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   "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": 12,
   "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": 13,
   "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": 14,
   "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": 15,
   "metadata": {},
   "outputs": [
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       "<table>\n",
       "    <tr>\n",
       "        <th colspan=\"2\" style=\"text-align:center\" title=\"Minimizer\"> Migrad </th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"text-align:left\" title=\"Minimum value of function\"> FCN = -4.08e+06 </td>\n",
       "        <td style=\"text-align:center\" title=\"Total number of function and (optional) gradient evaluations\"> Nfcn = 120 </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"text-align:left\" title=\"Estimated distance to minimum and goal\"> EDM = 1.25e-05 (Goal: 0.0002) </td>\n",
       "        <td style=\"text-align:center\" title=\"Total run time of algorithms\"> time = 0.9 sec </td>\n",
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       "    <tr>\n",
       "        <td style=\"text-align:center;background-color:#92CCA6;color:black\"> Valid Minimum </td>\n",
       "        <td style=\"text-align:center;background-color:#92CCA6;color:black\"> Below EDM threshold (goal x 10) </td>\n",
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       "        <td style=\"text-align:center;background-color:#92CCA6;color:black\"> Hesse ok </td>\n",
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       "    <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",
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       "        <th title=\"Minos upper error\"> Minos Error+ </th>\n",
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       "        <th> 0 </th>\n",
       "        <td> s </td>\n",
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       "        <th> 1 </th>\n",
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       "        <th> 2 </th>\n",
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       "┌─────────────────────────────────────────────────────────────────────────┐\n",
       "│                                Migrad                                   │\n",
       "├──────────────────────────────────┬──────────────────────────────────────┤\n",
       "│ FCN = -4.08e+06                  │              Nfcn = 120              │\n",
       "│ EDM = 1.25e-05 (Goal: 0.0002)    │            time = 0.9 sec            │\n",
       "├──────────────────────────────────┼──────────────────────────────────────┤\n",
       "│          Valid Minimum           │   Below EDM threshold (goal x 10)    │\n",
       "├──────────────────────────────────┼──────────────────────────────────────┤\n",
       "│      No parameters at limit      │           Below call limit           │\n",
       "├──────────────────────────────────┼──────────────────────────────────────┤\n",
       "│             Hesse ok             │         Covariance accurate          │\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 -0.005e-3  -0.04e-6   0.30e-6 -0.004e-3 │\n",
       "│     b │ -0.005e-3  2.36e-05         0  -0.46e-6  0.020e-3 │\n",
       "│    mu │  -0.04e-6         0  1.46e-07  -0.01e-6  -0.14e-6 │\n",
       "│ sigma │   0.30e-6  -0.46e-6  -0.01e-6  1.12e-07  -0.36e-6 │\n",
       "│   tau │ -0.004e-3  0.020e-3  -0.14e-6  -0.36e-6  4.76e-05 │\n",
       "└───────┴───────────────────────────────────────────────────┘"
      ]
     },
     "execution_count": 15,
     "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": 16,
   "metadata": {},
   "outputs": [
    {
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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "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": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table>\n",
       "    <tr>\n",
       "        <th colspan=\"2\" style=\"text-align:center\" title=\"Minimizer\"> Migrad </th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"text-align:left\" title=\"Minimum value of function\"> FCN = 190.9 (χ²/ndof = 1.0) </td>\n",
       "        <td style=\"text-align:center\" title=\"Total number of function and (optional) gradient evaluations\"> Nfcn = 110 </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"text-align:left\" title=\"Estimated distance to minimum and goal\"> EDM = 2.17e-06 (Goal: 0.0002) </td>\n",
       "        <td style=\"text-align:center\" title=\"Total run time of algorithms\">  </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"text-align:center;background-color:#92CCA6;color:black\"> Valid Minimum </td>\n",
       "        <td style=\"text-align:center;background-color:#92CCA6;color:black\"> Below EDM threshold (goal x 10) </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"text-align:center;background-color:#92CCA6;color:black\"> No parameters at limit </td>\n",
       "        <td 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\"> Hesse ok </td>\n",
       "        <td style=\"text-align:center;background-color:#92CCA6;color:black\"> Covariance accurate </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\"> -0.005e-3 <strong>(-0.284)</strong> </td>\n",
       "        <td style=\"background-color:rgb(246,246,250);color:black\"> -0.04e-6 <strong>(-0.029)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,213,213);color:black\"> 0.30e-6 <strong>(0.248)</strong> </td>\n",
       "        <td style=\"background-color:rgb(229,229,250);color:black\"> -0.004e-3 <strong>(-0.161)</strong> </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th> b </th>\n",
       "        <td style=\"background-color:rgb(213,213,250);color:black\"> -0.005e-3 <strong>(-0.284)</strong> </td>\n",
       "        <td> 2.37e-05 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0 </td>\n",
       "        <td style=\"background-color:rgb(213,213,250);color:black\"> -0.47e-6 <strong>(-0.286)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,162,162);color:black\"> 0.020e-3 <strong>(0.587)</strong> </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th> mu </th>\n",
       "        <td style=\"background-color:rgb(246,246,250);color:black\"> -0.04e-6 <strong>(-0.029)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0 </td>\n",
       "        <td> 1.46e-07 </td>\n",
       "        <td style=\"background-color:rgb(244,244,250);color:black\"> -0.01e-6 <strong>(-0.046)</strong> </td>\n",
       "        <td style=\"background-color:rgb(243,243,250);color:black\"> -0.14e-6 <strong>(-0.054)</strong> </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th> sigma </th>\n",
       "        <td style=\"background-color:rgb(250,213,213);color:black\"> 0.30e-6 <strong>(0.248)</strong> </td>\n",
       "        <td style=\"background-color:rgb(213,213,250);color:black\"> -0.47e-6 <strong>(-0.286)</strong> </td>\n",
       "        <td style=\"background-color:rgb(244,244,250);color:black\"> -0.01e-6 <strong>(-0.046)</strong> </td>\n",
       "        <td> 1.12e-07 </td>\n",
       "        <td style=\"background-color:rgb(229,229,250);color:black\"> -0.37e-6 <strong>(-0.159)</strong> </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th> tau </th>\n",
       "        <td style=\"background-color:rgb(229,229,250);color:black\"> -0.004e-3 <strong>(-0.161)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,162,162);color:black\"> 0.020e-3 <strong>(0.587)</strong> </td>\n",
       "        <td style=\"background-color:rgb(243,243,250);color:black\"> -0.14e-6 <strong>(-0.054)</strong> </td>\n",
       "        <td style=\"background-color:rgb(229,229,250);color:black\"> -0.37e-6 <strong>(-0.159)</strong> </td>\n",
       "        <td> 4.77e-05 </td>\n",
       "    </tr>\n",
