{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Binned vs. unbinned fits\n",
    "\n",
    "We compare binned with unbinned fit applied to a toy example of a gaussian signal peak over exponential background.\n",
    "\n",
    "For one-dimensional data, binned fit are preferred. They are usually considerably faster than an unbinned fit and more numerically stable. For multi-dimensional data, however, an unbinned fit can be faster.\n",
    "\n",
    "It is a common misconception that binned fits are inherently biased. This idea originates from the past when it was common (at least in particle physics) to fit binned data with the least-squares method, which is indeed biased, see [Dembinski, Schmelling, Waldi, *Application of the Iterated Weighted Least-Squares Fit to counting experiments*, NIM A 940 (2019) 135-141](https://doi.org/10.1016/j.nima.2019.05.086). That bias can be completely avoided, however, if the fit uses the maximum-likelihood method and a Poisson distribution to describe the observed bin contents as a function of the predicted ones, and if the model prediction for a bin content is properly computed by integrating over the model density, instead of computing it from the density at the bin center times the bin width. The cost functions `BinnedNLL` and `ExtendedBinnedNLL` from `iminuit.cost` use the correct calculation.\n",
    "\n",
    "So there is no need to worry bias, but some information is lost in the binning process - the densities of events inside each bin. This loss can be made negligible by making the bin width small enough. How small the bins have to be depends on the sensitivity of the model parameter on this particular loss of information. In this tutorial we demonstrate this and also demonstrate the difference in run-time of unbinned and binned fits.\n",
    "\n",
    "**Conclusions:** With only 20 bins, the binned fit reached an accuracy for the signal yield that is comparable to the unbinned fit. With 50 bins, also all shape parameters have uncertainties that are less than 5 % larger than those in the unbinned fit. At the same time, the binned fit is much faster. Even with 200 bins, the binned fit is two orders of magnitude faster than the unbinned fit. In practice, this is a huge difference, 3 seconds vs. 5 minutes.\n",
    "\n",
    "You can try to run this notebook with a data sample contains less points, then the difference will not be as dramatic."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "from numba_stats import norm, expon\n",
    "import matplotlib.pyplot as plt\n",
    "from iminuit import Minuit\n",
    "from iminuit.cost import ExtendedUnbinnedNLL, ExtendedBinnedNLL\n",
    "import joblib\n",
    "from IPython.display import display"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "# sample size, change this to see how the results of the comparison change\n",
    "n = 100_000\n",
    "truth = np.array((1.0, 1.0, 1.0, 0.1, 1.0))\n",
    "\n",
    "rng = np.random.default_rng(1)\n",
    "s = rng.normal(truth[2], truth[3], size=int(n * truth[0]))\n",
    "b = rng.exponential(truth[4], size=int(n * truth[1]))\n",
    "pts = np.append(s, b)\n",
    "pts = pts[(pts > 0) & (pts < 2)]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "def fit(c):\n",
    "    m = Minuit(c, s=1, b=1, mu=1, sigma=0.1, tau=1)\n",
    "    m.limits[\"s\", \"b\", \"sigma\", \"tau\"] = (0, None)\n",
    "    m.limits[\"mu\"] = (0, 2)\n",
    "    m.migrad()\n",
    "    assert m.valid\n",
    "    return m"
   ]
  },
  {
   "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 = -4.08e+06 </td>\n",
       "        <td colspan=\"3\" style=\"text-align:center\" title=\"Total number of function and (optional) gradient evaluations\"> Nfcn = 120 </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td colspan=\"2\" style=\"text-align:left\" title=\"Estimated distance to minimum and goal\"> EDM = 1.25e-05 (Goal: 0.0002) </td>\n",
       "        <td colspan=\"3\" style=\"text-align:center\" title=\"Total run time of algorithms\"> time = 0.6 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> s </td>\n",
       "        <td> 0.995 </td>\n",
       "        <td> 0.004 </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> b </td>\n",
       "        <td> 1.008 </td>\n",
       "        <td> 0.005 </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> mu </td>\n",
       "        <td> 999.3e-3 </td>\n",
       "        <td> 0.4e-3 </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
       "        <td> 0 </td>\n",
       "        <td> 2 </td>\n",
       "        <td>  </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th> 3 </th>\n",
       "        <td> sigma </td>\n",
       "        <td> 99.21e-3 </td>\n",
       "        <td> 0.34e-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> tau </td>\n",
       "        <td> 1.002 </td>\n",
       "        <td> 0.007 </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> s </th>\n",
       "        <th> b </th>\n",
       "        <th> mu </th>\n",
       "        <th> sigma </th>\n",
       "        <th> tau </th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th> s </th>\n",
       "        <td> 1.32e-05 </td>\n",
       "        <td style=\"background-color:rgb(213,213,250);color:black\"> -4.96e-06 <strong>(-0.281)</strong> </td>\n",
       "        <td style=\"background-color:rgb(246,246,250);color:black\"> -3.97e-08 <strong>(-0.029)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,213,213);color:black\"> 2.99e-07 <strong>(0.246)</strong> </td>\n",
       "        <td style=\"background-color:rgb(229,229,250);color:black\"> -3.97e-06 <strong>(-0.159)</strong> </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th> b </th>\n",
       "        <td style=\"background-color:rgb(213,213,250);color:black\"> -4.96e-06 <strong>(-0.281)</strong> </td>\n",
       "        <td> 2.36e-05 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 8.26e-10 </td>\n",
       "        <td style=\"background-color:rgb(213,213,250);color:black\"> -4.6e-07 <strong>(-0.283)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,162,162);color:black\"> 1.96e-05 <strong>(0.586)</strong> </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th> mu </th>\n",
       "        <td style=\"background-color:rgb(246,246,250);color:black\"> -3.97e-08 <strong>(-0.029)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 8.26e-10 </td>\n",
       "        <td> 1.46e-07 </td>\n",
       "        <td style=\"background-color:rgb(244,244,250);color:black\"> -5.62e-09 <strong>(-0.044)</strong> </td>\n",
       "        <td style=\"background-color:rgb(243,243,250);color:black\"> -1.42e-07 <strong>(-0.054)</strong> </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th> sigma </th>\n",
       "        <td style=\"background-color:rgb(250,213,213);color:black\"> 2.99e-07 <strong>(0.246)</strong> </td>\n",
       "        <td style=\"background-color:rgb(213,213,250);color:black\"> -4.6e-07 <strong>(-0.283)</strong> </td>\n",
