From c43d323bfaf93b1df6486074e5eff01ef19fe4d1 Mon Sep 17 00:00:00 2001
From: Mauro Donega <mauro.donega@cern.ch>
Date: Tue, 30 Mar 2021 18:15:13 +0200
Subject: [PATCH] likelihoods
---
notebooks/binnedLikelihood.ipynb | 727 ++++++++----------
notebooks/binnedLikelihood_probfit.ipynb | 540 +++++++++++++
notebooks/ubinnedLikelihood.ipynb | 457 +++++++++++
notebooks/unbinnedLikelihood.ipynb | 854 ---------------------
notebooks/unbinnedLikelihood_probfit.ipynb | 720 +++++++++++++++++
5 files changed, 2039 insertions(+), 1259 deletions(-)
create mode 100644 notebooks/binnedLikelihood_probfit.ipynb
create mode 100644 notebooks/ubinnedLikelihood.ipynb
delete mode 100644 notebooks/unbinnedLikelihood.ipynb
create mode 100644 notebooks/unbinnedLikelihood_probfit.ipynb
diff --git a/notebooks/binnedLikelihood.ipynb b/notebooks/binnedLikelihood.ipynb
index 1e29157..080fc3a 100644
--- a/notebooks/binnedLikelihood.ipynb
+++ b/notebooks/binnedLikelihood.ipynb
@@ -4,508 +4,425 @@
"cell_type": "markdown",
"metadata": {},
"source": [
- "# Binned Likelihood\n",
- "\n",
- "\n",
- "In this notebook we will be using probfit together with iminuit to perform a Binned Likelihood fit.\n",
- "\n",
- "probfit:\n",
- "https://probfit.readthedocs.io/en/latest/\n",
- "\n",
- "iMinuit:\n",
- "https://iminuit.readthedocs.io/en/latest/index.html#\n",
- "\n",
- " "
+ "# Solutions 7\n",
+ "Maximum Likelihood method"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 205,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "from __future__ import print_function\n",
+ "import numpy as np\n",
+ "%matplotlib inline\n",
+ "import matplotlib.pyplot as plt\n",
+ "from scipy.optimize import curve_fit, minimize, fsolve\n",
+ "from scipy.stats import norm, chi2, lognorm"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 151,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "measurements = np.array([97.8621, 114.105, 87.7593, 93.2134, 86.6624, 87.4629, 79.7712, \\\n",
+ "91.5024, 87.7737, 89.6926, 133.506, 91.4124, 94.4401, 97.3968, \\\n",
+ "108.424, 103.197, 88.2166, 142.217, 89.0393, 102.438, 95.7987, \\\n",
+ "94.5177, 96.8171, 90.903, 132.463, 92.3394, 84.1451, 87.3447, \\\n",
+ "92.2861, 84.4213, 124.017, 90.4941, 95.7992, 92.3484, 95.9813, \\\n",
+ "88.0641, 101.002, 97.7268, 137.379, 96.213, 140.795, 99.9332, \\\n",
+ "130.087, 108.839, 90.0145, 100.313, 87.5952, 92.995, 114.457, \\\n",
+ "90.7526, 112.181, 117.857, 95.2804, 115.922, 117.043, 104.317, \\\n",
+ "126.728, 87.8592, 89.9614, 100.377, 107.38, 88.8426, 93.3224, \\\n",
+ "138.947, 102.288, 123.431, 114.334, 88.5134, 124.7, 87.7316, 84.7141, \\\n",
+ "91.1646, 87.891, 121.257, 92.9314])"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## 1-D Maximum likelihood fit"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
- "### Fit an exponential"
+ "We have a set of measurements which are distributed according to the sum of two Gaussians (e.g. this can be signal and background).\n",
+ "\n",
+ "$\\rho = \\frac{1}{3}\\frac{1}{\\sqrt{2\\pi \\sigma^2}} e^{-\\frac{1}{2}\\left(\\frac{x-p}{\\sigma}\\right)^2} + \\frac{2}{3}\\frac{1}{\\sqrt{2\\pi \\sigma_b^2}} e^{-\\frac{1}{2}\\left(\\frac{x-p_b}{\\sigma_b}\\right)^2}$ \n",
+ "\n",
+ "where for one of the two peaks the parameters are known already\n",
+ "\n",
+ "$p_b = 91.0$ \n",
+ "$\\sigma_b = 5.0$ \n",
