrTp0+P2e0Qq2Z4gwYNGD16NKNHj2bTpk2RCpD5+fkAkQdEHG1mRujG9OLeffddfv7znwPQunVrWrRoQXZ2Ns2aNStVFdLduf7667nrrrsiDx9JSkqibt267N27lwYNGpRbIz3e/u6RI0eyadMmMjMzadGiBeeddx5JSUkcPHiQJ554grVr19K6dWtuv/12Jk2axP333x/XesujhC5Sjuqshx7L0KFD4+pPXbt2bbFbwsuqkX7XXXdx6qmn8tBDD/HKK68wYsQI+vTpE0mKZdUMh9BF4JkzZzJ79mwyMjJ48MEHI22VOUMvqimemppKYWEh33zzTcxyxGVp1qwZu3bt4owzzmDXrl2cfnrp5+fUqVMnUr4W/l0nPdbxf/DBB0lNTS313h04cIDk5OQKz9A7duwYV933OnXq8Nhjj0XGzzvvPNq1axf5sCgqvTxkyJBKXxcoixK6HPNq8meG0fXQ9+3bV6ytMvXQY9UvP1LLli1j6tSpLFmyJDLtww8/5Nprry01b8uWLfntb3/LQw89xKuvvsrjjz/OrbfeysSJE/npT38as2b4tm3bGD16NHv27GHEiBGsWLGiVAKuzBn6gAEDmDlzJr1792bevHlcfPHFMc+yK1p+woQJZdZYv/jii3n22WfJysrigw8+IDc3l3bt2lGvXj0OHTrE/v37SU5O5n//9395/fXXix07INIFdOKJJ3LiiSdW+BSjorrvw4YNKzOmffv24e7Ur1+fxYsXU6dOHTp16sSnn35KdnY2u3fvpmnTpixevDhxtYvKKsNY3YPK50pZarp8bnXWQ2/RokWk7nnRcldccYW7u8+YMcPHjh1bKp4ZM2Z4kyZNPCMjw9PS0vzSSy/15cuXR9oLCgq8Q4cOcZeE/fzzz/3NN99099g1w7dv3+7vvPNOJY9a2b7//nsfPHiwt2nTxnv06OEfffSRu7vv3LnTL7/88sh8w4YN8x/+8Idep04dT0lJ8aeeesrd3ffs2eMXX3yxt23b1rOysjwvL6/UNg4cOOA333yzd+nSxc8++2xfunRppG3kyJG+ePFid3fv06ePt2jRIrK/RTXaX3jhBb/rrrvi3qd46r5//PHH3q5dO+/QoYNnZWUVqzv/xBNPeIcOHTw9Pd2vvPJK37NnT8ztJLweenUNSuhSlppO6IkUXQ+9urz44ot+//33V9v6a7s1a9b49ddfX+48V111lW/evPkoRRS/6qiHLiJHqKgeeqxfQSRKYWEhd999d7Wtv7br3r07ffv2LffGokGDBhV7NF9tFVc99OqgeuhSlk2bNtGhQ4dK9bOKBI2788EHH1SqHrrO0OWYk5ycTF5eXsybT0SOB+5OXl4eycnJlVpOv3KRY05qaiq5ubkxfyoocrxITk4mNTW1Ussoocsx58QTT6RVq1Y1HYZIraMuFxGRgFBCFxEJCCV0EZGAUEIXEQmIuBK6mfU3s81mlmNmE2K032Rmu81sXXgYnfhQRUSkPBX+ysXMkoApwCVALrDKzBa6e8kizXPdfVw1xCgiInGI5wy9J5Dj7lvdvQCYA1T+ESwiIlKt4knoKcCOqPHc8LSSrjGz9WY2z8zOjLUiMxtjZqvNbLVuGhERSaxEXRT9X6Clu3cFFgMzY83k7lPdPdPdM0s+xUVERKomnoS+E4g+404NT4tw9zx3PxAefQo4JzHhiYhIvOJJ6KuANDNrZWZ1gWHAwugZzOyMqNEBQNUfFS4iIpVS4a9c3L3QzMYBrwJJwNPuvtHMHiZUaH0hcIeZDQAKgS+Bm6oxZhERiUH10EVEahHVQxcROQ4ooYuIBIQSuohIQCihi4gEhBK6iEhAKKGLiASEErqISEAooYuIBIQSuohIQCihi4gEhBK6iEhAKKGLiASEErqISEAooYuIBIQSuohIQFT4gAuR4829MwZVaflJI+YnJA6RytIZuohIQCihi4gEhBK6iEhAKKGLiASEErqISEAooYuIBERcCd3M+pvZZjPLMbMJ5cx3jZm5mWUmLkQREYlHhQndzJKAKcDlQCfgOjPrFGO+BsCdwDuJDlJERCoWzxl6TyDH3be6ewEwBxgYY77fAH8A9icwPhERiVM8CT0F2BE1nhueFmFm3YEz3f0fCYxNREQqocoXRc3sBOBR4O445h1jZqvNbPXu3burumkREYkST0LfCZwZNZ4anlakAdAFWGpm24BzgYWxLoy6+1R3z3T3zKZNmx551CIiUko8CX0VkGZmrcysLjAMWFjU6O7fuHsTd2/p7i2Bt4EB7r66WiIWEZGYKkzo7l4IjANeBTYBz7v7RjN72MwGVHeAIiISn7jK57r7ImBRiWkTy5i3T9XDEhGRytKdoiIiAaGELiISEEroIiIBoYQuIhIQSugiIgGhh0RLIFX1Qc8itZHO0EVEAkIJXUQkIJTQRUQCQgldRCQglNBFRAJCCV1EJCCU0EVEAkIJXUQkIJTQRUQCQneKiiRYVe5SnTRifsLikOOPztBFRAJCCV1EJCCU0EVEAkIJXUQkIJTQRUQCQgldRCQg4kroZtbfzDabWY6ZTYjRfquZvW9m68xsuZl1SnyoIiJSngoTupklAVOAy4FOwHUxEvZz7p7u7t2A/wQeTXSgIiJSvnjO0HsCOe6+1d0LgDnAwOgZ3D0/arQ+4IkLUURE4hHPnaIpwI6o8VygV8mZzGwscBdQF7g4IdGJiEjcEnZR1N2nuHsb4FfA/bHmMbMxZrbazFbv3r07UZsWERHiS+g7gTOjxlPD08oyBxgUq8Hdp7p7prtnNm3aNO4gRUSkYvEk9FVAmpm1MrO6wDBgYfQMZpYWNXoFsCVxIYqISDwq7EN390IzGwe8CiQBT7v7RjN7GFjt7guBcWbWDzgIfAUMr86gRUSktLjK57r7ImBRiWkTo17fmeC4RESkknSnqIhIQCihi4gEhBK6iEhAKKGLiASEErqISEAooYuIBIQSuohIQCihi4gEhBK6iEhAKKGLiASEErqISEAooYuIBIQSuohIQCihi4gEhBK6iEhAKKGLiASEErqISEAooYuIBIQSuohIQCihi4gEhBK6iEhAKKGLiASEErqISEDEldDNrL+ZbTazHDObEKP9LjPLNrP1ZvZPM2uR+FBFRKQ8FSZ0M0sCpgCXA52A68ysU4nZ1gKZ7t4VmAf8Z6IDFRGR8sVzht4TyHH3re5eAMwBBkbP4O5L3H1fePRtIDWxYYqISEXqxDFPCrAjajwX6FXO/KOAl2M1mNkYYAzAWWedFWeIUpvdO2PQES87acT8hMUhcjxI6EVRM7seyAT+K1a7u09190x3z2zatGkiNy0ictyL5wx9J3Bm1HhqeFoxZtYP+DVwkbsfSEx4IiISr3jO0FcBaWbWyszqAsOAhdEzmNnZwJPAAHf/IvFhiohIRSpM6O5eCIwDXgU2Ac+7+0Yze9jMBoRn+y/gFOAFM1tnZgvLWJ2IiFSTeLpccPdFwKIS0yZGve6X4LhERKSSdKeoiEhAKKGLiASEErqISEAooYuIBIQSuohIQCihi4gEhBK6iEhAKKGLiASEErqISEAooYuIBIQSuohIQCihi4gEhBK6iEhAKKGLiAREXOVzRWpCVZ5HKnI80hm6iEhAKKGLiASEErqISEAooYuIBIQSuohIQCihi4gEhBK6iEhAxJXQzay/mW02sxwzmxCj/UIze8/MCs1scOLDFBGRilSY0M0sCZgCXA50