       "        <td style=\"background-color:rgb(244,244,250);color:black\"> -5.62e-09 <strong>(-0.044)</strong> </td>\n",
       "        <td> 1.12e-07 </td>\n",
       "        <td style=\"background-color:rgb(230,230,250);color:black\"> -3.62e-07 <strong>(-0.157)</strong> </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th> tau </th>\n",
       "        <td style=\"background-color:rgb(229,229,250);color:black\"> -3.97e-06 <strong>(-0.159)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,162,162);color:black\"> 1.96e-05 <strong>(0.586)</strong> </td>\n",
       "        <td style=\"background-color:rgb(243,243,250);color:black\"> -1.42e-07 <strong>(-0.054)</strong> </td>\n",
       "        <td style=\"background-color:rgb(230,230,250);color:black\"> -3.62e-07 <strong>(-0.157)</strong> </td>\n",
       "        <td> 4.76e-05 </td>\n",
       "    </tr>\n",
       "</table>"
      ],
      "text/plain": [
       "┌─────────────────────────────────────────────────────────────────────────┐\n",
       "│                                Migrad                                   │\n",
       "├──────────────────────────────────┬──────────────────────────────────────┤\n",
       "│ FCN = -4.08e+06                  │              Nfcn = 120              │\n",
       "│ EDM = 1.25e-05 (Goal: 0.0002)    │            time = 0.6 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 │ s     │   0.995   │   0.004   │            │            │    0    │         │       │\n",
       "│ 1 │ b     │   1.008   │   0.005   │            │            │    0    │         │       │\n",
       "│ 2 │ mu    │ 999.3e-3  │  0.4e-3   │            │            │    0    │    2    │       │\n",
       "│ 3 │ sigma │ 99.21e-3  │  0.34e-3  │            │            │    0    │         │       │\n",
       "│ 4 │ tau   │   1.002   │   0.007   │            │            │    0    │         │       │\n",
       "└───┴───────┴───────────┴───────────┴────────────┴────────────┴─────────┴─────────┴───────┘\n",
       "┌───────┬───────────────────────────────────────────────────┐\n",
       "│       │         s         b        mu     sigma       tau │\n",
       "├───────┼───────────────────────────────────────────────────┤\n",
       "│     s │  1.32e-05 -4.96e-06 -3.97e-08  2.99e-07 -3.97e-06 │\n",
       "│     b │ -4.96e-06  2.36e-05  8.26e-10  -4.6e-07  1.96e-05 │\n",
       "│    mu │ -3.97e-08  8.26e-10  1.46e-07 -5.62e-09 -1.42e-07 │\n",
       "│ sigma │  2.99e-07  -4.6e-07 -5.62e-09  1.12e-07 -3.62e-07 │\n",
       "│   tau │ -3.97e-06  1.96e-05 -1.42e-07 -3.62e-07  4.76e-05 │\n",
       "└───────┴───────────────────────────────────────────────────┘"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "def density(x, s, b, mu, sigma, tau):\n",
    "    xrange = (0, 2)\n",
    "    s1 = s * n * np.diff(norm.cdf(xrange, mu, sigma))\n",
    "    b1 = b * n * np.diff(expon.cdf(xrange, 0, tau))\n",
    "    return s1 + b1, (\n",
    "        s * n * norm.pdf(x, mu, sigma) + \n",
    "        b * n * expon.pdf(x, 0, tau)\n",
    "    )\n",
    "\n",
    "m = fit(ExtendedUnbinnedNLL(pts, density))\n",
    "par_names = [m.params[i].name for i in range(m.npar)]\n",
    "results = {np.inf: (np.array(m.values), np.array(m.errors), m.fmin.time)}\n",
    "m"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "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": [
    "xm = np.linspace(np.min(pts), np.max(pts), 1000)\n",
    "_, ym = density(xm, *m.values)\n",
    "plt.hist(pts, bins=100, range=(0, 2), label=\"data\")\n",
    "dx = 2 / 100\n",
    "plt.plot(xm, ym * dx, label=\"fit\")\n",
    "plt.legend()\n",
    "plt.xlabel(\"x\");"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This fit is unbinned, the observed sample is binned here only for visualisation."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "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 = 190.9 (chi2/ndof = 1.0) </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 = 2.17e-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> s </td>\n",
       "        <td> 0.995 </td>\n",
       "        <td> 0.004 </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> b </td>\n",
       "        <td> 1.008 </td>\n",
       "        <td> 0.005 </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> mu </td>\n",
       "        <td> 999.3e-3 </td>\n",
       "        <td> 0.4e-3 </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
       "        <td> 0 </td>\n",
       "        <td> 2 </td>\n",
       "        <td>  </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th> 3 </th>\n",
       "        <td> sigma </td>\n",
       "        <td> 99.22e-3 </td>\n",
       "        <td> 0.34e-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> tau </td>\n",
       "        <td> 1.002 </td>\n",
       "        <td> 0.007 </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> s </th>\n",
       "        <th> b </th>\n",
       "        <th> mu </th>\n",
       "        <th> sigma </th>\n",
       "        <th> tau </th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th> s </th>\n",
       "        <td> 1.32e-05 </td>\n",
       "        <td style=\"background-color:rgb(213,213,250);color:black\"> -5.01e-06 <strong>(-0.284)</strong> </td>\n",
       "        <td style=\"background-color:rgb(246,246,250);color:black\"> -3.98e-08 <strong>(-0.029)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,213,213);color:black\"> 3.02e-07 <strong>(0.248)</strong> </td>\n",
       "        <td style=\"background-color:rgb(229,229,250);color:black\"> -4.04e-06 <strong>(-0.161)</strong> </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th> b </th>\n",
       "        <td style=\"background-color:rgb(213,213,250);color:black\"> -5.01e-06 <strong>(-0.284)</strong> </td>\n",
       "        <td> 2.37e-05 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 8.61e-10 </td>\n",
       "        <td style=\"background-color:rgb(213,213,250);color:black\"> -4.66e-07 <strong>(-0.286)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,162,162);color:black\"> 1.97e-05 <strong>(0.587)</strong> </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th> mu </th>\n",
       "        <td style=\"background-color:rgb(246,246,250);color:black\"> -3.98e-08 <strong>(-0.029)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 8.61e-10 </td>\n",
       "        <td> 1.46e-07 </td>\n",
       "        <td style=\"background-color:rgb(244,244,250);color:black\"> -5.93e-09 <strong>(-0.046)</strong> </td>\n",
       "        <td style=\"background-color:rgb(243,243,250);color:black\"> -1.43e-07 <strong>(-0.054)</strong> </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th> sigma </th>\n",
       "        <td style=\"background-color:rgb(250,213,213);color:black\"> 3.02e-07 <strong>(0.248)</strong> </td>\n",