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       "┌─────────────────────────────────────────────────────────────────────────┐\n",
       "│                                Migrad                                   │\n",
       "├──────────────────────────────────┬──────────────────────────────────────┤\n",
       "│ FCN = 190.9 (χ²/ndof = 1.0)      │              Nfcn = 110              │\n",
       "│ EDM = 2.17e-06 (Goal: 0.0002)    │                                      │\n",
       "├──────────────────────────────────┼──────────────────────────────────────┤\n",
       "│          Valid Minimum           │   Below EDM threshold (goal x 10)    │\n",
       "├──────────────────────────────────┼──────────────────────────────────────┤\n",
       "│      No parameters at limit      │           Below call limit           │\n",
       "├──────────────────────────────────┼──────────────────────────────────────┤\n",
       "│             Hesse ok             │         Covariance accurate          │\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 -0.005e-3  -0.04e-6   0.30e-6 -0.004e-3 │\n",
       "│     b │ -0.005e-3  2.37e-05         0  -0.47e-6  0.020e-3 │\n",
       "│    mu │  -0.04e-6         0  1.46e-07  -0.01e-6  -0.14e-6 │\n",
       "│ sigma │   0.30e-6  -0.47e-6  -0.01e-6  1.12e-07  -0.37e-6 │\n",
       "│   tau │ -0.004e-3  0.020e-3  -0.14e-6  -0.37e-6  4.77e-05 │\n",
       "└───────┴───────────────────────────────────────────────────┘"
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       "<table>\n",
       "    <tr>\n",
       "        <th colspan=\"2\" style=\"text-align:center\" title=\"Minimizer\"> Migrad </th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"text-align:left\" title=\"Minimum value of function\"> FCN = 87.19 (χ²/ndof = 0.9) </td>\n",
       "        <td style=\"text-align:center\" title=\"Total number of function and (optional) gradient evaluations\"> Nfcn = 110 </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"text-align:left\" title=\"Estimated distance to minimum and goal\"> EDM = 2.41e-06 (Goal: 0.0002) </td>\n",
       "        <td style=\"text-align:center\" title=\"Total run time of algorithms\">  </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"text-align:center;background-color:#92CCA6;color:black\"> Valid Minimum </td>\n",
       "        <td style=\"text-align:center;background-color:#92CCA6;color:black\"> Below EDM threshold (goal x 10) </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"text-align:center;background-color:#92CCA6;color:black\"> No parameters at limit </td>\n",
       "        <td style=\"text-align:center;background-color:#92CCA6;color:black\"> Below call limit </td>\n",
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       "    <tr>\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\"> Covariance accurate </td>\n",
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       "    <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",
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       "        <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",
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       "        <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",
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       "        <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",
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       "        <th> 3 </th>\n",
       "        <td> sigma </td>\n",
       "        <td> 99.24e-3 </td>\n",
       "        <td> 0.34e-3 </td>\n",
       "        <td>  </td>\n",
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       "        <td> 0 </td>\n",
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       "        <td> tau </td>\n",
       "        <td> 1.002 </td>\n",
       "        <td> 0.007 </td>\n",
       "        <td>  </td>\n",
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       "        <th> s </th>\n",
       "        <th> b </th>\n",
       "        <th> mu </th>\n",
       "        <th> sigma </th>\n",
       "        <th> tau </th>\n",
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       "        <th> s </th>\n",
       "        <td> 1.32e-05 </td>\n",
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       "        <td style=\"background-color:rgb(246,246,250);color:black\"> -0.04e-6 <strong>(-0.029)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,213,213);color:black\"> 0.30e-6 <strong>(0.249)</strong> </td>\n",
       "        <td style=\"background-color:rgb(229,229,250);color:black\"> -0.004e-3 <strong>(-0.161)</strong> </td>\n",
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       "        <td> 2.37e-05 </td>\n",
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       "        <td style=\"background-color:rgb(250,162,162);color:black\"> 0.020e-3 <strong>(0.587)</strong> </td>\n",
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       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0 </td>\n",
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       "        <td style=\"background-color:rgb(244,244,250);color:black\"> -0.01e-6 <strong>(-0.046)</strong> </td>\n",
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       "        <td style=\"background-color:rgb(229,229,250);color:black\"> -0.37e-6 <strong>(-0.159)</strong> </td>\n",
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       "┌─────────────────────────────────────────────────────────────────────────┐\n",
       "│                                Migrad                                   │\n",
       "├──────────────────────────────────┬──────────────────────────────────────┤\n",
       "│ FCN = 87.19 (χ²/ndof = 0.9)      │              Nfcn = 110              │\n",
       "│ EDM = 2.41e-06 (Goal: 0.0002)    │                                      │\n",
       "├──────────────────────────────────┼──────────────────────────────────────┤\n",
       "│          Valid Minimum           │   Below EDM threshold (goal x 10)    │\n",
       "├──────────────────────────────────┼──────────────────────────────────────┤\n",
       "│      No parameters at limit      │           Below call limit           │\n",
       "├──────────────────────────────────┼──────────────────────────────────────┤\n",
       "│             Hesse ok             │         Covariance accurate          │\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 -0.005e-3  -0.04e-6   0.30e-6 -0.004e-3 │\n",
       "│     b │ -0.005e-3  2.37e-05         0  -0.47e-6  0.020e-3 │\n",
       "│    mu │  -0.04e-6         0  1.47e-07  -0.01e-6  -0.14e-6 │\n",
       "│ sigma │   0.30e-6  -0.47e-6  -0.01e-6  1.13e-07  -0.37e-6 │\n",
       "│   tau │ -0.004e-3  0.020e-3  -0.14e-6  -0.37e-6  4.78e-05 │\n",
       "└───────┴───────────────────────────────────────────────────┘"
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       "<table>\n",
       "    <tr>\n",
       "        <th colspan=\"2\" style=\"text-align:center\" title=\"Minimizer\"> Migrad </th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"text-align:left\" title=\"Minimum value of function\"> FCN = 36.34 (χ²/ndof = 0.8) </td>\n",
       "        <td style=\"text-align:center\" title=\"Total number of function and (optional) gradient evaluations\"> Nfcn = 110 </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"text-align:left\" title=\"Estimated distance to minimum and goal\"> EDM = 1.7e-06 (Goal: 0.0002) </td>\n",
       "        <td style=\"text-align:center\" title=\"Total run time of algorithms\">  </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"text-align:center;background-color:#92CCA6;color:black\"> Valid Minimum </td>\n",
       "        <td style=\"text-align:center;background-color:#92CCA6;color:black\"> Below EDM threshold (goal x 10) </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"text-align:center;background-color:#92CCA6;color:black\"> No parameters at limit </td>\n",