Aq4zs04lZtsO3AQ8l+gARUQkPvHcKdoTyHH3rQBmNgcYCGQXzeDu28Jth6shRhERiUM8CT0F2BE1ngv0OpKNmdkYYAzAWWeddSSrEAm0qpQ7mDRifsLikNrpqF4Udfep7p7p7plNmzY9mpsWEQm8eBL6TuDMqPHU8DQRETmGxJPQVwFpZtbKzOoCw4CF1RuWiIhUVoUJ3d0LgXHAq8Am4Hl332hmD5vZAAAz62FmucC1wJNmtrE6gxYRkdLiqofu7ouARSWmTYx6vYpQV4yIiNQQ3SkqIhIQSugiIgGhhC4iEhBK6CIiAaGHRIsEhO4yFZ2hi4gEhBK6iEhAKKGLiASEErqISEAooYuIBIQSuohIQCihi4gEhBK6iEhAKKGLiASE7hSVClXlDkQROXp0hi4iEhBK6CIiAaGELiISEEroIiIBoYQuIhIQSugiIgGhhC4iEhBxJXQz629mm80sx8wmxGivZ2Zzw+3vmFnLhEcqIiLlqjChm1kSMAW4HOgEXGdmnUrMNgr4yt3bAo8Bf0h0oCIiUr54ztB7AjnuvtXdC4A5wMAS8wwEZoZfzwOyzMwSF6aIiFQknlv/U4AdUeO5QK+y5nH3QjP7BmgM7ImeyczGAGPCo9+a2eYjCRpoUnLdtZj25dgTlP2AOPdl8shacf513L0vZWhRVsNRreXi7lOBqVVdj5mtdvfMBIRU47Qvx56g7AdoX45V1bUv8XS57ATOjBpPDU+LOY+Z1QFOA/ISEaCIiMQnnoS+Ckgzs1ZmVhcYBiwsMc9CYHj49WDgDXf3xIUpIiIVqbDLJdwnPg54FUgCnnb3jWb2MLDa3RcC04G/mlkO8CWhpF+dqtxtcwzRvhx7grIfoH05VlXLvphOpEVEgkF3ioqIBIQSuohIQNTqhG5mt5vZB2a20cz+s6bjqSozu9vM3Mya1HQsR8LM/iv8fqw3s7+bWcOajqmyKipzUVuY2ZlmtsTMssN/H3fWdExVYWZJZrbWzF6q6Viqwswamtm88N/JJjPrncj119qEbmZ9Cd2hmuHunYFHajikKjGzM4FLge01HUsVLAa6uHtX4EPg3hqOp1LiLHNRWxQCd7t7J+BcYGwt3heAO4FNNR1EAvwP8Iq7dwAySPA+1dqEDtwGTHb3AwDu/kUNx1NVjwG/BGrtVWp3f83dC8OjbxO6Z6E2iafMRa3g7rvc/b3w672EEkdKzUZ1ZMwsFbgCeKqmY6kKMzsNuJDQrwJx9wJ3/zqR26jNCb0dcEG4uuMyM+tR0wEdKTMbCOx093/VdCwJNBJ4uaaDqKRYZS5qZRKMFq5+ejbwTg2HcqT+SOhk53ANx1FVrYDdwIxw99FTZlY/kRs4qrf+V5aZvQ78MEbTrwnF/gNCXyd7AM+bWetj9YamCvblPkLdLce88vbD3ReE5/k1oa/8s45mbFKamZ0C/A34ubvn13Q8lWVmVwJfuPsaM+tTw+FUVR2gO3C7u79jZv8DTAAeSOQGjlnu3q+sNjO7DXgxnMDfNbPDhAre7D5a8VVGWftiZumEPrn/FS5QmQq8Z2Y93f2zoxhiXMp7TwDM7CbgSiDrWP1wLUc8ZS5qDTM7kVAyn+XuL9Z0PEfofGCAmf0YSAZONbNn3f36Go7rSOQCue5e9E1pHqGEnjC1uctlPtAXwMzaAXWphZXY3P19dz/d3Vu6e0tCb3r3YzGZV8TM+hP6ajzA3ffVdDxHIJ4yF7VCuHz1dGCTuz9a0/EcKXe/191Tw38bwwiVFamNyZzw3/QOM2sfnpQFZCdyG8f0GXoFngaeNrMNQAEwvBaeEQbNn4B6wOLwt4233f3Wmg0pfmWVuajhsI7U+cANwPtmti487T53