       "        <td style=\"background-color:rgb(213,213,250);color:black\"> -4.66e-07 <strong>(-0.286)</strong> </td>\n",
       "        <td style=\"background-color:rgb(244,244,250);color:black\"> -5.93e-09 <strong>(-0.046)</strong> </td>\n",
       "        <td> 1.12e-07 </td>\n",
       "        <td style=\"background-color:rgb(229,229,250);color:black\"> -3.69e-07 <strong>(-0.159)</strong> </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th> tau </th>\n",
       "        <td style=\"background-color:rgb(229,229,250);color:black\"> -4.04e-06 <strong>(-0.161)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,162,162);color:black\"> 1.97e-05 <strong>(0.587)</strong> </td>\n",
       "        <td style=\"background-color:rgb(243,243,250);color:black\"> -1.43e-07 <strong>(-0.054)</strong> </td>\n",
       "        <td style=\"background-color:rgb(229,229,250);color:black\"> -3.69e-07 <strong>(-0.159)</strong> </td>\n",
       "        <td> 4.77e-05 </td>\n",
       "    </tr>\n",
       "</table>"
      ],
      "text/plain": [
       "┌─────────────────────────────────────────────────────────────────────────┐\n",
       "│                                Migrad                                   │\n",
       "├──────────────────────────────────┬──────────────────────────────────────┤\n",
       "│ FCN = 190.9 (chi2/ndof = 1.0)    │              Nfcn = 110              │\n",
       "│ EDM = 2.17e-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 │ s     │   0.995   │   0.004   │            │            │    0    │         │       │\n",
       "│ 1 │ b     │   1.008   │   0.005   │            │            │    0    │         │       │\n",
       "│ 2 │ mu    │ 999.3e-3  │  0.4e-3   │            │            │    0    │    2    │       │\n",
       "│ 3 │ sigma │ 99.22e-3  │  0.34e-3  │            │            │    0    │         │       │\n",
       "│ 4 │ tau   │   1.002   │   0.007   │            │            │    0    │         │       │\n",
       "└───┴───────┴───────────┴───────────┴────────────┴────────────┴─────────┴─────────┴───────┘\n",
       "┌───────┬───────────────────────────────────────────────────┐\n",
       "│       │         s         b        mu     sigma       tau │\n",
       "├───────┼───────────────────────────────────────────────────┤\n",
       "│     s │  1.32e-05 -5.01e-06 -3.98e-08  3.02e-07 -4.04e-06 │\n",
       "│     b │ -5.01e-06  2.37e-05  8.61e-10 -4.66e-07  1.97e-05 │\n",
       "│    mu │ -3.98e-08  8.61e-10  1.46e-07 -5.93e-09 -1.43e-07 │\n",
       "│ sigma │  3.02e-07 -4.66e-07 -5.93e-09  1.12e-07 -3.69e-07 │\n",
       "│   tau │ -4.04e-06  1.97e-05 -1.43e-07 -3.69e-07  4.77e-05 │\n",
       "└───────┴───────────────────────────────────────────────────┘"
      ]
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     "data": {
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       "<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 = 87.19 (chi2/ndof = 0.9) </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 = 2.41e-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> s </td>\n",
       "        <td> 0.995 </td>\n",
       "        <td> 0.004 </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> b </td>\n",
       "        <td> 1.008 </td>\n",
       "        <td> 0.005 </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> mu </td>\n",
       "        <td> 999.3e-3 </td>\n",
       "        <td> 0.4e-3 </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
       "        <td> 0 </td>\n",
       "        <td> 2 </td>\n",
       "        <td>  </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th> 3 </th>\n",
       "        <td> sigma </td>\n",
       "        <td> 99.24e-3 </td>\n",
       "        <td> 0.34e-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> tau </td>\n",
       "        <td> 1.002 </td>\n",
       "        <td> 0.007 </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> s </th>\n",
       "        <th> b </th>\n",
       "        <th> mu </th>\n",
       "        <th> sigma </th>\n",
       "        <th> tau </th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th> s </th>\n",
       "        <td> 1.32e-05 </td>\n",
       "        <td style=\"background-color:rgb(213,213,250);color:black\"> -5.02e-06 <strong>(-0.284)</strong> </td>\n",
       "        <td style=\"background-color:rgb(246,246,250);color:black\"> -3.97e-08 <strong>(-0.029)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,213,213);color:black\"> 3.04e-07 <strong>(0.249)</strong> </td>\n",
       "        <td style=\"background-color:rgb(229,229,250);color:black\"> -4.05e-06 <strong>(-0.161)</strong> </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th> b </th>\n",
       "        <td style=\"background-color:rgb(213,213,250);color:black\"> -5.02e-06 <strong>(-0.284)</strong> </td>\n",
       "        <td> 2.37e-05 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 4.72e-10 </td>\n",
       "        <td style=\"background-color:rgb(213,213,250);color:black\"> -4.69e-07 <strong>(-0.286)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,162,162);color:black\"> 1.98e-05 <strong>(0.587)</strong> </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th> mu </th>\n",
       "        <td style=\"background-color:rgb(246,246,250);color:black\"> -3.97e-08 <strong>(-0.029)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 4.72e-10 </td>\n",
       "        <td> 1.47e-07 </td>\n",
       "        <td style=\"background-color:rgb(244,244,250);color:black\"> -5.92e-09 <strong>(-0.046)</strong> </td>\n",
       "        <td style=\"background-color:rgb(243,243,250);color:black\"> -1.44e-07 <strong>(-0.054)</strong> </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th> sigma </th>\n",
       "        <td style=\"background-color:rgb(250,213,213);color:black\"> 3.04e-07 <strong>(0.249)</strong> </td>\n",
       "        <td style=\"background-color:rgb(213,213,250);color:black\"> -4.69e-07 <strong>(-0.286)</strong> </td>\n",
       "        <td style=\"background-color:rgb(244,244,250);color:black\"> -5.92e-09 <strong>(-0.046)</strong> </td>\n",
       "        <td> 1.13e-07 </td>\n",
       "        <td style=\"background-color:rgb(229,229,250);color:black\"> -3.71e-07 <strong>(-0.159)</strong> </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th> tau </th>\n",
       "        <td style=\"background-color:rgb(229,229,250);color:black\"> -4.05e-06 <strong>(-0.161)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,162,162);color:black\"> 1.98e-05 <strong>(0.587)</strong> </td>\n",
       "        <td style=\"background-color:rgb(243,243,250);color:black\"> -1.44e-07 <strong>(-0.054)</strong> </td>\n",
       "        <td style=\"background-color:rgb(229,229,250);color:black\"> -3.71e-07 <strong>(-0.159)</strong> </td>\n",
       "        <td> 4.78e-05 </td>\n",
       "    </tr>\n",
       "</table>"
      ],
      "text/plain": [
       "┌─────────────────────────────────────────────────────────────────────────┐\n",