       "        <td 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\"> Hesse ok </td>\n",
       "        <td style=\"text-align:center;background-color:#92CCA6;color:black\"> Covariance accurate </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",
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       "</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\"> -0.005e-3 <strong>(-0.285)</strong> </td>\n",
       "        <td style=\"background-color:rgb(246,246,250);color:black\"> -0.04e-6 <strong>(-0.029)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,213,213);color:black\"> 0.31e-6 <strong>(0.250)</strong> </td>\n",
       "        <td style=\"background-color:rgb(229,229,250);color:black\"> -0.004e-3 <strong>(-0.162)</strong> </td>\n",
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       "    <tr>\n",
       "        <th> b </th>\n",
       "        <td style=\"background-color:rgb(213,213,250);color:black\"> -0.005e-3 <strong>(-0.285)</strong> </td>\n",
       "        <td> 2.38e-05 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0 </td>\n",
       "        <td style=\"background-color:rgb(213,213,250);color:black\"> -0.48e-6 <strong>(-0.287)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,162,162);color:black\"> 0.020e-3 <strong>(0.588)</strong> </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th> mu </th>\n",
       "        <td style=\"background-color:rgb(246,246,250);color:black\"> -0.04e-6 <strong>(-0.029)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0 </td>\n",
       "        <td> 1.48e-07 </td>\n",
       "        <td style=\"background-color:rgb(244,244,250);color:black\"> -0.01e-6 <strong>(-0.046)</strong> </td>\n",
       "        <td style=\"background-color:rgb(243,243,250);color:black\"> -0.15e-6 <strong>(-0.055)</strong> </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th> sigma </th>\n",
       "        <td style=\"background-color:rgb(250,213,213);color:black\"> 0.31e-6 <strong>(0.250)</strong> </td>\n",
       "        <td style=\"background-color:rgb(213,213,250);color:black\"> -0.48e-6 <strong>(-0.287)</strong> </td>\n",
       "        <td style=\"background-color:rgb(244,244,250);color:black\"> -0.01e-6 <strong>(-0.046)</strong> </td>\n",
       "        <td> 1.16e-07 </td>\n",
       "        <td style=\"background-color:rgb(229,229,250);color:black\"> -0.38e-6 <strong>(-0.160)</strong> </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th> tau </th>\n",
       "        <td style=\"background-color:rgb(229,229,250);color:black\"> -0.004e-3 <strong>(-0.162)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,162,162);color:black\"> 0.020e-3 <strong>(0.588)</strong> </td>\n",
       "        <td style=\"background-color:rgb(243,243,250);color:black\"> -0.15e-6 <strong>(-0.055)</strong> </td>\n",
       "        <td style=\"background-color:rgb(229,229,250);color:black\"> -0.38e-6 <strong>(-0.160)</strong> </td>\n",
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       "┌─────────────────────────────────────────────────────────────────────────┐\n",
       "│                                Migrad                                   │\n",
       "├──────────────────────────────────┬──────────────────────────────────────┤\n",
       "│ FCN = 36.34 (χ²/ndof = 0.8)      │              Nfcn = 110              │\n",
       "│ EDM = 1.7e-06 (Goal: 0.0002)     │                                      │\n",
       "├──────────────────────────────────┼──────────────────────────────────────┤\n",
       "│          Valid Minimum           │   Below EDM threshold (goal x 10)    │\n",
       "├──────────────────────────────────┼──────────────────────────────────────┤\n",
       "│      No parameters at limit      │           Below call limit           │\n",
       "├──────────────────────────────────┼──────────────────────────────────────┤\n",
       "│             Hesse ok             │         Covariance accurate          │\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 -0.005e-3  -0.04e-6   0.31e-6 -0.004e-3 │\n",
       "│     b │ -0.005e-3  2.38e-05         0  -0.48e-6  0.020e-3 │\n",
       "│    mu │  -0.04e-6         0  1.48e-07  -0.01e-6  -0.15e-6 │\n",
       "│ sigma │   0.31e-6  -0.48e-6  -0.01e-6  1.16e-07  -0.38e-6 │\n",
       "│   tau │ -0.004e-3  0.020e-3  -0.15e-6  -0.38e-6  4.79e-05 │\n",
       "└───────┴───────────────────────────────────────────────────┘"
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       "<table>\n",
       "    <tr>\n",
       "        <th colspan=\"2\" style=\"text-align:center\" title=\"Minimizer\"> Migrad </th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"text-align:left\" title=\"Minimum value of function\"> FCN = 7.555 (χ²/ndof = 0.5) </td>\n",
       "        <td style=\"text-align:center\" title=\"Total number of function and (optional) gradient evaluations\"> Nfcn = 102 </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"text-align:left\" title=\"Estimated distance to minimum and goal\"> EDM = 5.22e-05 (Goal: 0.0002) </td>\n",
       "        <td style=\"text-align:center\" title=\"Total run time of algorithms\">  </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"text-align:center;background-color:#92CCA6;color:black\"> Valid Minimum </td>\n",
       "        <td style=\"text-align:center;background-color:#92CCA6;color:black\"> Below EDM threshold (goal x 10) </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"text-align:center;background-color:#92CCA6;color:black\"> No parameters at limit </td>\n",
       "        <td style=\"text-align:center;background-color:#92CCA6;color:black\"> Below call limit </td>\n",
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       "    <tr>\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\"> Covariance accurate </td>\n",
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       "        <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",
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       "        <th> 0 </th>\n",
       "        <td> s </td>\n",
       "        <td> 0.995 </td>\n",
       "        <td> 0.004 </td>\n",
       "        <td>  </td>\n",
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       "        <td> 0 </td>\n",
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       "        <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",
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       "        <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",
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       "        <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",
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       "        <th> 4 </th>\n",
       "        <td> tau </td>\n",
       "        <td> 1.002 </td>\n",
       "        <td> 0.007 </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
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       "        <th> s </th>\n",
       "        <th> b </th>\n",
       "        <th> mu </th>\n",
       "        <th> sigma </th>\n",
       "        <th> tau </th>\n",
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       "        <th> s </th>\n",
       "        <td> 1.34e-05 </td>\n",
       "        <td style=\"background-color:rgb(211,211,250);color:black\"> -0.005e-3 <strong>(-0.297)</strong> </td>\n",
       "        <td style=\"background-color:rgb(246,246,250);color:black\"> -0.04e-6 <strong>(-0.030)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,211,211);color:black\"> 0.35e-6 <strong>(0.260)</strong> </td>\n",
       "        <td style=\"background-color:rgb(228,228,250);color:black\"> -0.004e-3 <strong>(-0.169)</strong> </td>\n",
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       "        <td> 2.42e-05 </td>\n",