X1RzIQlwOzArfMKwFRiRyJXr1n8RkYCozV0uIiISRQldRCQglNBFRAJCCV1EJCCU0EVEAkIJXaQCZnaTmf0p/PpBM7unpmMSiUUJXUQkIJTQ5bhjZi3D9ahnhWtSzzOzk81sW1EtejPLNLOlNRyqSKUoocvxqj3wZ3fvCOQDP6vheESqTAldjlc73H1F+PWzwI9qMhiRRFBCl+NVyZoXTqjkb9HfRPLRDUek6pTQ5Xh1VtTzHH8CLAe2AeeEp11TE0GJVIUSuhyvNhN6zuYmoBHwBPAQ8D9mtho4VJPBiRwJVVuU4074kWwvuXuXmo5FJJF0hi4iEhA6QxcRCQidoYuIBIQSuohIQCihi4gEhBK6iEhAKKGLiATE/weu0lLT9uGh8AAAAABJRU5ErkJggg==",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "for nmc, r in results.items():\n",
    "    plt.figure()\n",
    "    for i, label in enumerate((\"BB\", \"BBL(JSC)\", \"BBL(HPD)\")):\n",
    "        s = r[:, i, 1]\n",
    "        vs = r[:, i, 3]\n",
    "        z = (s - truth[1]) / vs ** 0.5\n",
    "        plt.hist(z,\n",
    "            label=(\n",
    "                f\"{label:4} \"\n",
    "                f\"<z>={np.mean(z):5.2f} \"\n",
    "                f\"σ(z)={np.std(z):.2f}\"),\n",
    "            density=True, alpha=0.5, bins=20, range=(-6, 6))\n",
    "    plt.xlabel(\"pull\")\n",
    "    plt.title(f\"N(data) = {np.sum(truth)} N(mc) = {nmc}\")\n",
    "    plt.ylim(0, 0.7)\n",
    "    plt.legend();"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The performance of the BBL methods is comparable to that of the BB method. In all cases, biases are small and the estimated variance is close to the actual variance. When the experiments are repeated with a high number of toy simulations, we find that the alternative BBL method performs slightly better than Conway's method."
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3.8.12 ('venv': venv)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.8.13"
  },
  "orig_nbformat": 4,
  "vscode": {
   "interpreter": {
    "hash": "bdbf20ff2e92a3ae3002db8b02bd1dd1b287e934c884beb29a73dced9dbd0fa3"
   }
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}