       "│                                Migrad                                   │\n",
       "├──────────────────────────────────┬──────────────────────────────────────┤\n",
       "│ FCN = 87.19 (chi2/ndof = 0.9)    │              Nfcn = 110              │\n",
       "│ EDM = 2.41e-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 │ s     │   0.995   │   0.004   │            │            │    0    │         │       │\n",
       "│ 1 │ b     │   1.008   │   0.005   │            │            │    0    │         │       │\n",
       "│ 2 │ mu    │ 999.3e-3  │  0.4e-3   │            │            │    0    │    2    │       │\n",
       "│ 3 │ sigma │ 99.24e-3  │  0.34e-3  │            │            │    0    │         │       │\n",
       "│ 4 │ tau   │   1.002   │   0.007   │            │            │    0    │         │       │\n",
       "└───┴───────┴───────────┴───────────┴────────────┴────────────┴─────────┴─────────┴───────┘\n",
       "┌───────┬───────────────────────────────────────────────────┐\n",
       "│       │         s         b        mu     sigma       tau │\n",
       "├───────┼───────────────────────────────────────────────────┤\n",
       "│     s │  1.32e-05 -5.02e-06 -3.97e-08  3.04e-07 -4.05e-06 │\n",
       "│     b │ -5.02e-06  2.37e-05  4.72e-10 -4.69e-07  1.98e-05 │\n",
       "│    mu │ -3.97e-08  4.72e-10  1.47e-07 -5.92e-09 -1.44e-07 │\n",
       "│ sigma │  3.04e-07 -4.69e-07 -5.92e-09  1.13e-07 -3.71e-07 │\n",
       "│   tau │ -4.05e-06  1.98e-05 -1.44e-07 -3.71e-07  4.78e-05 │\n",
       "└───────┴───────────────────────────────────────────────────┘"
      ]
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      "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 = 36.34 (chi2/ndof = 0.8) </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 = 1.7e-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> s </td>\n",
       "        <td> 0.995 </td>\n",
       "        <td> 0.004 </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> b </td>\n",
       "        <td> 1.008 </td>\n",
       "        <td> 0.005 </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> mu </td>\n",
       "        <td> 999.3e-3 </td>\n",
       "        <td> 0.4e-3 </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
       "        <td> 0 </td>\n",
       "        <td> 2 </td>\n",
       "        <td>  </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th> 3 </th>\n",
       "        <td> sigma </td>\n",
       "        <td> 99.20e-3 </td>\n",
       "        <td> 0.34e-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> tau </td>\n",
       "        <td> 1.002 </td>\n",
       "        <td> 0.007 </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> s </th>\n",
       "        <th> b </th>\n",
       "        <th> mu </th>\n",
       "        <th> sigma </th>\n",
       "        <th> tau </th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th> s </th>\n",
       "        <td> 1.32e-05 </td>\n",
       "        <td style=\"background-color:rgb(213,213,250);color:black\"> -5.06e-06 <strong>(-0.285)</strong> </td>\n",
       "        <td style=\"background-color:rgb(246,246,250);color:black\"> -4.03e-08 <strong>(-0.029)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,213,213);color:black\"> 3.09e-07 <strong>(0.250)</strong> </td>\n",
       "        <td style=\"background-color:rgb(229,229,250);color:black\"> -4.07e-06 <strong>(-0.162)</strong> </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th> b </th>\n",
       "        <td style=\"background-color:rgb(213,213,250);color:black\"> -5.06e-06 <strong>(-0.285)</strong> </td>\n",
       "        <td> 2.38e-05 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 4.56e-10 </td>\n",
       "        <td style=\"background-color:rgb(213,213,250);color:black\"> -4.76e-07 <strong>(-0.287)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,162,162);color:black\"> 1.98e-05 <strong>(0.588)</strong> </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th> mu </th>\n",
       "        <td style=\"background-color:rgb(246,246,250);color:black\"> -4.03e-08 <strong>(-0.029)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 4.56e-10 </td>\n",
       "        <td> 1.48e-07 </td>\n",
       "        <td style=\"background-color:rgb(244,244,250);color:black\"> -6.05e-09 <strong>(-0.046)</strong> </td>\n",
       "        <td style=\"background-color:rgb(243,243,250);color:black\"> -1.46e-07 <strong>(-0.055)</strong> </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th> sigma </th>\n",
       "        <td style=\"background-color:rgb(250,213,213);color:black\"> 3.09e-07 <strong>(0.250)</strong> </td>\n",
       "        <td style=\"background-color:rgb(213,213,250);color:black\"> -4.76e-07 <strong>(-0.287)</strong> </td>\n",
       "        <td style=\"background-color:rgb(244,244,250);color:black\"> -6.05e-09 <strong>(-0.046)</strong> </td>\n",
       "        <td> 1.16e-07 </td>\n",
       "        <td style=\"background-color:rgb(229,229,250);color:black\"> -3.77e-07 <strong>(-0.160)</strong> </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th> tau </th>\n",
       "        <td style=\"background-color:rgb(229,229,250);color:black\"> -4.07e-06 <strong>(-0.162)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,162,162);color:black\"> 1.98e-05 <strong>(0.588)</strong> </td>\n",
       "        <td style=\"background-color:rgb(243,243,250);color:black\"> -1.46e-07 <strong>(-0.055)</strong> </td>\n",
       "        <td style=\"background-color:rgb(229,229,250);color:black\"> -3.77e-07 <strong>(-0.160)</strong> </td>\n",
       "        <td> 4.79e-05 </td>\n",
       "    </tr>\n",
       "</table>"
      ],
      "text/plain": [
       "┌─────────────────────────────────────────────────────────────────────────┐\n",
       "│                                Migrad                                   │\n",
       "├──────────────────────────────────┬──────────────────────────────────────┤\n",
       "│ FCN = 36.34 (chi2/ndof = 0.8)    │              Nfcn = 110              │\n",
       "│ EDM = 1.7e-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 │ s     │   0.995   │   0.004   │            │            │    0    │         │       │\n",
       "│ 1 │ b     │   1.008   │   0.005   │            │            │    0    │         │       │\n",
       "│ 2 │ mu    │ 999.3e-3  │  0.4e-3   │            │            │    0    │    2    │       │\n",
       "│ 3 │ sigma │ 99.20e-3  │  0.34e-3  │            │            │    0    │         │       │\n",
       "│ 4 │ tau   │   1.002   │   0.007   │            │            │    0    │         │       │\n",
       "└───┴───────┴───────────┴───────────┴────────────┴────────────┴─────────┴─────────┴───────┘\n",
       "┌───────┬───────────────────────────────────────────────────┐\n",
       "│       │         s         b        mu     sigma       tau │\n",
       "├───────┼───────────────────────────────────────────────────┤\n",