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       "        <td style=\"background-color:rgb(211,211,250);color:black\"> -0.54e-6 <strong>(-0.298)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,161,161);color:black\"> 0.020e-3 <strong>(0.591)</strong> </td>\n",
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       "        <th> mu </th>\n",
       "        <td style=\"background-color:rgb(246,246,250);color:black\"> -0.04e-6 <strong>(-0.030)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> -0 </td>\n",
       "        <td> 1.61e-07 </td>\n",
       "        <td style=\"background-color:rgb(244,244,250);color:black\"> -0.01e-6 <strong>(-0.048)</strong> </td>\n",
       "        <td style=\"background-color:rgb(242,242,250);color:black\"> -0.16e-6 <strong>(-0.059)</strong> </td>\n",
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       "        <td style=\"background-color:rgb(211,211,250);color:black\"> -0.54e-6 <strong>(-0.298)</strong> </td>\n",
       "        <td style=\"background-color:rgb(244,244,250);color:black\"> -0.01e-6 <strong>(-0.048)</strong> </td>\n",
       "        <td> 1.37e-07 </td>\n",
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       "        <td style=\"background-color:rgb(228,228,250);color:black\"> -0.43e-6 <strong>(-0.167)</strong> </td>\n",
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       "┌─────────────────────────────────────────────────────────────────────────┐\n",
       "│                                Migrad                                   │\n",
       "├──────────────────────────────────┬──────────────────────────────────────┤\n",
       "│ FCN = 7.555 (χ²/ndof = 0.5)      │              Nfcn = 102              │\n",
       "│ EDM = 5.22e-05 (Goal: 0.0002)    │                                      │\n",
       "├──────────────────────────────────┼──────────────────────────────────────┤\n",
       "│          Valid Minimum           │   Below EDM threshold (goal x 10)    │\n",
       "├──────────────────────────────────┼──────────────────────────────────────┤\n",
       "│      No parameters at limit      │           Below call limit           │\n",
       "├──────────────────────────────────┼──────────────────────────────────────┤\n",
       "│             Hesse ok             │         Covariance accurate          │\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 -0.005e-3  -0.04e-6   0.35e-6 -0.004e-3 │\n",
       "│     b │ -0.005e-3  2.42e-05        -0  -0.54e-6  0.020e-3 │\n",
       "│    mu │  -0.04e-6        -0  1.61e-07  -0.01e-6  -0.16e-6 │\n",
       "│ sigma │   0.35e-6  -0.54e-6  -0.01e-6  1.37e-07  -0.43e-6 │\n",
       "│   tau │ -0.004e-3  0.020e-3  -0.16e-6  -0.43e-6  4.83e-05 │\n",
       "└───────┴───────────────────────────────────────────────────┘"
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       "<table>\n",
       "    <tr>\n",
       "        <th colspan=\"2\" style=\"text-align:center\" title=\"Minimizer\"> Migrad </th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"text-align:left\" title=\"Minimum value of function\"> FCN = 2.084 (χ²/ndof = 0.4) </td>\n",
       "        <td style=\"text-align:center\" title=\"Total number of function and (optional) gradient evaluations\"> Nfcn = 114 </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"text-align:left\" title=\"Estimated distance to minimum and goal\"> EDM = 4.65e-08 (Goal: 0.0002) </td>\n",
       "        <td style=\"text-align:center\" title=\"Total run time of algorithms\">  </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"text-align:center;background-color:#92CCA6;color:black\"> Valid Minimum </td>\n",
       "        <td style=\"text-align:center;background-color:#92CCA6;color:black\"> Below EDM threshold (goal x 10) </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"text-align:center;background-color:#92CCA6;color:black\"> No parameters at limit </td>\n",
       "        <td style=\"text-align:center;background-color:#92CCA6;color:black\"> Below call limit </td>\n",
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       "    <tr>\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\"> Covariance accurate </td>\n",
       "    </tr>\n",
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       "        <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",
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       "        <th> 0 </th>\n",
       "        <td> s </td>\n",
       "        <td> 0.995 </td>\n",
       "        <td> 0.004 </td>\n",
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       "        <td> 0 </td>\n",
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       "        <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",
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       "        <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",
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       "        <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",
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       "        <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",
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       "    <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\"> -0.008e-3 <strong>(-0.397)</strong> </td>\n",
       "        <td style=\"background-color:rgb(245,245,250);color:black\"> -0.07e-6 <strong>(-0.042)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,188,188);color:black\"> 1.1e-6 <strong>(0.413)</strong> </td>\n",
       "        <td style=\"background-color:rgb(219,219,250);color:black\"> -0.007e-3 <strong>(-0.238)</strong> </td>\n",
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       "    <tr>\n",
       "        <th> b </th>\n",
       "        <td style=\"background-color:rgb(198,198,250);color:black\"> -0.008e-3 <strong>(-0.397)</strong> </td>\n",
       "        <td> 2.9e-05 </td>\n",
       "        <td style=\"background-color:rgb(250,249,249);color:black\"> 0.02e-6 <strong>(0.009)</strong> </td>\n",
       "        <td style=\"background-color:rgb(190,190,250);color:black\"> -1.8e-6 <strong>(-0.464)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,156,156);color:black\"> 0.024e-3 <strong>(0.624)</strong> </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th> mu </th>\n",
       "        <td style=\"background-color:rgb(245,245,250);color:black\"> -0.07e-6 <strong>(-0.042)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,249,249);color:black\"> 0.02e-6 <strong>(0.009)</strong> </td>\n",
       "        <td> 2.06e-07 </td>\n",
       "        <td style=\"background-color:rgb(241,241,250);color:black\"> -0.02e-6 <strong>(-0.071)</strong> </td>\n",
       "        <td style=\"background-color:rgb(242,242,250);color:black\"> -0.21e-6 <strong>(-0.063)</strong> </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th> sigma </th>\n",
       "        <td style=\"background-color:rgb(250,188,188);color:black\"> 1.1e-6 <strong>(0.413)</strong> </td>\n",
       "        <td style=\"background-color:rgb(190,190,250);color:black\"> -1.8e-6 <strong>(-0.464)</strong> </td>\n",
       "        <td style=\"background-color:rgb(241,241,250);color:black\"> -0.02e-6 <strong>(-0.071)</strong> </td>\n",
       "        <td> 4.95e-07 </td>\n",
       "        <td style=\"background-color:rgb(214,214,250);color:black\"> -1.4e-6 <strong>(-0.275)</strong> </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th> tau </th>\n",
       "        <td style=\"background-color:rgb(219,219,250);color:black\"> -0.007e-3 <strong>(-0.238)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,156,156);color:black\"> 0.024e-3 <strong>(0.624)</strong> </td>\n",
       "        <td style=\"background-color:rgb(242,242,250);color:black\"> -0.21e-6 <strong>(-0.063)</strong> </td>\n",