+ " "
]
},
{
"cell_type": "code",
- "execution_count": 1,
+ "execution_count": 228,
"metadata": {},
"outputs": [],
"source": [
- "import numpy as np\n",
- "%matplotlib inline\n",
- "import matplotlib.pyplot as plt\n",
- "from math import exp, pi, sqrt\n",
- "import probfit\n",
- "from probfit import BinnedLH\n",
- "from iminuit import Minuit, describe\n",
- "from scipy.stats import norm, chi2, lognorm\n",
- "import scipy.stats"
+ "def likelihood_point(x, position, width):\n",
+ " return 1.0/3/np.sqrt(2*np.pi*width**2)*np.exp(-0.5*((x-position)/(width))**2.0) + 2.0/3/np.sqrt(2*np.pi*5**2)*np.exp(-0.5*((x-91)/(5))**2.0)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "First, we assume the width of the peak we want to fit is already known: $\\sigma = 15.0$.\n",
+ "Perform a 1-D Maximum Likelihood fit for the position of the peak $p$.\n",
+ "\n",
+ "Complete the functions below which return the likelihood and negative log likelihood (NLL)."
]
},
{
"cell_type": "code",
- "execution_count": 2,
+ "execution_count": 347,
"metadata": {},
"outputs": [],
"source": [
- "# Generate data\n",
- "# set the seed to always get the same samples\n",
- "np.random.seed(seed=123456)\n",
+ "def likelihood_1d(params):\n",
+ " return np.prod([likelihood_point(x, params[0], 15.0) for x in measurements])\n",
"\n",
- "# Generate a toy dataset on an exponential distribution (background)\n",
- "# pdf = lambda * exp(-lambda * x) ; scale = 1/lambda\n",
- "data = scipy.stats.expon.rvs(loc= 100, scale = 25, size=10000)"
+ "def nll_1d(params):\n",
+ " return -np.log(likelihood_1d(params))"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Minimize the NLL and give the best-fit result, including asymetric errors and plot the NLL."
]
},
{
"cell_type": "code",
- "execution_count": 3,
+ "execution_count": 355,
"metadata": {},
"outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "position: 117.72333147980623\n",
+ "negative error: [3.31211666]\n",
+ "positive error: [3.39091994]\n"
+ ]
+ },
{
"data": {
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\n",
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\n",
"text/plain": [
- "<Figure size 360x360 with 1 Axes>"
+ "<Figure size 432x288 with 1 Axes>"
]
},
- "metadata": {
- "needs_background": "light"
- },
+ "metadata": {},
"output_type": "display_data"
}
],
"source": [
- "plt.figure(figsize=[5,5])\n",
- "plt.subplot(111)\n",
- "plt.hist(data, bins=150, range=[100,400], color='blue', alpha=0.5)\n",
- "plt.xlabel(r'x [units]')\n",
- "plt.ylabel(r'Entries / bins size = 2')\n",
- "plt.yscale('log', nonposy='clip')"
+ "solution = minimize(nll_1d, [100.0], method='CG')\n",
+ "min_pos = solution.x[0]\n",
+ "min0 = solution.fun\n",
+ "scan_points = np.linspace(110.0,126.0,50)\n",
+ "plt.plot(scan_points, [nll_1d([x]) - min0 for x in scan_points])\n",
+ "\n",
+ "nll_1sigma = lambda x: nll_1d([x]) - min0 - 0.5\n",
+ "print(\"position:\", min_pos)\n",
+ "print(\"negative error:\", min_pos - fsolve(nll_1sigma, min_pos-0.5))\n",
+ "print(\"positive error:\", fsolve(nll_1sigma, min_pos+0.5) - min_pos)\n",
+ "plt.show()"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## 2-D Likelihood fit"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Now we perform the 2-D Maximum Likelihood fit, fitting for both $\\sigma$ and $p$ at the same time."