       "│     s │  1.32e-05 -5.06e-06 -4.03e-08  3.09e-07 -4.07e-06 │\n",
       "│     b │ -5.06e-06  2.38e-05  4.56e-10 -4.76e-07  1.98e-05 │\n",
       "│    mu │ -4.03e-08  4.56e-10  1.48e-07 -6.05e-09 -1.46e-07 │\n",
       "│ sigma │  3.09e-07 -4.76e-07 -6.05e-09  1.16e-07 -3.77e-07 │\n",
       "│   tau │ -4.07e-06  1.98e-05 -1.46e-07 -3.77e-07  4.79e-05 │\n",
       "└───────┴───────────────────────────────────────────────────┘"
      ]
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     "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 = 7.555 (chi2/ndof = 0.5) </td>\n",
       "        <td colspan=\"3\" style=\"text-align:center\" title=\"Total number of function and (optional) gradient evaluations\"> Nfcn = 102 </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td colspan=\"2\" style=\"text-align:left\" title=\"Estimated distance to minimum and goal\"> EDM = 5.22e-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> s </td>\n",
       "        <td> 0.995 </td>\n",
       "        <td> 0.004 </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> b </td>\n",
       "        <td> 1.008 </td>\n",
       "        <td> 0.005 </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> mu </td>\n",
       "        <td> 999.2e-3 </td>\n",
       "        <td> 0.4e-3 </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
       "        <td> 0 </td>\n",
       "        <td> 2 </td>\n",
       "        <td>  </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th> 3 </th>\n",
       "        <td> sigma </td>\n",
       "        <td> 99.5e-3 </td>\n",
       "        <td> 0.4e-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> tau </td>\n",
       "        <td> 1.002 </td>\n",
       "        <td> 0.007 </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> s </th>\n",
       "        <th> b </th>\n",
       "        <th> mu </th>\n",
       "        <th> sigma </th>\n",
       "        <th> tau </th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th> s </th>\n",
       "        <td> 1.34e-05 </td>\n",
       "        <td style=\"background-color:rgb(211,211,250);color:black\"> -5.35e-06 <strong>(-0.297)</strong> </td>\n",
       "        <td style=\"background-color:rgb(246,246,250);color:black\"> -4.45e-08 <strong>(-0.030)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,211,211);color:black\"> 3.51e-07 <strong>(0.260)</strong> </td>\n",
       "        <td style=\"background-color:rgb(228,228,250);color:black\"> -4.31e-06 <strong>(-0.169)</strong> </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th> b </th>\n",
       "        <td style=\"background-color:rgb(211,211,250);color:black\"> -5.35e-06 <strong>(-0.297)</strong> </td>\n",
       "        <td> 2.42e-05 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -3.58e-10 </td>\n",
       "        <td style=\"background-color:rgb(211,211,250);color:black\"> -5.42e-07 <strong>(-0.298)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,161,161);color:black\"> 2.02e-05 <strong>(0.591)</strong> </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th> mu </th>\n",
       "        <td style=\"background-color:rgb(246,246,250);color:black\"> -4.45e-08 <strong>(-0.030)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -3.58e-10 </td>\n",
       "        <td> 1.61e-07 </td>\n",
       "        <td style=\"background-color:rgb(244,244,250);color:black\"> -7.05e-09 <strong>(-0.048)</strong> </td>\n",
       "        <td style=\"background-color:rgb(242,242,250);color:black\"> -1.64e-07 <strong>(-0.059)</strong> </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th> sigma </th>\n",
       "        <td style=\"background-color:rgb(250,211,211);color:black\"> 3.51e-07 <strong>(0.260)</strong> </td>\n",
       "        <td style=\"background-color:rgb(211,211,250);color:black\"> -5.42e-07 <strong>(-0.298)</strong> </td>\n",
       "        <td style=\"background-color:rgb(244,244,250);color:black\"> -7.05e-09 <strong>(-0.048)</strong> </td>\n",
       "        <td> 1.37e-07 </td>\n",
       "        <td style=\"background-color:rgb(228,228,250);color:black\"> -4.28e-07 <strong>(-0.167)</strong> </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th> tau </th>\n",
       "        <td style=\"background-color:rgb(228,228,250);color:black\"> -4.31e-06 <strong>(-0.169)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,161,161);color:black\"> 2.02e-05 <strong>(0.591)</strong> </td>\n",
       "        <td style=\"background-color:rgb(242,242,250);color:black\"> -1.64e-07 <strong>(-0.059)</strong> </td>\n",
       "        <td style=\"background-color:rgb(228,228,250);color:black\"> -4.28e-07 <strong>(-0.167)</strong> </td>\n",
       "        <td> 4.83e-05 </td>\n",
       "    </tr>\n",
       "</table>"
      ],
      "text/plain": [
       "┌─────────────────────────────────────────────────────────────────────────┐\n",
       "│                                Migrad                                   │\n",
       "├──────────────────────────────────┬──────────────────────────────────────┤\n",
       "│ FCN = 7.555 (chi2/ndof = 0.5)    │              Nfcn = 102              │\n",
       "│ EDM = 5.22e-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 │ s     │   0.995   │   0.004   │            │            │    0    │         │       │\n",
       "│ 1 │ b     │   1.008   │   0.005   │            │            │    0    │         │       │\n",
       "│ 2 │ mu    │ 999.2e-3  │  0.4e-3   │            │            │    0    │    2    │       │\n",
       "│ 3 │ sigma │  99.5e-3  │  0.4e-3   │            │            │    0    │         │       │\n",
       "│ 4 │ tau   │   1.002   │   0.007   │            │            │    0    │         │       │\n",
       "└───┴───────┴───────────┴───────────┴────────────┴────────────┴─────────┴─────────┴───────┘\n",
       "┌───────┬───────────────────────────────────────────────────┐\n",
       "│       │         s         b        mu     sigma       tau │\n",
       "├───────┼───────────────────────────────────────────────────┤\n",
       "│     s │  1.34e-05 -5.35e-06 -4.45e-08  3.51e-07 -4.31e-06 │\n",
       "│     b │ -5.35e-06  2.42e-05 -3.58e-10 -5.42e-07  2.02e-05 │\n",
       "│    mu │ -4.45e-08 -3.58e-10  1.61e-07 -7.05e-09 -1.64e-07 │\n",
       "│ sigma │  3.51e-07 -5.42e-07 -7.05e-09  1.37e-07 -4.28e-07 │\n",
       "│   tau │ -4.31e-06  2.02e-05 -1.64e-07 -4.28e-07  4.83e-05 │\n",
       "└───────┴───────────────────────────────────────────────────┘"
      ]
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    },
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     "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 = 2.084 (chi2/ndof = 0.4) </td>\n",
       "        <td colspan=\"3\" style=\"text-align:center\" title=\"Total number of function and (optional) gradient evaluations\"> Nfcn = 114 </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td colspan=\"2\" style=\"text-align:left\" title=\"Estimated distance to minimum and goal\"> EDM = 4.65e-08 (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> s </td>\n",
       "        <td> 0.995 </td>\n",
       "        <td> 0.004 </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> b </td>\n",
       "        <td> 1.007 </td>\n",
       "        <td> 0.005 </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> mu </td>\n",
       "        <td> 999.4e-3 </td>\n",
       "        <td> 0.5e-3 </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
       "        <td> 0 </td>\n",
       "        <td> 2 </td>\n",
       "        <td>  </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th> 3 </th>\n",
       "        <td> sigma </td>\n",
       "        <td> 99.8e-3 </td>\n",
       "        <td> 0.7e-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> tau </td>\n",
       "        <td> 1.003 </td>\n",
       "        <td> 0.007 </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> s </th>\n",
       "        <th> b </th>\n",
       "        <th> mu </th>\n",
       "        <th> sigma </th>\n",
       "        <th> tau </th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th> s </th>\n",
       "        <td> 1.54e-05 </td>\n",
       "        <td style=\"background-color:rgb(198,198,250);color:black\"> -8.38e-06 <strong>(-0.397)</strong> </td>\n",
       "        <td style=\"background-color:rgb(245,245,250);color:black\"> -7.48e-08 <strong>(-0.042)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,188,188);color:black\"> 1.14e-06 <strong>(0.413)</strong> </td>\n",
       "        <td style=\"background-color:rgb(219,219,250);color:black\"> -6.75e-06 <strong>(-0.238)</strong> </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th> b </th>\n",
       "        <td style=\"background-color:rgb(198,198,250);color:black\"> -8.38e-06 <strong>(-0.397)</strong> </td>\n",
       "        <td> 2.9e-05 </td>\n",
       "        <td style=\"background-color:rgb(250,249,249);color:black\"> 2.17e-08 <strong>(0.009)</strong> </td>\n",
       "        <td style=\"background-color:rgb(190,190,250);color:black\"> -1.76e-06 <strong>(-0.464)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,156,156);color:black\"> 2.43e-05 <strong>(0.624)</strong> </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th> mu </th>\n",
       "        <td style=\"background-color:rgb(245,245,250);color:black\"> -7.48e-08 <strong>(-0.042)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,249,249);color:black\"> 2.17e-08 <strong>(0.009)</strong> </td>\n",
       "        <td> 2.06e-07 </td>\n",
       "        <td style=\"background-color:rgb(241,241,250);color:black\"> -2.27e-08 <strong>(-0.071)</strong> </td>\n",
       "        <td style=\"background-color:rgb(242,242,250);color:black\"> -2.06e-07 <strong>(-0.063)</strong> </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th> sigma </th>\n",
       "        <td style=\"background-color:rgb(250,188,188);color:black\"> 1.14e-06 <strong>(0.413)</strong> </td>\n",
       "        <td style=\"background-color:rgb(190,190,250);color:black\"> -1.76e-06 <strong>(-0.464)</strong> </td>\n",
       "        <td style=\"background-color:rgb(241,241,250);color:black\"> -2.27e-08 <strong>(-0.071)</strong> </td>\n",
       "        <td> 4.95e-07 </td>\n",
       "        <td style=\"background-color:rgb(214,214,250);color:black\"> -1.4e-06 <strong>(-0.275)</strong> </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th> tau </th>\n",
       "        <td style=\"background-color:rgb(219,219,250);color:black\"> -6.75e-06 <strong>(-0.238)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,156,156);color:black\"> 2.43e-05 <strong>(0.624)</strong> </td>\n",
       "        <td style=\"background-color:rgb(242,242,250);color:black\"> -2.06e-07 <strong>(-0.063)</strong> </td>\n",
       "        <td style=\"background-color:rgb(214,214,250);color:black\"> -1.4e-06 <strong>(-0.275)</strong> </td>\n",
       "        <td> 5.22e-05 </td>\n",
       "    </tr>\n",
       "</table>"
      ],
      "text/plain": [
       "┌─────────────────────────────────────────────────────────────────────────┐\n",
       "│                                Migrad                                   │\n",
       "├──────────────────────────────────┬──────────────────────────────────────┤\n",
       "│ FCN = 2.084 (chi2/ndof = 0.4)    │              Nfcn = 114              │\n",
       "│ EDM = 4.65e-08 (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 │ s     │   0.995   │   0.004   │            │            │    0    │         │       │\n",
       "│ 1 │ b     │   1.007   │   0.005   │            │            │    0    │         │       │\n",
       "│ 2 │ mu    │ 999.4e-3  │  0.5e-3   │            │            │    0    │    2    │       │\n",
       "│ 3 │ sigma │  99.8e-3  │  0.7e-3   │            │            │    0    │         │       │\n",
       "│ 4 │ tau   │   1.003   │   0.007   │            │            │    0    │         │       │\n",
       "└───┴───────┴───────────┴───────────┴────────────┴────────────┴─────────┴─────────┴───────┘\n",
       "┌───────┬───────────────────────────────────────────────────┐\n",
       "│       │         s         b        mu     sigma       tau │\n",
       "├───────┼───────────────────────────────────────────────────┤\n",
       "│     s │  1.54e-05 -8.38e-06 -7.48e-08  1.14e-06 -6.75e-06 │\n",
       "│     b │ -8.38e-06   2.9e-05  2.17e-08 -1.76e-06  2.43e-05 │\n",
       "│    mu │ -7.48e-08  2.17e-08  2.06e-07 -2.27e-08 -2.06e-07 │\n",
       "│ sigma │  1.14e-06 -1.76e-06 -2.27e-08  4.95e-07  -1.4e-06 │\n",
       "│   tau │ -6.75e-06  2.43e-05 -2.06e-07  -1.4e-06  5.22e-05 │\n",
       "└───────┴───────────────────────────────────────────────────┘"
      ]
     },
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     "output_type": "display_data"
    },
    {
     "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 = 2.677e-06 </td>\n",
       "        <td colspan=\"3\" style=\"text-align:center\" title=\"Total number of function and (optional) gradient evaluations\"> Nfcn = 112 </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td colspan=\"2\" style=\"text-align:left\" title=\"Estimated distance to minimum and goal\"> EDM = 2.68e-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> s </td>\n",
       "        <td> 0.996 </td>\n",
       "        <td> 0.005 </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> b </td>\n",
       "        <td> 1.006 </td>\n",
       "        <td> 0.007 </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> mu </td>\n",
       "        <td> 0.9998 </td>\n",
       "        <td> 0.0019 </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
       "        <td> 0 </td>\n",
       "        <td> 2 </td>\n",
       "        <td>  </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th> 3 </th>\n",
       "        <td> sigma </td>\n",