       "        <td style=\"background-color:rgb(214,214,250);color:black\"> -1.4e-6 <strong>(-0.275)</strong> </td>\n",
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       "┌─────────────────────────────────────────────────────────────────────────┐\n",
       "│                                Migrad                                   │\n",
       "├──────────────────────────────────┬──────────────────────────────────────┤\n",
       "│ FCN = 2.084 (χ²/ndof = 0.4)      │              Nfcn = 114              │\n",
       "│ EDM = 4.65e-08 (Goal: 0.0002)    │                                      │\n",
       "├──────────────────────────────────┼──────────────────────────────────────┤\n",
       "│          Valid Minimum           │   Below EDM threshold (goal x 10)    │\n",
       "├──────────────────────────────────┼──────────────────────────────────────┤\n",
       "│      No parameters at limit      │           Below call limit           │\n",
       "├──────────────────────────────────┼──────────────────────────────────────┤\n",
       "│             Hesse ok             │         Covariance accurate          │\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 -0.008e-3  -0.07e-6    1.1e-6 -0.007e-3 │\n",
       "│     b │ -0.008e-3   2.9e-05   0.02e-6   -1.8e-6  0.024e-3 │\n",
       "│    mu │  -0.07e-6   0.02e-6  2.06e-07  -0.02e-6  -0.21e-6 │\n",
       "│ sigma │    1.1e-6   -1.8e-6  -0.02e-6  4.95e-07   -1.4e-6 │\n",
       "│   tau │ -0.007e-3  0.024e-3  -0.21e-6   -1.4e-6  5.22e-05 │\n",
       "└───────┴───────────────────────────────────────────────────┘"
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       "<table>\n",
       "    <tr>\n",
       "        <th colspan=\"2\" style=\"text-align:center\" title=\"Minimizer\"> Migrad </th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"text-align:left\" title=\"Minimum value of function\"> FCN = 2.677e-06 </td>\n",
       "        <td style=\"text-align:center\" title=\"Total number of function and (optional) gradient evaluations\"> Nfcn = 112 </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"text-align:left\" title=\"Estimated distance to minimum and goal\"> EDM = 2.68e-06 (Goal: 0.0002) </td>\n",
       "        <td style=\"text-align:center\" title=\"Total run time of algorithms\">  </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"text-align:center;background-color:#92CCA6;color:black\"> Valid Minimum </td>\n",
       "        <td style=\"text-align:center;background-color:#92CCA6;color:black\"> Below EDM threshold (goal x 10) </td>\n",
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       "    <tr>\n",
       "        <td style=\"text-align:center;background-color:#92CCA6;color:black\"> No parameters at limit </td>\n",
       "        <td style=\"text-align:center;background-color:#92CCA6;color:black\"> Below call limit </td>\n",
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       "    <tr>\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\"> Covariance accurate </td>\n",
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       "    <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",
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       "        <th> 0 </th>\n",
       "        <td> s </td>\n",
       "        <td> 0.996 </td>\n",
       "        <td> 0.005 </td>\n",
       "        <td>  </td>\n",
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       "        <td> 0 </td>\n",
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       "        <th> 1 </th>\n",
       "        <td> b </td>\n",
       "        <td> 1.006 </td>\n",
       "        <td> 0.007 </td>\n",
       "        <td>  </td>\n",
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       "        <td> 0 </td>\n",
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       "        <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",
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       "        <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",
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       "        <th> 4 </th>\n",
       "        <td> tau </td>\n",
       "        <td> 1.002 </td>\n",
       "        <td> 0.008 </td>\n",
       "        <td>  </td>\n",
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       "        <td> 0 </td>\n",
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       "        <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\"> -0.020e-3 <strong>(-0.599)</strong> </td>\n",
       "        <td style=\"background-color:rgb(227,227,250);color:black\"> -2e-6 <strong>(-0.173)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,150,150);color:black\"> 3.8e-6 <strong>(0.663)</strong> </td>\n",
       "        <td style=\"background-color:rgb(204,204,250);color:black\"> -0.014e-3 <strong>(-0.350)</strong> </td>\n",
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       "        <th> b </th>\n",
       "        <td style=\"background-color:rgb(172,172,250);color:black\"> -0.020e-3 <strong>(-0.599)</strong> </td>\n",
       "        <td> 4.64e-05 </td>\n",
       "        <td style=\"background-color:rgb(250,244,244);color:black\"> 1e-6 <strong>(0.041)</strong> </td>\n",
       "        <td style=\"background-color:rgb(161,161,250);color:black\"> -5.5e-6 <strong>(-0.684)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,149,149);color:black\"> 0.04e-3 <strong>(0.673)</strong> </td>\n",
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       "    <tr>\n",
       "        <th> mu </th>\n",
       "        <td style=\"background-color:rgb(227,227,250);color:black\"> -2e-6 <strong>(-0.173)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,244,244);color:black\"> 1e-6 <strong>(0.041)</strong> </td>\n",
       "        <td> 3.72e-06 </td>\n",
       "        <td style=\"background-color:rgb(212,212,250);color:black\"> -0.7e-6 <strong>(-0.291)</strong> </td>\n",
       "        <td style=\"background-color:rgb(216,216,250);color:black\"> -4e-6 <strong>(-0.259)</strong> </td>\n",
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       "        <th> sigma </th>\n",
       "        <td style=\"background-color:rgb(250,150,150);color:black\"> 3.8e-6 <strong>(0.663)</strong> </td>\n",
       "        <td style=\"background-color:rgb(161,161,250);color:black\"> -5.5e-6 <strong>(-0.684)</strong> </td>\n",
       "        <td style=\"background-color:rgb(212,212,250);color:black\"> -0.7e-6 <strong>(-0.291)</strong> </td>\n",
       "        <td> 1.4e-06 </td>\n",
       "        <td style=\"background-color:rgb(202,202,250);color:black\"> -3.7e-6 <strong>(-0.369)</strong> </td>\n",
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       "        <td style=\"background-color:rgb(204,204,250);color:black\"> -0.014e-3 <strong>(-0.350)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,149,149);color:black\"> 0.04e-3 <strong>(0.673)</strong> </td>\n",
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       "        <td style=\"background-color:rgb(202,202,250);color:black\"> -3.7e-6 <strong>(-0.369)</strong> </td>\n",
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       "┌─────────────────────────────────────────────────────────────────────────┐\n",
       "│                                Migrad                                   │\n",
       "├──────────────────────────────────┬──────────────────────────────────────┤\n",
       "│ FCN = 2.677e-06                  │              Nfcn = 112              │\n",
       "│ EDM = 2.68e-06 (Goal: 0.0002)    │                                      │\n",
       "├──────────────────────────────────┼──────────────────────────────────────┤\n",
       "│          Valid Minimum           │   Below EDM threshold (goal x 10)    │\n",
       "├──────────────────────────────────┼──────────────────────────────────────┤\n",