]
},
{
"cell_type": "code",
- "execution_count": 4,
+ "execution_count": 350,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "def likelihood(params):\n",
+ " return np.prod([likelihood_point(x, params[0], params[1]) for x in measurements])\n",
+ "\n",
+ "def nll(params):\n",
+ " return -np.log(likelihood(params))"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Minimize the NLL and find the best-fit result."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 353,
"metadata": {},
"outputs": [
{
- "data": {
- "text/plain": [
- "['loc', 'scale']"
- ]
- },
- "execution_count": 4,
- "metadata": {},
- "output_type": "execute_result"
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "position: 118.31548192622421 width: 13.629783202046086\n"
+ ]
}
],
"source": [
- "def exp_func(x, loc, scale):\n",
- " return scipy.stats.expon.pdf(x, loc, scale)\n",
- "\n",
- "blh = BinnedLH(exp_func, data, bins=150, bound=(100,400))\n",
- "describe(blh)"
+ "solution = minimize(nll, [120.0, 10], method='CG')\n",
+ "print(\"position:\", solution.x[0], \"width:\", solution.x[1])"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Create a 2D contour plot of the 1, 2 and 3 $\\sigma$ contours of the NLL and plot the best-fit solution."
]
},
{
"cell_type": "code",
- "execution_count": 5,
+ "execution_count": 354,
"metadata": {},
"outputs": [
{
"data": {
- "image/png": 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FGzvkCbQQLiQJMZwIm80Fg3IZ0CMzMM65oal5fhx5Ai2Ee0hCDMd8sLJyJTQ2ht3V2nQ2KaBfjo/HVuyKT3xCiJiShBjOuefC0KFQWgpbt4bd1RznnONrHg3pUVBV10CJzJ8ohCtIQgwnwvIb07J7p/LCzROa50/0KE5U1AUersx9Yj3XPbMpjgELIaIhCbE9EfYjmsw7xbzcTL5XODDQr1hb38Se45WUnKqhui5881sIYQ9JiO0pKgKfD7Ztg2PHIvrIsnunsuGB6a3mT2xo1BSX1XDgRJU0oYVwIEmI7cnKgmnTjNcrVnToo9b5E6201lKKI4QDSUKMRAebzVbL7p3KTRcNCdqqpBRHCAeShBgJMyGuWmUsU9pB1pKcdI/i7B4+Cgblhv+QECLhEpYQlVLfVUr9QSn1hlJqVqLOGxP5+UYJzqlTsHlzhz9unRln6R2TOVVTL0+bhXCgqBKiUup5pdRxpdSOoO1zlFK7lVL7lFIPAmit/6q1vg24CbgumvPaogPlN6GYC1UVDMqlqUlLbaIQDhTtHeIiYI51g1IqDXgSuBwYBVyvlBpl2eVh/+/dJYp+RKtth8qorW+U2kQhHCiqhKi1Xg+cDNo8Adintd6vta4DlgDXKMOjwHKtdehZV51s6lTjifNnn0FJSacPs3l/aYvaxF3fVHDgRKXcLQrhAEpr3f5e4Q6g1GDgba31aP/7ecAcrfUC//sfABOBPcCPgK3Ap1rrp9s43u3A7QB9+/YtWLJkScSxVFZW0q1bt05/l/aM/tnP6L1xI7vuu49vrriiU8eormukqrKSb2pabldKMbR3V7Iy0mIQaezE+5rGilviBPfE6pY4oeOxTps2bZvWujB4ezyWIQ21MqfWWv8G+E17H9ZaLwQWAhQWFuqioqKIT7xu3To6sn+H3XgjbNzIiP37GRHFeZ59+W3+sNdLeW3LJ9Z5uYoND3T+uPEQ92saI26JE9wTq1vihNjFGo+nzMXAQMv7POBIHM6TeGY/4urVUF/f6cPkn9WNF26e0OpfjrqGRulTFMJG8UiIW4FhSqkhSqkMYD7wZkcOYOu6zOEMHmwsQFVRAR98ENWhCgblMrJ/NulpitysdBTG5LI7j0qfohB2ibbs5iVgEzBcKVWslLpVa90A3A2sBHYCL2utv+jIcW1flzmcKMtvrLJ9XgrOyWXBlO8EHrRojMQoSw8IkXjRPmW+XmvdX2vt1Vrnaa2f829fprU+V2v9Ha31r2ITqkPEqPwGYOkdk1l6x+SQk8vK0gNCJJ4M3euoSy4x1lv54gs4fDgmh7ROAmHmRQ2883lydL0K4RaOTIiO7UMEYyW+mTON18uXx+ywy+6dytafzWRkf2MuxXN6ZlFe2yDNZiESyJEJ0dF9iBDTZnOwbJ+XHF86h09WU1xWw/ee3ihJUYgEcWRCdDwzIb77Lpw5E9NDL71jMleMOTuwjGmThr98XBzTcwghQnNkQnR0kxkgLw/GjIGqKnj//ZgfftLQXi1qFF/dVix3iUIkgCMTouObzBDT8ptgBYNyW8yy3dgoT5yFSARHJkRXiGM/IsBTNxYGSnFksXshEkMSYmdNngzdu8Pu3bB/f8wPb129b2jvrrLYvRAJIAmxs7xemOWf+DuG5TdW2T4vA3pkku3zxuX4QoiWHJkQHf9QxRTnZrM5kqWitl5m2BYiARyZEF3xUAVgjn+y8LVroaYm/L6dtO1QGbu+qQjMsC1JUYj4cWRCdI3+/WHcOCMZ/u1vcTnF5v2lgZrE2vom7l3ySVzOI4SQhBi9OJbfQMslTBXGnIlylyhEfEhCjFac+xGtEz+AMTXY957eKBPJChEHjkyIrnmoAjBxIvTsCV99BXv3xuUU2T4vXdLTAnMmNmlaLT8ghIieIxOiax6qAKSlwezZxus4Pm1+Yv6FgaazR0G6R8mTZyFizJEJ0XXi3GyG5qZzepqie2Y6h0qr5cmzEDEWj1X3Us/s2aCU8aS5qgq6do3bqRoaNWXVzc3l2vomrv/DZi4c2COwbekdkwECfYzmeyFEeHKHGAtnnQXjxxtTga1dG7fThOo3NJvPQojoSUKMlTiX3wAt+hEVcFZ2BiP6ZQNQcqqGitqWS6PKCBchOkYSYqxY+xG1Dr9vJ1knfBjZP5shvbtRXddIdV0jxWU1LZYwlREuQnScIxOiq8puTIWF0KcPHDoEu+I3M411woeK2noOlVYHfmddwvS1j4sDI1xkBT8hIuPIhOiqshuTx9M8tjmOzWZzwgdzqYFQ96L1DU1okPkUheggRyZE10pA+Y1V8HrO5ktvuoe/H5cXaF4vXjCJgkG5CYlJCDeTsptYmjXLuFN8/32oqIDs7LiezuxT3PdtFfl9jFKf8toGnph/IQWDcsn2ecn2eSUZChEhuUOMpV69YNIkqK83VuRLAGNYnyeQ/Ab0yAyZAK97ZpOMfRaiHZIQYy0B5TfBRvXPCVl8bfY1tkeSpRAGaTLH2uWXw8MPN5ffqPgWTVsTXqTJL9J9hUg1cocYa2PHQr9+UFICO3bYEkKoOz6zSDu4eFsI0cyRCdGVdYgmjyfhT5vDue6ZTcx9Yn2gSHvXNxWSFIVogyMToivrEK0clBDBePJsFmmHmktRhvgJYXBkQnS9mTONeRI/+AAccJeb40tvcxkCGeInRDNJiPHQowdcfDE0NsLq1Qk/ffAdX7bP22oZAjP5WRexkiF+ItVJQowXG8pvoPUd37HyWkpOGUukWpchMJOfdbSLN93DO58fkRIckbIkIcaL2Y+4fDk0NSXstNY7vrr6psDM2ru+qSDdo1qNb7bOoLN4wSSyfV5AahNFapKEGC/nnw8DBsA338BnnyXstNY7Po9HtViYqqFJhxzfnO3zcrqmnsdWxG+WHiHcQBJivChlS7PZesf3y2tGt1iYKseXHnZ4nxCpThJiPNlUfmMmvX+YeE4gOb5y50Usu3dqi/2kgFuIliQhxtNll4HXC5s3w8mTtoQQ6o7wy6PlLRLh0jsmM6p/DhW19YEHMubs29V1jXaELYQtJCHGU04OTJliPFRZtcruaIDm5Besorae4rKawAMZc/btAyeqpDZRpAxJiPFmQz9ipLPcmMxSnVCr+mmtpTZRpAxHJkRXj2UOZvYjrliR0PIbU7jkaPYXWtdfAcjKSAvMvq2UarX8gJTkiGTlyITo+rHMViNHwqBB8O23sG2b3dEEWPsLX/no60AC9CgY3CuLkf2NhzFDeneVJ9IiZTgyISYVm8pvwgnuL2xs0vTOziAvN5MR/bJbzL6dlZFmb7BCJJAkxERw0Ow3ofoLveke+nTrEljeVIhUJQkxEaZPh4wM2LrVaDrbyDq0D4xibeuQvWD7T1QF+gs72ncofY3CbSQhJkLXrlBUZCwpsHKlraG0GNqnIC+3ZY1iJE+oZf5EkawkISaKQ/oRrUP7zP7CUNpKjNaHMTJ/okg2khATxexHXLnSmCfRRuYDk870F1pn35b5E0WykVX3EmXYMPjOd+Crr8jZtcsY1ucgkRZym7NvN+nmKcSESBZyh5golvKbnlu22BxM5JqadKC/sKK2nvLaBs7pmdVqCrFQpK9RuI0kxETyN5t7bd5scyCG9h6gbDtURm19I8VlNVy/cBM7jxp9h4dPVpPjS6dgUG6bT5JlrRbhRtJkTqSiIvD5yN6715g4tl8/W8KItHm8eX9p85IDjbrFZLOhxj0Hfza4r1FGvAinkzvERMrMNGoSwRjb7HCThvYKDOnzpqkWw/tyfOH/LQ1eq0X6GoUbSEJMNIeU30SiYFAuPm8aebmZvHT75MD45rbKdazN5+C1WuTuULiBNJkTzSy/WbUKGhog3dl/BB6PCkwwa45xjpS5vyRD4RZyh5hoQ4dSPXCgsYD9JhnWJoSTSEK0QenEicYLFzSbQzEfylz3zKZAac3cJ9bz5dFymyMTIjoJS4hKqaFKqeeUUq8m6pxOddLlCdFkHca365sKGq2zRgjhQlElRKXU80qp40qpHUHb5yildiul9imlHgTQWu/XWt8azfmSxakxYyArCz7/HEpK7A6n06zD+Mx1n4Vws2jvEBcBc6wblFJpwJPA5cAo4Hql1Kgoz5NUdEYGzJhhvFm+3N5gIhC8Sp/JHMYHRimOAhmZIlwtqoSotV4PBK+vOQHY578jrAOWANdEc56k5JLym6G9uwZW6Qse2ZLt8wZKa87pmcWZhqYWI1M6utiVEHZTWkfXzFFKDQbe1lqP9r+fB8zRWi/wv/8BMBH438CvgJnAs1rr/2jjeLcDtwP07du3YMmSJRHHUllZSbdu3Tr9XRKlsrKSXlVVTJ4/n4bMTD544w2015kzVVdWVnK81rgNHNq7a2D7/hNVLfarb2iirtFYREsBfXN89MnuktA43fBnD+6J1S1xQsdjnTZt2jatdWHw9ngUwakQ27TWuhS4s70Pa60XAgsBCgsLdVFRUcQnXrduHR3Z3y7r1q1j8pVXwr//O+lffMGl6enGsD4HWrduHX8qMRLb0nnNd3uPPbGe8toGcnzpZPu8HCuv5WBpNQA+r4fFCyaErD80m95L75jc4nUs4nTDnz24J1a3xAmxizUeT5mLgYGW93nAkTicx/1c0mwOZp24Ydc3FRwrr+XwSSMZKuAXV54nxdjCleKRELcCw5RSQ5RSGcB84M2OHCCp1mUOx0GLT3WEdeKGJg0nq+oC7zVQVl1nW2xCRCPaspuXgE3AcKVUsVLqVq11A3A3sBLYCbystf6iI8dNqnWZw7n4YsjOhi+/hEOH7I6mTcHzGgavy9Kza0aL9zKRg3CraJ8yX6+17q+19mqt87TWz/m3L9Nan6u1/o7W+lexCTUJZWTAzJnGa4eW31TXNbaa1zB4XZa+OT5G9MsmI93DiH7ZUTWXw63UJ6v4iXhz5NC9lGkyg+ObzVVnQq+hErwuS7bPS5d0j6zrLFzNkQkxZZrM0JwQ330XzpyxN5YQunZJl3kNRcpwZEJMKQMGwAUXQHU1rF9vdzStZGWkhZ3XsKPF19b+SFlzRTiNJEQncHj5jdk8jraUxlquY12jRdZcEU7hyISYUn2I4Ph+xFhpsc6KZY0WWd9ZOIUjE2JK9SECTJ4M3bvDnj3w1Vd2R9Npo/rnhG0+t1hnxbJGi/RNCqdwZEJMOenpMHu28dqh5TexYC3Xsa7RImuuCKeQhOgUKdJstvZHhuqbDPegRR7CiHiThOgUc/zTSq5dCzU19sZik3CL28vC9yIRHLnkm1LqKuCq/Px8u0NJnH79oKAAtm2Ddeua7xgdKrivsL3Sm3AjTMzflZyqaXNxe1n4XiSCI+8QU+6hisnh5TfxluNr/vc5+EGLLHwvEsGRCTFlWfsRo5y4142yfV6yMtJCPmiRhe9FIkhCdJIJE6BnT9i/H/butTsaW6R5VJtF4LEqEBeiLZIQnSQtrfnhioOazbI2ikgVjkyIKTdSxSpFym+EcCJHJsSUfagCRoG2UvC3v0FVVfv7CyFixpFlNymtTx+jL3HLFnjvPbjqKrsjitp1z2ziy6PlgeVMO/pZ6NhCVMElPuE+G8uFroT7OfIOMeWlePmNEHaRhOhESVx+Y31AIw9rhNNIQnSiggKj6Xz4MOzcaXc0MdHYpNsdo3ysvJYzDU1U1NbbEKEQkhCdyeNJqqfNFbX1VNc1tjtG+WBpNXUNTez6pkLGKgtbODIhpnTZjSmJEmJ5bUPgdfBksNYxyqYmjUwYK2zhyISY