       "        <td> 0.1001 </td>\n",
       "        <td> 0.0012 </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> tau </td>\n",
       "        <td> 1.002 </td>\n",
       "        <td> 0.008 </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> s </th>\n",
       "        <th> b </th>\n",
       "        <th> mu </th>\n",
       "        <th> sigma </th>\n",
       "        <th> tau </th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th> s </th>\n",
       "        <td> 2.31e-05 </td>\n",
       "        <td style=\"background-color:rgb(172,172,250);color:black\"> -1.96e-05 <strong>(-0.599)</strong> </td>\n",
       "        <td style=\"background-color:rgb(227,227,250);color:black\"> -1.6e-06 <strong>(-0.173)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,150,150);color:black\"> 3.77e-06 <strong>(0.663)</strong> </td>\n",
       "        <td style=\"background-color:rgb(204,204,250);color:black\"> -1.41e-05 <strong>(-0.350)</strong> </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th> b </th>\n",
       "        <td style=\"background-color:rgb(172,172,250);color:black\"> -1.96e-05 <strong>(-0.599)</strong> </td>\n",
       "        <td> 4.64e-05 </td>\n",
       "        <td style=\"background-color:rgb(250,244,244);color:black\"> 5.35e-07 <strong>(0.041)</strong> </td>\n",
       "        <td style=\"background-color:rgb(161,161,250);color:black\"> -5.5e-06 <strong>(-0.684)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,149,149);color:black\"> 3.84e-05 <strong>(0.673)</strong> </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th> mu </th>\n",
       "        <td style=\"background-color:rgb(227,227,250);color:black\"> -1.6e-06 <strong>(-0.173)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,244,244);color:black\"> 5.35e-07 <strong>(0.041)</strong> </td>\n",
       "        <td> 3.72e-06 </td>\n",
       "        <td style=\"background-color:rgb(212,212,250);color:black\"> -6.63e-07 <strong>(-0.291)</strong> </td>\n",
       "        <td style=\"background-color:rgb(216,216,250);color:black\"> -4.19e-06 <strong>(-0.259)</strong> </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th> sigma </th>\n",
       "        <td style=\"background-color:rgb(250,150,150);color:black\"> 3.77e-06 <strong>(0.663)</strong> </td>\n",
       "        <td style=\"background-color:rgb(161,161,250);color:black\"> -5.5e-06 <strong>(-0.684)</strong> </td>\n",
       "        <td style=\"background-color:rgb(212,212,250);color:black\"> -6.63e-07 <strong>(-0.291)</strong> </td>\n",
       "        <td> 1.4e-06 </td>\n",
       "        <td style=\"background-color:rgb(202,202,250);color:black\"> -3.66e-06 <strong>(-0.369)</strong> </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th> tau </th>\n",
       "        <td style=\"background-color:rgb(204,204,250);color:black\"> -1.41e-05 <strong>(-0.350)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,149,149);color:black\"> 3.84e-05 <strong>(0.673)</strong> </td>\n",
       "        <td style=\"background-color:rgb(216,216,250);color:black\"> -4.19e-06 <strong>(-0.259)</strong> </td>\n",
       "        <td style=\"background-color:rgb(202,202,250);color:black\"> -3.66e-06 <strong>(-0.369)</strong> </td>\n",
       "        <td> 7.03e-05 </td>\n",
       "    </tr>\n",
       "</table>"
      ],
      "text/plain": [
       "┌─────────────────────────────────────────────────────────────────────────┐\n",
       "│                                Migrad                                   │\n",
       "├──────────────────────────────────┬──────────────────────────────────────┤\n",
       "│ FCN = 2.677e-06                  │              Nfcn = 112              │\n",
       "│ EDM = 2.68e-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 │ s     │   0.996   │   0.005   │            │            │    0    │         │       │\n",
       "│ 1 │ b     │   1.006   │   0.007   │            │            │    0    │         │       │\n",
       "│ 2 │ mu    │  0.9998   │  0.0019   │            │            │    0    │    2    │       │\n",
       "│ 3 │ sigma │  0.1001   │  0.0012   │            │            │    0    │         │       │\n",
       "│ 4 │ tau   │   1.002   │   0.008   │            │            │    0    │         │       │\n",
       "└───┴───────┴───────────┴───────────┴────────────┴────────────┴─────────┴─────────┴───────┘\n",
       "┌───────┬───────────────────────────────────────────────────┐\n",
       "│       │         s         b        mu     sigma       tau │\n",
       "├───────┼───────────────────────────────────────────────────┤\n",
       "│     s │  2.31e-05 -1.96e-05  -1.6e-06  3.77e-06 -1.41e-05 │\n",
       "│     b │ -1.96e-05  4.64e-05  5.35e-07  -5.5e-06  3.84e-05 │\n",
       "│    mu │  -1.6e-06  5.35e-07  3.72e-06 -6.63e-07 -4.19e-06 │\n",
       "│ sigma │  3.77e-06  -5.5e-06 -6.63e-07   1.4e-06 -3.66e-06 │\n",
       "│   tau │ -1.41e-05  3.84e-05 -4.19e-06 -3.66e-06  7.03e-05 │\n",
       "└───────┴───────────────────────────────────────────────────┘"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 720x576 with 6 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "def integral(xe, s, b, mu, sigma, tau):\n",
    "    return s * n * norm.cdf(xe, mu, sigma) + b * n * expon.cdf(xe, 0, tau)\n",
    "\n",
    "fig, ax = plt.subplots(3, 2, figsize=(10, 8), sharex=True, constrained_layout=True)\n",
    "for axi, bins in zip(ax.flat, (200, 100, 50, 20, 10, 5)):\n",
    "    w, xe = np.histogram(pts, bins=bins, range=(0, 2))\n",
    "    c = ExtendedBinnedNLL(w, xe, integral)\n",
    "    m = fit(c)\n",
    "    display(m)\n",
    "    axi.stairs(w, xe, fill=True, label=\"data\")\n",
    "    axi.stairs(np.diff(integral(xe, *m.values)), xe, label=\"fit\")\n",
    "    axi.legend()\n",
    "    results[bins] = (np.array(m.values), np.array(m.errors), m.fmin.time)\n",
    "fig.supxlabel(\"x\");"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1008x1440 with 10 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "npar = len(results[np.inf][0])\n",
    "\n",
    "fig, ax = plt.subplots(npar, 2, sharex=True, figsize=(14, 20))\n",
    "for j, (k, (v, e, _)) in enumerate(results.items()):\n",
    "    for i, (vi, ei) in enumerate(zip(v, e)):\n",
    "        c = f\"C{i}\"\n",
    "        ax[i, 0].errorbar(j, vi, ei, color=c, fmt=\"o\")\n",
    "        ax[i, 0].set_ylabel(par_names[i])\n",
    "        einf = results[np.inf][1][i]\n",
    "        ax[i, 1].plot(j, ei /einf, \"o\", color=c)\n",
    "for i in range(npar):\n",
    "    ax[i, 1].set_ylim(0.95, 1.2)\n",
    "    ax[i, 1].axhline(1.05, ls=\"--\", color=\"0.5\")\n",
    "plt.xticks(np.arange(7), [f\"{x}\" for x in results.keys()]);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Shown on the left is the fitted value and its uncertainty estimate. Shown of the right is the relative size of the error bar of the binned fit compared to the unbinned fit."