       "│      No parameters at limit      │           Below call limit           │\n",
       "├──────────────────────────────────┼──────────────────────────────────────┤\n",
       "│             Hesse ok             │         Covariance accurate          │\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 -0.020e-3     -2e-6    3.8e-6 -0.014e-3 │\n",
       "│     b │ -0.020e-3  4.64e-05      1e-6   -5.5e-6   0.04e-3 │\n",
       "│    mu │     -2e-6      1e-6  3.72e-06   -0.7e-6     -4e-6 │\n",
       "│ sigma │    3.8e-6   -5.5e-6   -0.7e-6   1.4e-06   -3.7e-6 │\n",
       "│   tau │ -0.014e-3   0.04e-3     -4e-6   -3.7e-6  7.03e-05 │\n",
       "└───────┴───────────────────────────────────────────────────┘"
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",
      "text/plain": [
       "<Figure size 1000x800 with 6 Axes>"
      ]
     },
     "metadata": {},
     "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.fmin)\n",
    "    axi.stairs(w, xe, fill=True, label=\"data\")\n",
    "    axi.stairs(np.diff(integral(xe, *m.values)), xe, label=\"fit\")\n",
    "    axi.legend(title=f\"bins = {len(w)}\")\n",
    "    results[bins] = (np.array(m.values), np.array(m.errors), m.fmin.time)\n",
    "fig.supxlabel(\"x\");"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 1400x2000 with 10 Axes>"
      ]
     },
     "metadata": {},
     "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": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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GVHQ6nSovL9f555/v7UX7xY9Hlt6+fTtnhAAAaEEac0aIkaXrwaUxAABaHkaWBgAAaACCEAAAsCyCEAAAsKwmB6GdO3fqkUce0S233KKDBw9Kkj788EN9+eWXXisOAADAl5oUhFauXKlLLrlEa9as0cKFC1VVVSVJ2rx5s/Ly8rxaIAAAgK80KQhNnjxZM2fO1PLlyxUSEuKe/qtf/Uqff/6514oDAADwpSYFoS1btmj06NG1psfExOjQoUPnXBQAAIA/NCkIdejQQaWlpbWmb9y4UV26dDnnogAAAPyhSUHo5ptv1kMPPaSysjLZbDa5XC59+umnmjRpkn796197u0YAAACfaFIQevzxx9W7d28lJiaqqqpKdrtdAwcO1C9+8Qs98sgj3q7R7xwOh+x2u9LT0wNdCgAA8KFzesTGnj17VFxcrKqqKl122WXq2bOnN2sLOB6xAQBAy9OY43ebc/mipKQkJSUlncsiAAAAAqZJQcgYo3fffVdFRUU6ePCgXC6Xx/yFCxd6pTgAAABfalIQmjBhgl5++WUNGTJEsbGxstls3q4LAADA55oUhP7yl79o4cKFuvrqq71dDwAAgN806a6xqKgo9ejRw9u1AAAA+FWTgtD06dM1Y8YMHT161Nv1AAAA+E2TLo3deOONevPNNxUTE6Pu3burbdu2HvM3bNjgleIAAAB8qUlBaOzYsVq/fr1uu+02OksDAIAWq0lBaNmyZfr73/+uAQMGeLseAAAAv2lSH6HExERGWgYAAC1ek4LQs88+qz/84Q/avXu3l8sBAADwnyZdGrvtttv0ww8/6IILLlC7du1qdZYuLy/3SnEAAAC+1KQgNHv2bC+X0bw4HA45HA45nc5AlwIAAHzonJ4+39rx9HkAAFoenzx9vrKy0r2wysrKetsSGgAAQEvQ4CDUsWNHlZaWKiYmRh06dKhz7CBjjGw2G5eUAABAi9DgILRixQpFR0dLkoqKinxWEAAAgL80OAgNGjTI/e/k5GQlJibWOitkjNHevXu9Vx0AAIAPNWkcoeTkZP3zn/+sNb28vFzJycnnXBQAAIA/NCkI1fQF+qmqqiqFhYWdc1EAAAD+0KhxhHJzcyVJNptNU6dOVbt27dzznE6n1qxZo9TUVK8WCAAA4CuNCkIbN26UdPqM0JYtWxQSEuKeFxISopSUFE2aNMm7FQIAAPhIo4JQzd1i2dnZ+uMf/8h4QQAAoEVr0iM28vPzvV0HAACA3zWpszQAAEBrQBACAACWRRACAACWRRACAACWRRACAACWRRACAACWRRCqg8PhkN1uV3p6eqBLAQAAPmQzxphAF9FcVVZWKioqShUVFQweCQBAC9GY4zdnhAAAgGURhAAAgGURhAAAgGURhAAAgGURhAAAgGURhAAAgGURhAAAgGURhAAAgGURhAAAgGURhAAAgGURhAAAgGURhAAAgGURhAAAgGURhAAAgGURhAAAgGURhAAAgGURhAAAgGURhAAAgGURhAAAgGURhAAAgGURhAAAgGURhAAAgGURhAAAgGURhOrgcDhkt9uVnp4e6FIAAIAP2YwxJtBFNFeVlZWKiopSRUWFIiMjA10OAABogMYcvzkjBAAALIsgBAAALIsgBAAALIsgBAAALIsgBAAALIsgBAAALIsgBAAALIsgBAAALIsgBAAALIsgBAAALIsgBAAALIsgBAAALIsgBAAALIsgBAAALIsgBAAALIsgBAAALIsgBAAALIsgBAAALIsgBAAALIsgBAAALIsgBAAALIsgBAAALIsgBAAALIsgBAAALIsgBAAALIsgBAAALIsgBAAALIsgBAAALIsgBAAALIsgBAAALIsgBL9YtWqVsrKylJCQIJvNpsWLF3vMN8Zo2rRpio+PV3h4uDIzM/XNN9/UWs6yZcvUv39/hYeHq2PHjho1apR/VgAA0CoRhOAX1dXVSklJkcPhqHP+U089pTlz5mju3Llas2aNzjvvPA0bNkzHjh1zt/nb3/6m22+/XdnZ2dq8ebM+/fRTjRkzxl+rAABohWzGGBPoIpqryspKRUVFqaKiQpGRkYEup9Ww2WxatGiR+2yOMUYJCQmaOHGiJk2aJEmqqKhQbGys5s2bp5tvvlmnTp1S9+7dNWPGDI0bN67O5T766KOaO3eutmzZok6dOkmSRo4cqR9++EGFhYUKCiL3A4AVNOb4zZEBAVdSUqKysjJlZma6p0VFRal///5avXq1JGnDhg3at2+fgoKCdNlllyk+Pl4jRoxQcXGx+zMPP/ywunfvrjvvvFOS5HA49Nlnn+n1118nBAEA6tTqjw579+7V4MGDZbfbdemll+qdd94JdEn4ibKyMklSbGysx/TY2Fj3vF27dkmSpk+frkceeUTvv/++OnbsqMGDB6u8vFySFBwcrPnz56uwsFCTJ0/Wgw8+KIfDoaSkJD+uDQCgJWn1QahNmzaaPXu2tm7dqo8++kgTJkxQdXV1oMtCI7lcLkmnz/pcf/31SktLU35+vmw2m0e47dGjh5555hk9+eSTuuaaa+hDBACoV6sPQvHx8UpNTZUkxcXFqXPnzu4zCGge4uLiJEkHDhzwmH7gwAH3vPj4eEmS3W53zw8NDVWPHj20Z88ej8+tWrVKwcHB2r17t06dOuXL0gEALVzAg9DZbquWTvf16N69u8LCwtS/f3+tXbu2Sd+1fv16OZ1OJSYmnmPV8Kbk5GTFxcWpsLDQPa2yslJr1qxRRkaGJCktLU2hoaHatm2bu83Jkye1e/dudevWzT1twYIFWrhwoT7++GPt2bNHjz32mP9WBADQ4rQJdAE1t1X/5je/0XXXXVdr/oIFC5Sbm6u5c+eqf//+mj17toYNG6Zt27YpJiZGkpSamlrnX/4fffSREhISJEnl5eX69a9/rVdeecW3K4Q6VVVVaceOHe73JSUl2rRpk6Kjo5WUlKQJEyZo5syZ6tmzp5KTkzV16lQlJCS47yyLjIzUPffco7y8PCUmJqpbt256+umnJUk33HCDJOnbb7/VvffeqyeffFIDBgxQfn6+/u3f/k0jRozQ5Zdf7vd1BgC0AKYZkWQWLVrkMa1fv34mJyfH/d7pdJqEhATzxBNPNHi5x44dM7/85S/Nn//857O2q6iocL/27t1rJJmKiopGrQdqKyoqMpJqvcaOHWuMMcblcpmpU6ea2NhYExoaaoYOHWq2bdvmsYwTJ06YiRMnmpiYGBMREWEyMzNNcXGx+/NDhw41w4YNMy6Xy/2Z+++/31xwwQXmyJEjfltXAEBgVVRUNPj43azGEfrp+DInTpxQu3bt9O6773qMIDx27FgdPnxYS5YsOesyjTEaM2aMevXqpenTp9fbdvr06ZoxY0at6YwjBABAy9FqxhE6dOiQnE5nvbdVn82nn36qBQsWaPHixUpNTVVqaqq2bNlSZ9spU6aooqLC/dq7d+85rwMAAGi+At5HyNcGDBjgvvX6bEJDQxUaGurjigAAQHPRrM8Ide7cWcHBwfXeVg0AANBUzToIhYSEKC0tzeO2apfLpcLCQvdt1QAAAE0V8EtjZ7utOjc3V2PHjlXfvn3Vr18/zZ49W9XV1crOzg5g1fAXp8tobUm5Dh45ppiIMPVLjlZwkC3QZQEAWomAB6EvvvhCQ4YMcb/Pzc2VdPrOsHnz5ummm27SP//5T02bNk1lZWVKTU1VQUFBrQ7UaH0Kiks1Y+lWlVYcc0+LjwpTXpZdw/vEB7AyAEBr0axun28uHA6HHA6HnE6ntm/fzu3zAVBQXKp752/QT/9z1pwLeum2nxOGAAB1aszt8wShejRmQ8J7nC6jAU+u8DgT9GM2SXFRYfrkoV9xmQwAUEurGUcI1rS2pPyMIUg6PSR1acUxrS3h4bkAgHNDEEKzc/DImUNQU9oBAHAmBCE0OzERYV5tBwDAmRCE0Oz0S45WfFSYztT7x6bTd4/1S472Z1kAgFaIIIRmJzjIprwsuyTVCkM17/Oy7HSUBgCcM4JQHRwOh+x2u9LT0wNdimUN7xOvl277ueKiPC9/xUWFces8AMBruH2+Htw+H3iMLA0AaKzGHL8DPrI0UJ/gIJsyLugU6DIAAK0Ul8YAAIBlEYQAAIBlEYQAAIBlEYQAAIBlEYQAAIBlEYTqwDhCAABYA+MI1YNxhAAAaHkac/zmjBAAAGiyVatWKSsrSwkJCbLZbFq8eLHH/KqqKo0fP15du3ZVeHi47Ha75s6d69Fm8ODBstlsHq977rnHL/UThAC0aGf7ET5w4IDuuOMOJSQkqF27dho+fLi++eYbjzbHjh1TTk6OOnXqpPbt2+v666/XgQMH/LgWQMtVXV2tlJQUORyOOufn5uaqoKBA8+fP11dffaUJEyZo/Pjxeu+99zza3XXXXSotLXW/nnrqKX+UTxAC0LLV9yNsjNGoUaO0a9cuLVmyRBs3blS3bt2UmZmp6upqd7vf//73Wrp0qd555x2tXLlS+/fv13XXXefP1QBarBEjRmjmzJkaPXp0nfM/++wzjR07VoMHD1b37t119913KyUlRWvXrvVo165dO8XFxblfP76k9eijjyohIUHfffede9rIkSM1ZMgQuVyuc1sBgzOqqKgwkkxFRUWgSwHQAJLMokWL3O+3bdtmJJni4mL3NKfTac4//3zzyiuvGGOMOXz4sGnbtq1555133G2++uorI8msXr3aGGPMjBkzTHx8vDl06JC7zdVXX20GDx5snE6nj9cKaDl+ug8aY8xdd91l+vbta7799lvjcrnMihUrTPv27c3KlSvdbQYNGmQ6d+5sOnXqZC6++GIzefJkU11d7Z5/6tQpk5GRYUaNGmWMMeaFF14wHTp0MP/3f/9XZx2NOX5zRghAq3X8+HFJUlhYmHtaUFCQQkND9cknn0iS1q9fr5MnTyozM9Pdpnfv3kpKStLq1aslSQ8//LC6d++uO++8U9LpO0s/++wzvf766woK4mcUqM/zzz8vu92url27KiQkRMOHD5fD4dDAgQPdbcaMGaP58+erqKhIU6ZM0V/+8hfddttt7vnBwcGaP3++CgsLNXnyZD344INyOBxKSko65/p46CqAVqsm0EyZMkUvv/yyzjvvPD333HP69ttvVVpaKkkqKytTSEiIOnTo4PHZ2NhYlZWVSfrXj3BqaqomT56sOXPm6NVXX/XKjzDQ2j3//PP6/PPP9d5776lbt25atWqVcnJylJCQ4P4D5O6773a3v+SSSxQfH6+hQ4dq586duuCCCyRJPXr00DPPPKPf/va3uummmzRmzBiv1MefMkAz88QTTyg9PV0RERGKiYnRqFGjtG3bNo82Z+vc+91332n48OFKSEhQaGioEhMTNX78eFVWVvp7dQKqbdu2WrhwobZv367o6Gi1a9dORUVFGjFiRKPP5NT8CD/55JO65pprvPYjDLRmR48e1X/8x39o1qxZysrK0qWXXqrx48frpptu0jPPPHPGz/Xv31+StGPHDo/pq1atUnBwsHbv3q1Tp055pUaCENDMrFy5Ujk5Ofr888+1fPlynTx5UldddVWjOvcGBQXp2muv1Xvvvaft27dr3rx5+sc//uG321Gbk7S0NG3atEmHDx9WaWmpCgoK9N1336lHjx6SpLi4OJ04cUKHDx/2+NyBAwcUFxfnMc0XP8JAa3by5EmdPHmy1h8ewcHB9XZy3rRpkyQpPj7ePW3BggVauHChPv74Y+3Zs0ePPfaYd4psQl+oVu+FF14wP/vZz8xFF11EZ2kE3MGDB40kd8fChnTurcsf//hH07VrV2OMMS6XywwdOtRcddVVxuVyGWOM+e6770yXLl3M1KlTfbg2vqU6Omr+1Pbt201QUJD5+9//boz51/Z899133W2+/vrrWtvzrbfeMuHh4eZ//ud/THx8vJk2bZpP1gFoaY4cOWI2btxoNm7caCSZWbNmmY0bN7o7Mg8aNMhcfPHFpqioyOzatcvk5+ebsLAw8+KLLxpjjNmxY4d59NFHzRdffGFKSkrMkiVLTI8ePczAgQPd37F3717TsWNHM2fOHGOMMQUFBaZNmzZn/M1rTGdpglA9uGsMzcE333xjJJktW7YYY4wpLCw0ksz333/v0S4pKcnMmjWrzmXs27fPDBo0yNx6663uad9++63p2LGjmT17tjHGmBtuuMH069fPnDx50jcr4iNn+xF+++23TVFRkdm5c6dZvHix6datm7nuuus8lnHPPfeYpKQks2LFCvPFF1+YjIwMk5GR4Z7f2B9hwEqKioqMpFqvsWPHGmOMKS0tNXfccYdJSEgwYWFhplevXubZZ591/xG2Z88eM3DgQBMdHW1CQ0PNhRdeaB588EH3sbfmD7dhw4a5P2OMMffff7+54IILzJEjR2rVRBDyEoIQAs3pdJqRI0eaK664wj3tr3/9qwkJCanVNj093fzhD3/wmHbzzTeb8PBwI8lkZWWZo0ePesx/++23TVhYmJk8ebI577zzzPbt232zIj50th/hmjNhbdu2NUlJSeaRRx4xx48f91jG0aNHzX333Wc6duxo2rVrZ0aPHm1KS0uNMU37EQYQWI05fvOssXrwrDEE2r333qsPP/xQn3zyibp27SpJeuONN5Sdne2+NbxGv379NGTIED355JPuaWVlZTp8+LC2b9+uKVOmaNCgQXrxxRc9PjdmzBi9+eabeumllyzZhwhA69OY4ze3zwPN1Pjx4/X+++9r1apV7hAkeXbu/fEt33V17q0ZobV3796Kjo7WL3/5S02dOtXdAfGHH37Q+vXrFRwcXOuxEwBgBdw1BjQzxhiNHz9eixYt0ooVK5ScnOwxPy0tTW3btlVhYaF72rZt27Rnzx5lZGSccbk1d2j8+EzSxIkTFRQUpA8//FBz5szRihUrvLw2QMtztiEsysvLdf/996tXr14KDw9XUlKSfve736miosJjOevWrdPQoUPVoUMHdezYUcOGDdPmzZv9vTo4C4IQ0Mzk5ORo/vz5euONNxQREaGysjKVlZXp6NGjkqSoqCiNGzdOubm5Kioq0vr165Wdna2MjAxdfvnlkqQPPvhA+fn5Ki4u1u7du7Vs2TLdc889uuKKK9S9e3dJ0rJly/Taa6/pr3/9q6688ko9+OCDGjt2rL7//vtArTp8qCHjU/32t7/VBRdcoPDwcJ1//vm69tpr9fXXX3u0+d3vfqe0tDSFhoYqNTXVj2vgP2cbwmL//v3av3+/nnnmGRUXF2vevHkqKCjQuHHj3MuoqqrS8OHDlZSUpDVr1uiTTz5RRESEhg0bppMnTwZq1VAXX3dYasnoLI1AUB0dfyWZ/Px8d5v6OvcaY8yKFStMRkaGiYqKMmFhYaZnz57moYcect9pdvDgQRMbG2sef/xx92dOnDhh0tLSzI033uivVYUfDRs2zOTn55vi4mKzadMmc/XVV5ukpCRTVVXlbvPyyy+blStXmpKSErN+/XqTlZVlEhMTzalTp9xt7r//fvPCCy+Y22+/3aSkpARgTfzvp0NY1OXtt982ISEh7rsu161bZySZPXv2uNv87//+r5FkvvnmG2OMMdnZ2eaSSy4xx44dM8YYc/z4cZOammpuv/12H66NNXDXmJcQhAC0Vg05uG/evNlIMjt27Kg1Ly8vr84g1BoP7j8dwqIur7zyiuncubP7fWVlpenUqZPJy8szx48fNz/88IN54IEHzM9+9jN3WDpy5Ijp0aOHmTBhgjHGmEmTJpnu3btb5phzyukyn+04ZBZv/NZ8tuOQOeV0nf1DDdSY4zedpQFYjtNltLakXAePHFNMRJj6JUcrOMgW6LL8qqY/S3R0dJ3zq6urlZ+fr+TkZCUmJjZ4uXPmzFFKSoomT56s5557Tg8//LAOHz6sF154wSt1+5vL5dKECRN0xRVXqE+fPnW2OXTokB577DGP52VFRETo448/1qhRo9wjIPfs2VN///vf1abN6UNv+/btNX/+fA0aNEgRERGaPXu2ioqKLHGXckFxqWYs3arSimPuafFRYcrLsmt4n/h6Pul9BCEAltKcfoADpb6D+4svvqg//OEPqq6uVq9evbR8+XKFhIQ0eNmt7eCek5Oj4uJiffLJJ3XOr6ys1MiRI2W32zV9+nT39KNHj2rcuHG64oor9Oabb8rpdOqZZ57RyJEjtW7dOoWHh0uSMjIyNGnSJD322GN66KGHNGDAAH+sVkAVFJfq3vkb9NOxe8oqjune+Rv00m0/9+u+SGfpOjgcDtntdqWnpwe6FABeVPMD/OMQJP3rB7iguDRAlflXzcH9rbfeqjXv1ltv1caNG7Vy5UpddNFFuvHGG3Xs2LE6lnJmPz64T5w4scUe3GuGsCgqKvIYwqLGkSNHNHz4cEVERGjRokVq27ate94bb7yh3bt3Kz8/X+np6br88sv1xhtvqKSkREuWLHG3c7lc+vTTTxUcHFzrAaOtkdNlNGPp1lohSJJ72oylW+V0+W+IQ4JQHXJycrR161atW7cu0KUA8JLm+AMcCGc7uEdFRalnz54aOHCg3n33XX399ddatGhRo76jpR/czVmGsJBOnwm66qqrFBISovfee09hYWEe83/44QcFBQXJZvvXJdea9z9+2OjTTz+tr7/+WitXrlRBQYHy8/N9t2LNwNqS8lp/iPyYkVRacUxrS8r9VhNBCIAlNMcfYH9qyMG9rs8YY2qNYn42Lf3gfrYhLGpCUHV1tf70pz+psrLS3cbpdEqSrrzySn3//ffKycnRV199pS+//FLZ2dlq06aNhgwZIknauHGjpk2bpldffVVXXHGFZs2apQceeEC7du0K2Lr72sEjDTu72NB23kAfIaCVoANw/ZrjD7A/5eTk6I033tCSJUvcB3fp9Bmg8PBw7dq1SwsWLNBVV12l888/X99++63+67/+S+Hh4br66qvdy9mxY4eqqqrcwWDTpk2SJLvdrpCQEPfB/d133/U4uA8aNEg9evQIxKo32ksvvSRJGjx4sMf0/Px83XHHHdqwYYPWrFkjSbrwwgs92pSUlKh79+7q3bu3li5dqhkzZigjI0NBQUG67LLLVFBQoPj4eB07dky33Xab7rjjDmVlZUmS7r77bi1btky33367Vq1apeDgYN+vrJ/FRISdvVEj2nkDzxqrB88aQ0tBB+CzW73zO93yyudnbffmXZcr44JOfqjIv358iebHag7u+/fv15133qn169fr+++/V2xsrAYOHKhp06apV69e7vaDBw/WypUray2npKREcXFxSktL04ABA/Tyyy+751177bU6dOhQqz24o+GcLqMBT65QWcWxOi9T2yTFRYXpk4d+dU5/yDXm+E0QqgdBCC3Bme7AqPkJ8fcdGM2Vv36AAdSv5jdLkse+6M3frMYcv+kjBLRgdABuuOAgm/Ky7JL+9YNbo+Z9XpadEAT42PA+8Xrptp8rLsrz8ldcVFhA/nCjjxDQgjWmA3BrvNzTWDU/wD+9jBjHZUTAr4b3ideV9rhm0a+RIAS0YFbvANwUzekHGLCy4CBbs/gDjSAEtGDN8Q6MlqC5/AADCDyCENCC9UuOVnxU2Fk7APdLrvt5UkBDMDRDw7GtWh6CENCC1XQAvnf+BtlU9x0YdADGuWBohoZjW7VM3DUGtHDN7Q4MtB48m63h2FYtF+MI1YNxhNCScEoe3lQz7tKZ7kpk3KV/YVs1P405fnNprA4Oh0MOh8P9zBigJaADMLyJoRkajm3VsnFprA48fR6A1TE0Q8OxrVo2ghAAoBaGZmg4tlXLRhACANRSMzTDmXq02HT6jiiGZmBbtXQEIQBALTybreHYVi0bQQgAUCeGZmg4tlXLxe3z9eD2eQBgaIbGYFs1D9w+DwDwGoZmaDi2VcvDpTEAAGBZBCEAAGBZBCEAAGBZBCEAAGBZBCEAAGBZBCEAAGBZBCEAAGBZBCEAAGBZBCEAAGBZjCxdj5qnj1RWVga4EgAA0FA1x+2GPEWMIFQHh8Mhh8OhEydOSJISExMDXBEAAGisI0eOKCoqqt42PHS1Hi6XS/v371dERIRsNu8+NK+yslKJiYnau3cvD3Q9C7ZVw7GtGo5t1Thsr4ZjWzWcr7aVMUZHjhxRQkKCgoLq7wXEGaF6BAUFqWvXrj79jsjISHaUBmJbNRzbquHYVo3D9mo4tlXD+WJbne1MUA06SwMAAMsiCAEAAMsiCAVIaGio8vLyFBoaGuhSmj22VcOxrRqObdU4bK+GY1s1XHPYVnSWBgAAlsUZIQAAYFkEIQAAYFkEIQAAYFkEIR8aPHiwJkyY0OD2X3/9tS6//HKFhYUpNTXVZ3UBAIDTCEI+tHDhQj322GMNbp+Xl6fzzjtP27ZtU2FhoQ8rC7wnnnhC6enpioiIUExMjEaNGqVt27Z5tDl27JhycnLUqVMntW/fXtdff70OHDjg0WbPnj0aOXKk2rVrp5iYGD344IM6deqUP1fFL1atWqWsrCwlJCTIZrNp8eLFHvONMZo2bZri4+MVHh6uzMxMffPNNx5tysvLdeuttyoyMlIdOnTQuHHjVFVV5ce1CIzp06fLZrN5vHr37u2e35D/Z1bhrf3SKryxX1rV2fZLfyII+VB0dLQiIiIa3H7nzp0aMGCAunXrpk6dOvmwssBbuXKlcnJy9Pnnn2v58uU6efKkrrrqKlVXV7vb/P73v9fSpUv1zjvvaOXKldq/f7+uu+4693yn06mRI0fqxIkT+uyzz/T6669r3rx5mjZtWiBWyaeqq6uVkpIih8NR5/ynnnpKc+bM0dy5c7VmzRqdd955GjZsmI4dO+Zuc+utt+rLL7/U8uXL9f7772vVqlW6++67/bUKAXXxxRertLTU/frkk0/c8872/8xKvLFfWok39ksrq2+/9CsDnxk0aJB54IEHjDHGdOvWzfznf/6nyc7ONu3btzeJiYnm5ZdfdreV5PHKy8sLTNEBcvDgQSPJrFy50hhjzOHDh03btm3NO++8427z1VdfGUlm9erVxhhjPvjgAxMUFGTKysrcbV566SUTGRlpjh8/7t8V8CNJZtGiRe73LpfLxMXFmaeffto97fDhwyY0NNS8+eabxhhjtm7daiSZdevWudt8+OGHxmazmX379vmt9kDIy8szKSkpdc5ryP8zK2vKfmlVTdkvray+/dLfOCPkR88++6z69u2rjRs36r777tO9997rPu1cWlqqiy++WBMnTlRpaakmTZoU4Gr9q6KiQtLps2iStH79ep08eVKZmZnuNr1791ZSUpJWr14tSVq9erUuueQSxcbGutsMGzZMlZWV+vLLL/1YfWCVlJSorKzMY1tFRUWpf//+HtuqQ4cO6tu3r7tNZmamgoKCtGbNGr/X7G/ffPONEhIS1KNHD916663as2ePpIb9P7OypuyXOK0h+6XVnWm/9DeCkB9dffXVuu+++3ThhRfqoYceUufOnVVUVCRJiouLU5s2bdS+fXvFxcWpffv2Aa7Wf1wulyZMmKArrrhCffr0kSSVlZUpJCREHTp08GgbGxursrIyd5sfh6Ca+TXzrKJmXevaFj/eVjExMR7z27Rpo+jo6Fa/rfr376958+apoKBAL730kkpKSvTLX/5SR44cadD/M6tq6n6J0xqyX1pZffulv/H0eT+69NJL3f+22WyKi4vTwYMHA1hR85CTk6Pi4uLAXR9GqzZixAj3vy+99FL1799f3bp109tvv63w8PAAVta8sV/Cl+rbL8eNG+fXWjgj5Edt27b1eG+z2eRyuQJUTfMwfvx4vf/++yoqKlLXrl3d0+Pi4nTixAkdPnzYo/2BAwcUFxfnbvPTu1Vq3te0sYKada1rW/x4W/00dJ86dUrl5eWW2laS1KFDB1100UXasWNHg/6fWdG57Jc4rSH7Jf7lx/ulvxGEEBDGGI0fP16LFi3SihUrlJyc7DE/LS1Nbdu29RhGYNu2bdqzZ48yMjIkSRkZGdqyZYvHAX758uWKjIyU3W73z4o0A8nJyYqLi/PYVpWVlVqzZo3Htjp8+LDWr1/vbrNixQq5XC7179/f7zUHUlVVlXbu3Kn4+PgG/T+zEm/slzitIfsl/uXH+6W/cWkMAZGTk6M33nhDS5YsUUREhPuaeVRUlMLDwxUVFaVx48YpNzdX0dHRioyM1P3336+MjAxdfvnlkqSrrrpKdrtdt99+u5566imVlZXpkUceUU5OTqt76nNVVZXHX0olJSXatGmToqOjlZSUpAkTJmjmzJnq2bOnkpOTNXXqVCUkJGjUqFGSpJ/97GcaPny47rrrLs2dO1cnT57U+PHjdfPNNyshISFAa+UfkyZNUlZWlrp166b9+/crLy9PwcHBuuWWWxr0/8xKvLFfWsm57pdWVt9+6XeBvm2tNfvp7fPPPfecx/yUlBSP2+R/+r4100+GC6h55efnu9scPXrU3HfffaZjx46mXbt2ZvTo0aa0tNRjObt37zYjRoww4eHhpnPnzmbixInm5MmTfl4b3ysqKqpze40dO9YYc/pW3alTp5rY2FgTGhpqhg4darZt2+axjO+++87ccsstpn379iYyMtJkZ2ebI0eOBGBt/Oumm24y8fHxJiQkxHTp0sXcdNNNZseOHe75Dfl/ZhXe2i+twhv7pVWdbb/0J5sxxvgzeAEAADQX9BECAACWRRACAACWRRACAACWRRACAACWRRACAACWRRACAACWRRACAACWRRACAACWRRACAACWRRACAACWRRACAACWRRACAACW9f/Ma+334vVzRQAAAABJRU5ErkJggg==",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "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": 20,
   "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": null,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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ARiG8AAAAoxBeAACAUQgvAADAKIQXAABgFMILAAAwCuEFAAAYhfACAACMQngBAABGIbwAAACjEF4AAIBRCC8AAMAohBcAAGAUwgsAADAK4QW3jdIyq+3rzBPn7ZYBAOYgvOC2sOlAjmIXbbMtj/7zVxrw+8+06UCOC7sCANQG4QWN3qYDOUpatVd5hUV247kFV5W0ai8BBgAMQ3hBo1ZaZtXcDw+qshNE5WNzPzzIKSQAMAjhBY1a5onzyim46vB5q6ScgqvKPHG+/poCANwSwgsatbMXHQeX2tQBAFyP8IJG7Y7mPnVaBwBwPcILGrWo8ACF+PvI4uB5i6QQfx9FhQfUZ1sAgFtAeEGj5u5m0exHIiSpQoApX579SITc3RzFGwBAQ0N4QaM3qFuI3hhxj+7w87YbD/b30Rsj7tGgbiEu6gwAUBserm4AqA+DuoWof8fWipzziSQpLfFe3dcpkCMuAGAgjrzgtnFjUIkKDyC4AIChCC8AAMAohBcAAGAUwgsAADAK4QUAABiF8AIAAIxCeAEAAEYhvAAAAKMQXgAAQLWUllltX2eeOG+3XJ8ILwCM0FAmTeB2telAjmIXbbMtj/7zVxrw+8+06UBOvfdSL+Fl6dKlCgsLk4+Pj/r27avMzMwq69euXasuXbrIx8dHkZGR+uijj+qjTQANVEOaNIHb0aYDOUpatVd5hUV247kFV5W0am+9vxadHl7effddpaSkaPbs2dq7d6969OihuLg4nT17ttL6nTt3avjw4RozZoz27dunoUOHaujQoTpw4ICzWwXQADW0SRO43ZSWWTX3w4Oq7Fhn+djcDw/W69FQp9+YcdGiRRo7dqwSExMlScuXL9fGjRv19ttva9q0aRXqU1NTNWjQIP3mN7+RJL300ktKT0/XH//4Ry1fvrza37e4uFjFxcUVxt3c3OTh4WFX54jFYpGnp6dt2UOltnU8VFZl7bVr12S1Vr4jnVUrSV5eXrWqLSkpUVlZWZ3Uenp6ymKxOLW2tLRUpaWlNaotLi6pdB96eHjIzc2tWtutj9qysjKVlJQ4rHV3d5e7u3uDqbVarbp27Vqd1N74+rRarbpaVKw5G752OGladH3SjO0apLJSx/3W5HV/K3NETWpvxzmi/DVYcsPfzQ1pjnDkdp8jdp04r5yCqw63YZWUU3BVO4/mqW94QIXt1mSOqC6nhpfi4mLt2bNH06dPt425ubkpNjZWGRkZla6TkZGhlJQUu7G4uDitW7eu0vqioiIVFf3nL7LCwkJJ0sKFC+Xj41OhvlOnTnrqqadsy6+++qrDf9T27dtr9OjRtuVhPvvlYylR6sJ9FWrbtGmjsWPH2paXLl2qgoKCSrcbGBio8ePH25ZXrFih/Pz8Smv9/f01efJk23JaWprOnDlTaa2vr68t9EnS6tWrderUqUprPT09NWPGDNvye++9p6NHj1ZaK0mzZ8+2ff3BBx/o4MGDDmunT59um8j+53/+R//7v//rsPb5559X06ZNJUmbN2/W7t27HdZOmjRJLVq0kCRt2bLF4f9DkpSUlKQ77rhDkrR9+3Zt23b9lMPIJtefv3EfPvPMM2rbtq0k6csvv9Snn37qcLujRo1SWFiYJGnPnj36+OOPHdYOHz5cd911lyRp//79Wr9+vcPaX/ziF7r77rslSYcOHdLf/vY3h7Xx8fHq2bOnJOnYsWNas2aNw9rBgwcrKipKkpSdna2VK1c6rI2NjVX//v0lSTk5OXrrrbcc1g4cOFAxMTGSpPz8fL3xxhsOa6Ojo/XQQw9JkgoKCpSamuqwtk+fPhoyZIgk6cqVK5ry+zeVW9zZYX35pJlx7Kw+++ubDusiIiI0bNgw2/L8+fMd1t7KHJGamqorV65UWssccd3IJtL/+6GXbbmhzRGVud3niG9LAiR1cLiNcm+tWqvPPM5Lqv0cUV1OPW107tw5lZaWKigoyG48KChIubm5la6Tm5tbo/r58+fL39/f9ggNDa2b5gG43A9Wz5sXScq/WHTzIgC10sTi+KhJberqgsVa1THDW3TmzBm1bdtWO3fuVHR0tG38hRde0LZt27Rr164K63h5eWnlypUaPny4bWzZsmWaO3eu8vLyKtRXduQlNDRU+fn58vPzq1Bf20PCV4pL1H3W9QuHd8+Mla+Xh8Na6fY8JFyuoZ42ulJcoj4vX/+L6cZ9eLsfEr7VWmeeNvrHN3ka+ec9DuvLrRnbV71DK77eK9uuxGmj2tTWxRxR/hoskZsOzhskXy+PBjVHOHK7zxGlZVY9sGi78gqLKj2Fa5EU7Oetz1Luk7ubpcJ2qztHFBYWyt/fXwUFBZX+/r6RU08btW7dWu7u7hVCR15enoKDgytdJzg4uEb13t7e8vb2rjDu5eVl92JypDo15UrkfsO2q/6nu3EyuZmGUHvjZG1CbU3OkZbXlsjtpvuwNtut61o3N7dq/3/ZEGotFovTavt1ClKIv49yC646njT9fRQV3so2aVZHTV73zqptCK/7+p4jbnwN1uV2K9MQXsuNaY6Y8+jdSlq1VxbJ7rVY/qqb/ejdauJT8XexVLPXfXU59bSRl5eXevfurS1bttjGysrKtGXLFrsjMTeKjo62q5ek9PR0h/UAGi93N4tmPxIh6T+TZDnbpPlIRI2CC4CaG9QtRG+MuEd3+NkHlGB/H70x4h4N6hZSr/04/a3SKSkpWrFihVauXKlDhw4pKSlJly9ftr37KCEhwe6C3kmTJmnTpk1auHChDh8+rDlz5mj37t1KTk52dqsAGqCGNmkCt6tB3UL0acpA23Ja4r36x9SfuuQ16PS3Sj/xxBPKz8/XrFmzlJubq549e2rTpk22i3Kzs7Nt5/EkqV+/fnrnnXc0c+ZMzZgxQ506ddK6devUrVs3Z7cKoIEa1C1E/Tu2VuScTyRdnzTv6xTIERegnt34mosKD3DZa9Dp4UWSkpOTHR452bp1a4WxYcOG2b2tEQAayqQJwPW4txEAADAK4QUAABiF8AIAqBfcGRx1hfACAHA67gyOukR4AQA4FXcGR10jvAAAnKa0zKq5Hx50eGdw6fqdwTmFhJogvAAAnCbzxHnlFFx1+Hz5ncEzT5yvv6ZgPMILAMBpzl50HFxqUwdIhBcAgBPd0dynTusAifACAHCiqPAAhfj7VLixZjmLpBB/H0WFB9RnWzAc4QUA4DTcGRzOQHgBADgVdwZHXauXGzMCAG5v3BkcdYkjLwCAesGdwVFXCC8AAMAohJdq4oZiAAA0DISXauCGYgAANByEl5vghmIAADQshJcqcEMxAAAaHsJLFbihGAAADQ/hpQrcUAwAgIaH8FIFbigGAEDDQ3ipAjcUAwCg4SG8VIEbigEA0PAQXm6CG4oBANCwcGPGauCGYgAANBwceakmbigGAEDDQHgBAABGIbwAAACjEF4AAIBRCC8AAMAohBcAAGAUwgsAADAK4QUAABiF8AIAAIxCeAEAAEYhvAAAAKMQXgAAgFEILwAAwCiEFwAAYBTCCwAAMArhBQAAGIXwAgAAjEJ4AQAARiG8AAAAoxBeAACAUQgvAADAKIQXAABgFMILAAAwCuEFAAAYhfACAACMQngBAABGIbwAAACjEF4AAIBRCC8AAMAohBcAAGAUwgsAADAK4QUAABiF8AIAAIxCeAEAAEYhvAAAAKMQXgAAgFGcGl7Onz+vp59+Wn5+fmrRooXGjBmjS5cuVblOTEyMLBaL3ePZZ591ZpsAAMAgHs7c+NNPP62cnBylp6fr2rVrSkxM1Lhx4/TOO+9Uud7YsWM1b94827Kvr68z2wQAAAZxWng5dOiQNm3apK+++kp9+vSRJL3++ut6+OGH9eqrr6pNmzYO1/X19VVwcLCzWgMAAAZz2mmjjIwMtWjRwhZcJCk2NlZubm7atWtXleuuXr1arVu3Vrdu3TR9+nRduXLFYW1RUZEKCwvtHgAAoPFy2pGX3Nxc3XHHHfbfzMNDAQEBys3NdbjeU089pfbt26tNmzb65z//qalTp+rIkSN6//33K62fP3++5s6dW6e9AwCAhqvG4WXatGn6/e9/X2XNoUOHat3QuHHjbF9HRkYqJCREDz74oI4fP64777yzQv306dOVkpJiWy4sLFRoaGitvz8AAGjYahxepkyZotGjR1dZ06FDBwUHB+vs2bN24yUlJTp//nyNrmfp27evJOnYsWOVhhdvb295e3tXe3sAAMBsNQ4vgYGBCgwMvGlddHS0Lly4oD179qh3796SpM8++0xlZWW2QFIdWVlZkqSQkJCatgoAABohp12w27VrVw0aNEhjx45VZmamduzYoeTkZD355JO2dxr961//UpcuXZSZmSlJOn78uF566SXt2bNHJ0+e1IYNG5SQkKD7779f3bt3d1arAADAIE79kLrVq1erS5cuevDBB/Xwww9rwIAB+tOf/mR7/tq1azpy5Ijt3UReXl769NNP9dBDD6lLly6aMmWKHn/8cX344YfObBMAABjEqR9SFxAQUOUH0oWFhclqtdqWQ0NDtW3bNme2BAAADMe9jQAAgFEILwAAwCiEFwAAYBTCCwAAMArhBQAAGIXwAgAAjEJ4AQAARiG8AAAAoxBeAACAUQgvAADAKIQXAABgFMILAAAwCuEFAAAYhfACAACMQngBAABGIbwAAACjEF4AAIBRCC8AAMAohBcAAGAUwgsAADAK4QUAABiF8AIAAIxCeAEAAEYhvAAAAKMQXgAAgFEILwAAwCiEFwAAYBTCCwAAMArhBQAAGIXwAgAAjEJ4AQAARiG8AAAAoxBeAACAUQgvAADAKIQXAABgFMILAAAwCuEFAAAYhfACAACMQngBAABGIbwAAACjEF4AAIBRCC8AAMAohBcAAGAUwgsAADAK4QUAABjFw9UNAPXF18tDJ18Z4uo2AAC3iCMvAADAKIQXAABgFMILAAAwCuEFAAAYhfACAACMQngBAABGIbwAAACjEF4AAIBRCC8AAMAohBcAAGAUwgsAADAK4QUAABiF8AIAAIxCeAEAAEYhvAAAAKM4Lbz89re/Vb9+/eTr66sWLVpUax2r1apZs2YpJCRETZo0UWxsrI4ePeqsFgEAgIGcFl6Ki4s1bNgwJSUlVXudP/zhD3rttde0fPly7dq1S02bNlVcXJyuXr3qrDYBAIBhPJy14blz50qS0tLSqlVvtVq1ZMkSzZw5U/Hx8ZKkv/zlLwoKCtK6dev05JNPOqtVAABgEKeFl5o6ceKEcnNzFRsbaxvz9/dX3759lZGR4TC8FBUVqaioyLZcWFjo9F4BALgd+Xp56OQrQ1zdRsMJL7m5uZKkoKAgu/GgoCDbc5WZP3++7SgPgMaroUyaAFyvRte8TJs2TRaLpcrH4cOHndVrpaZPn66CggLb4/Tp0/X6/QEAQP2q0ZGXKVOmaPTo0VXWdOjQoVaNBAcHS5Ly8vIUEhJiG8/Ly1PPnj0druft7S1vb+9afU8AAGCeGoWXwMBABQYGOqWR8PBwBQcHa8uWLbawUlhYqF27dtXoHUsAAKBxc9pbpbOzs5WVlaXs7GyVlpYqKytLWVlZunTpkq2mS5cu+uCDDyRJFotFkydP1ssvv6wNGzZo//79SkhIUJs2bTR06FBntQkAAAzjtAt2Z82apZUrV9qWe/XqJUn6/PPPFRMTI0k6cuSICgoKbDUvvPCCLl++rHHjxunChQsaMGCANm3aJB8fH2e1CQAADOO08JKWlnbTz3ixWq12yxaLRfPmzdO8efOc1RYAADAc9zYCAABGIbwAAACjEF4AAIBRCC8AAMAohBcAAGAUwgsAADAK4QUAABilwdxVGgDQuHFncNQVjrwAAACjEF4AAIBRCC8AAMAohBcAAGAUwgsAADAK4QUAABiF8AIAAIxCeAEAAEYhvAAAAKMQXgAAgFEILwAAwCjc26iauCcHAAANA0deAACAUQgvAADAKIQXAABgFMILAAAwCuEFAAAYhfACAACMQngBAABGIbwAAACjEF4AAIBRCC8AAMAohBcAAGAUwgsAADAK4QUAABiF8AIAAIxCeAEAAEbxcHUDdc1qtUqSCgsLXdwJAACorvLf2+W/x6vS6MLLxYsXJUmhoaEu7gQAANTUxYsX5e/vX2WNxVqdiGOQsrIynTlzRs2bN5fFYqnTbRcWFio0NFSnT5+Wn59fnW4b9YN9aDb2n/nYh+Zz1j60Wq26ePGi2rRpIze3qq9qaXRHXtzc3NSuXTunfg8/Pz9edIZjH5qN/Wc+9qH5nLEPb3bEpRwX7AIAAKMQXgAAgFEILzXg7e2t2bNny9vb29WtoJbYh2Zj/5mPfWi+hrAPG90FuwAAoHHjyAsAADAK4QUAABiF8AIAAIxCeAEAAEYhvKDRi4mJ0eTJk13dBtAojR49WkOHDnV1G7jNNLpP2AUA1J/U1NRq3UgPZoiJiVHPnj21ZMkSV7dSJcILAKDWqvtx7kBd4rRRNf3tb39TZGSkmjRpolatWik2NlaXL192dVuoppKSEiUnJ8vf31+tW7fWiy++yF+LDUxMTIwmTpyoyZMnq2XLlgoKCtKKFSt0+fJlJSYmqnnz5urYsaM+/vhjSVJaWppatGhht41169bV+Q1ZcZ2jOfDHp40uXryop59+Wk2bNlVISIgWL15c4dRtWFiYXn75ZSUkJKhZs2Zq3769NmzYoPz8fMXHx6tZs2bq3r27du/ebVvn3//+t4YPH662bdvK19dXkZGRWrNmTT3+CzR+o0eP1rZt25SamiqLxSKLxaLjx49rzJgxCg8PV5MmTdS5c2elpqbarVfZqfmhQ4dq9OjRTuuV8FINOTk5Gj58uH71q1/p0KFD2rp1qx577DF++Rlk5cqV8vDwUGZmplJTU7Vo0SK99dZbrm4LP7Jy5Uq1bt1amZmZmjhxopKSkjRs2DD169dPe/fu1UMPPaSRI0fqypUrrm71tlKTOTAlJUU7duzQhg0blJ6eru3bt2vv3r0V6hYvXqz+/ftr3759GjJkiEaOHKmEhASNGDFCe/fu1Z133qmEhATb97h69ap69+6tjRs36sCBAxo3bpxGjhypzMxMp//8t4vU1FRFR0dr7NixysnJUU5Ojtq1a6d27dpp7dq1OnjwoGbNmqUZM2bovffec22zVtzUnj17rJKsJ0+edHUrqIWBAwdau3btai0rK7ONTZ061dq1a1cXdoUfGzhwoHXAgAG25ZKSEmvTpk2tI0eOtI3l5ORYJVkzMjKsf/7zn63+/v522/jggw+sTGt1r6o5cNSoUdb4+Hir1Wq1FhYWWj09Pa1r1661PX/hwgWrr6+vddKkSbax9u3bW0eMGGFbLt+vL774om0sIyPDKsmak5PjsK8hQ4ZYp0yZcgs/GX5s4MCBdvuqMhMmTLA+/vjjVa4THx9vHTVqVN03+H848lINPXr00IMPPqjIyEgNGzZMK1as0Pfff+/qtlADP/nJT+xOJ0RHR+vo0aMqLS11YVf4se7du9u+dnd3V6tWrRQZGWkbCwoKkiSdPXu23nu7nVV3Dvz222917do1RUVF2cb8/f3VuXPnCrU37uvy/VrVvi4tLdVLL72kyMhIBQQEqFmzZtq8ebOys7Pr5oeEQ0uXLlXv3r0VGBioZs2a6U9/+pPL/90JL9Xg7u6u9PR0ffzxx4qIiNDrr7+uzp0768SJE65uDWhUPD097ZYtFovdWHkALSsrk5ubW4XTFteuXXN+k7chZ8yBle1XR/takhYsWKDU1FRNnTpVn3/+ubKyshQXF6fi4uJa94Cb++tf/6rnn39eY8aM0SeffKKsrCwlJiba/bu74rVIeKkmi8Wi/v37a+7cudq3b5+8vLz0wQcfuLotVNOuXbvslr/88kt16tRJ7u7uLuoItyowMFAXL160u3A+KyvLdQ01ctWZAzt06CBPT0999dVXtrGCggJ98803t/z9d+zYofj4eI0YMUI9evRQhw4d6mS7sOfl5WV3RHrHjh3q16+fxo8fr169eqljx446fvy43TqBgYHKycmxLZeWlurAgQNO7ZPwUg27du3S7373O+3evVvZ2dl6//33lZ+fr65du7q6NVRTdna2UlJSdOTIEa1Zs0avv/66Jk2a5Oq2cAv69u0rX19fzZgxQ8ePH9c777yjtLQ0V7fVKFV3DmzevLlGjRql3/zmN/r888/19ddfa8yYMXJzc7vld4F16tRJ6enp2rlzpw4dOqRf//rXysvLu6VtoqKwsDDt2rVLJ0+e1Llz59SpUyft3r1bmzdv1jfffKMXX3zRLpxK0k9/+lNt3LhRGzdu1OHDh5WUlKQLFy44tU/CSzX4+fnpiy++0MMPP6y77rpLM2fO1MKFCzV48GBXt4ZqSkhI0A8//KCoqChNmDBBkyZN0rhx41zdFm5BQECAVq1apY8++sj2ttk5c+a4uq1GqSZz4KJFixQdHa2f/exnio2NVf/+/dW1a1f5+PjcUg8zZ87UPffco7i4OMXExCg4OJhP9nWC559/Xu7u7oqIiFBgYKDi4uL02GOP6YknnlDfvn3173//W+PHj7db51e/+pVGjRqlhIQEDRw4UB06dNADDzzg1D4t1h+fqAIAoI5cvnxZbdu21cKFCzVmzBhXt4NGgk/YBQDUmX379unw4cOKiopSQUGB5s2bJ0mKj493cWdoTAgvAIA69eqrr+rIkSPy8vJS7969tX37drVu3drVbaER4bQRAAAwChfsAgAAoxBeAACAUQgvAADAKIQXAABgFMILAAAwCuEFAAAYhfACAACMQngBAABG+f+OlMvxhxr3NwAAAABJRU5ErkJggg==",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "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": "3.9.18"
  },
  "orig_nbformat": 4
 },
 "nbformat": 4,
 "nbformat_minor": 2
}