   ]
  },
  {
   "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": [
    "plt.figure()\n",
    "x = np.arange(7)\n",
    "y = [v[2] for v in results.values()]\n",
    "plt.plot(x, y, \"o\")\n",
    "for xi, yi in zip(x[1:], y[1:]):\n",
    "    plt.text(xi, yi * 1.2, f\"{y[0]/yi:.0f}x\", ha=\"center\")\n",
    "plt.xticks(x, [f\"{x}\" for x in results.keys()])\n",
    "plt.ylabel(\"time / sec\")\n",
    "plt.semilogy();"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We now demonstrate that the binned fits and the unbinned fit are unbiased. We repeat the fit many times with independent random samples, the mean of the results minus the truth is the bias. In each iteration, the binned fits use the same data that the unbinned fit uses."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [],
   "source": [
    "@joblib.delayed\n",
    "def run(seed):\n",
    "    rng = np.random.default_rng(seed)\n",
    "    s = rng.normal(truth[2], truth[3], size=int(n * truth[0]))\n",
    "    b = rng.exponential(truth[4], size=int(n * truth[1]))\n",
    "    pts = np.append(s, b)\n",
    "    pts = pts[(pts > 0) & (pts < 2)]\n",
    "\n",
    "    if bins == np.inf:\n",
    "        m = fit(ExtendedUnbinnedNLL(pts, density))\n",
    "        assert m.valid\n",
    "    else:\n",
    "        w, xe = np.histogram(pts, bins=bins, range=(0, 2))\n",
    "        m = fit(ExtendedBinnedNLL(w, xe, integral))\n",
    "        assert m.valid\n",
    "    return np.array(m.values)\n",
    "\n",
    "results = {}\n",
    "for bins in (np.inf, 200, 100, 50, 20, 10, 5):\n",
    "    results[bins] = joblib.Parallel(-1)(run(seed) for seed in range(100))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "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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",
      "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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C3g3cBnwbuKGqNvTWbUnSRPX6LZ2bgJvGOP4w8Ntd+7cAt/TSliSpN660laRGGPiS1AgDX5IaYeBLUiMMfElqhIEvSY0w8CWpEQa+JDViKm6tMOVc+i5Jo3mFL0mNMPAlqREGviQ1wsCXpEYY+JLUCANfkhph4EtSIwx8SWqEgS9JjUhVDboPY0qyA/h+D6dYCDzap+60wPGaGMdrYhyviellvE6qqkVjFUzbwO9VkuGqGhp0P2YKx2tiHK+JcbwmZrLGyykdSWqEgS9JjZjNgX/NoDswwzheE+N4TYzjNTGTMl6zdg5fkrS32XyFL0nqYuBLUiMM/MYlWZJk/aD7oZkpyaeSnD7ofsw0SRYk+TdT3a6BL+mQVdU7quqBQfdjBloAGPi9SvJPk3wxyX1J1id586D7NAPMTXJdkm8n+VySwwfdoemg89fPPyRZleTBzhidl+QrSb6T5OwkVyV5T9dz1idZMsBuT5qx3ltJ/i7JUKf89zrj9I0k/yvJRzvHVyX5eJKvJdmc5DVJru283lZ1nf/jSYaTbEjy3wb0Y06Vq4EXJlmb5CNJ7kjyrSTrklwAo//6TvKeJFf10uisC3xgBfBwVb2kql4M3DroDs0ApwH/s6p+DXicAVx5TGMvAj4M/Grn8TbgnwPvAf7zAPs1COO+t5IcB/wX4BXAOYyMVbejgOXAvwdWAx8BzgDOTLKsU+fKzurSs4BXJzlrEn+WQbsc+G5VLQPeC1xUVS8Dfgv4cJJMRqOzMfDXAa9N8sEkv1lVuwbdoRlgS1V9pbP9l4wEmkY8VFXrquoZYANwR418l3kdsGSgPZt6+3tvnQ18uaoeq6o9wGf3ee6arnF7ZJ8xXdKpc0mSbwH3MvLLoJXPBgL8UZL7gduBxcALJqOhWRf4VfUg8DJGXlh/kOR9A+7STLDvYgwXZ/zSz7u2n+nafwaYCzzF3u+j505Rv6Zcj++t7nHbd0znJlnKyF9N51bVWcAXmcVjuY+VwCLg1ztX/I8w8rP3/bU16wK/86fl7qr6S+BDjLxAtX8nJlne2X4b8H8H2ZkZ5nt0XmNJXgYsHWhvJtEB3lv3MDINc1SSucCbJnj6I4B/BHYleQHwun70eRr7KfD8zvaRwI+qak+S3wJO6hx/BPhnSY5Ochjw+l4bndvrCaahM4EPJXkG2AP86wH3ZybYCLwrybXAA8DHB9yfmeRvgN9NsgH4OvDggPszmcZ6b/0xQFVtS/JHwDeAx4B/AA56OrWq7ktyb+d5W4CvHOApM1pV7ex8+L+ekV+Wv5pkHTDMyBjQ+QXwfkbGdNuzx3vhrRUk9UWS51XVzzpX+DcB11bVTYPul35p1k3pSBqYq5KsBdYDDwE3D7Q3GsUrfElqhFf4ktQIA1+SGmHgS1IjDHxJaoSBL0mN+P8wPcO4hshVGwAAAABJRU5ErkJggg==",
      "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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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "ref = None\n",
    "for bin, values in results.items():\n",
    "    plt.figure()\n",
    "    m = np.mean(values, axis=0) - truth\n",
    "    s = np.std(values, axis=0, ddof=1)\n",
    "    plt.title(f\"{bin=}\")\n",
    "    plt.errorbar(np.arange(len(m)), m / s, 1, fmt=\"o\", label=f\"{bin=}\")\n",
    "    plt.axhline(0, ls=\"--\", color=\"0.5\")\n",
    "    plt.xticks(np.arange(len(m)), [\"s\", \"b\", \"mu\", \"sigma\", \"tau\"]);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The plots show the bias relative to the standard deviation for each parameter. All results are unbiased, whatever the binning. The bias is not exactly zero, since we used only 100 repetitions, it shrinks further with more. One can observe that the residual bias that is coming from the finite sampling is the same for the unbinned fit and the fits with 100 and 200 bins, which are essentially equivalent."
   ]
  }
 ],
 "metadata": {
  "interpreter": {
   "hash": "bdbf20ff2e92a3ae3002db8b02bd1dd1b287e934c884beb29a73dced9dbd0fa3"
  },
  "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": "3.8.12"
  },
  "orig_nbformat": 4
 },
 "nbformat": 4,
 "nbformat_minor": 2
}