0mU3plmzjDvFDRugvNzuaKIS6Rhlk6ztLOziyIQoMIbwTZ4M9fXGinwuFukY5cG9smKytrMQnSV1iE42dy588IHRbL72WrujiUp7Y5TN9Zz75vjafPIsT6RFvMkdopOZ/YjLlydd+Y0QTiR3iE42diz07w8lJbB9O4wZY3dEEYnH6I+2jmluv2t48/vgUTGRjlwJF3d730lGvCQHuUN0MqWS4mlzRW19p+sLzRrFjnzWrHk8Vl7b7mdlnRZhJQnR6VyeEM06w87UF1prFHd9UxFRUrTWPB4srQ772eB1WqQgXDgyIUodosXMmcY8iRs3wqlTdkfTYdY6w47WFwZ/1lrP2JZQ+7T12eB1WiI5vkhujkyIUodo0b07XJ3lnAYAAA+XSURBVHIJNDbC6tV2R9Nh1jrDjtYXBn/WWs/YllD7tPXZ4HVaIjm+SG6OTIgiiItnvzHrDDtTX2itURzRLztQmhOOteZxcK+ssJ8NXqclkuOL5CYJ0Q2s5TdNTfbG0gnZPi9d0j2dSjjmOiod+axZ89g3x9fuZ2WdFmElCdENRo+GvDw4dgw+/dTuaIRIWpIQ3UApVzebhXALSYhu4fLyGyHcQBKiW1x2GXi9xlorpTI1lhDxIAnRLbKzYepU46HKqlV2RyNEUpKE6CbSjyhEXElCdBOzH3HFCkeX38RjfHBbxzS3V9c1Bt4Hj5u2rtkSLq5wcbf3nWRMdHKQhOgmI0bA4MFw4gR89JHd0YQUPD44FgmiorY+5DGt5zpwoor/2XK4xbjpitr6Fp81xzaHiitc3O19p3h8Z2EPR45VUkpdBVyVn59vdyjOYpbf/P73RrN5wgS7I2oleHywOXZ5VP+cDk38ap2yq7y2ocUx713yCQN6ZFJyqsYy1lnzf5fvDDn2OXjNltp6Iy5rMXZw3OY5lt4xOeR3KhiUG4hx6rl9Qv4++LuEmxosGaYPS4bv4Mg7RBnLHIbDy2+CxwfHYm2UHF96yDHH1rHHCujZNaPV2GfrZ02hxlSHG9fc3neKx3cW9nBkQhRhTJsGXboYTebjx+2OppXg8cGxGBKX7fOGHHNsHbfs86bRN8fXYty0uTRBJGu2hBvX3N53isd3FvaQhOg2XbtCUZGxpMDKlXZHE1I8xge3dUxz3LLHf4sWaty0+dm+Ob6wY6rDxd3ed5Ix0clBEqIbSfmNEHEhCdGNzH7ElSuhQSY1FSJWJCG60bBhkJ8PZWXw4Yd2RyNE0pCE6FbSbBYi5iQhupXDy2+EcCNJiG516aWQmQmffAJHj9odjRBJQRKiW2VmwvTpxusVK+yNRYgkIQnRzaQfUYiYkoToZmY/4qpVUC+LrAsRLUmIbjZkiDEDTnk5bNrU/v5CiLAcOduN6IC5c2HXLqPZPHWq3dGEFM3sJ+ZnrbPftCd4Zp1wn3XzzCwi9uQO0e2k/EaImJGE6HZTphgTPmzfDsXFdkcjhKslLCEqpboqpV5USv1BKXVDos6b9Lp0gRkzjNfLl9sbixAuF1VCVEo9r5Q6rpTaEbR9jlJqt1Jqn1LqQf/mvwNe1VrfBlwdzXlFECm/ESImor1DXATMsW5QSqUBTwKXA6OA65VSo4A84Gv/bo1RnldYmf2Ia9ZAXZ29scRIJAs+HSuvDSwo1dSkKTlV02JxqVAa/fu1t+5JJItGRbqwVCyP5WTJ8B2iSoha6/XAyaDNE4B9Wuv9Wus6YAlwDVCMkRSjPq8IMnAgjB4NlZWwYYPd0UQt0gWfDpZWU9fQxM6jFdTUN1JcVhNYXCqUitp6qusa210MKpJFo4L3aeucnTmWGxNKMnwHAKW1bn+vcAdQajDwttZ6tP/9PGCO1nqB//0PgInAA8DvgFpgg9Z6cRvHux24HaBv374FS5YsiTiWyspKunXr1unvkijxiHPoM89wzpIlfP397/PVXXfF7LidiXX/iSojpt5dO3XObyvO8E15LWCsldI3x0fFGWPex+wu6YHfWfXNhGM1xuuMNA/D+2W3iqe+oYm6xqYWx+2T3aXVftZzBJ/f/E7BMXrTPHjTPa2+c6jvkqnqW1zTUPtY47JLR/7s7f4OHf3/dNq0adu01oXB2+NRh6hCbNNa6yrg5vY+rLVeCCwEKCws1EVFRRGfeN26dXRkf7vELc4lSxi4fTsDY3jszsT6lLn62rzO1fhtO1TGA09vpEmDz+th8YIJPLZiFwD/OmdE4HcmBfz0/Ab+c7uxoNSIftksm99ck2nGU1Fbz5dHK4Dm41qn/Df3s54j+PzmdwqOcWjvrmT7vK2+c6jvUnHgsxbXNNQ+TliKoCN/9nZ/h1j9nYpH07UYGGh5nwccicN5hNXFF0N2NuzcCQcP2h1NVMIt2mT9nblo1Mj+2WR6jcWmzMWlQrEuShVuMahIFo0KtyhVtMdyQjLsqGT4DhCfhLgVGKaUGqKUygDmA2925ABKqauUUgtPnz4dh/CSlNcLs2YZr5Og/CaSBZ+si0Z5/ItNtZWYTOaiVO39hY1k0ahIF5aK5bGcLBm+Q7RlNy8Bm4DhSqlipdStWusG4G5gJbATeFlr/UVHjivrMneSlN8IEZWo+hC11te3sX0ZIH8rE22OvwLq3XehthZ8PnvjEcJlHFn+Ik3mTjr7bBg7FmpqYP16u6MRwnUcmRClyRwFaTYL0WmOTIgiCjL7jRCdJgkx2UyaBD16wN69sG+f3dEI4SqOTIjShxiF9HSYPdt4nQTlN0IkkiMTovQhRkn6EYXoFEcmRBEl8w5x7VqorrY3FiFcRBJiMurbFwoL4cwZWLfO7miEcA1JiMlKms1CdJgjE6I8VIkBa/lNlFO8CZEqHLkMqdb6LeCtwsLC2+yOxbXGj4deveDAAdizB4YPT9ip47G0Z1vHNJccff7Vd9rcLxZLkrb3nWQ50+TgyDtEEQNpac1jm6XZLEREJCEmM+lHFKJDJCEms1mzQCljoofKSrujEcLxHJkQ5aFKjPTuDRMnGivxvfee3dEI4XiOTIgyUiWGpNksRMQcmRBFDEn5jRARk4SY7MaNg7POgq+/hi+/tDsaIRxNEmKy83hkjkQhIiQJMRVIP6IQEZGEmApmzjTuFDdsgPJyu6MRwrEcmRCl7CbGcnPhoougoQHWrLE7GiEcy5EJUcpu4kCazUK0y5EJUcSB+WBl+XIpvxGiDZIQU8UFF0D//nDkCHz+ud3RCOFIkhBThVLSbBaiHZIQU4kkRCHCkoSYSmbMMJYp3bgRysrsjkYIx5GEmEpycuCSS6CpCVavtjsaIRzHkQlR6hDjSJrNQrTJkQlR6hDjyFp+09RkbyxCOIwjE6KIo/POg4ED4fhx+OQTu6MRwlEkIaYaKb8Rok2SEFORJEQhQpKEmIqmT4eMDNiyBU6csDsaIRxDEmIq6tYNpk41xjSvWmV3NEI4hiTEVCXNZiFakYSYqszymxUroLHR3liEcAhJiKlq+HAYMgRKS+Gjj+yORghHkISYqqT8RohWJCGmMkmIQrTgyIQoY5kTpKgIunQxmszHjtkdjRC2c2RClLHMCZKVBdOmGa9XrrQ3FiEcwJEJUSSQNJuFCJCEmOrM8puVK41lSoVIYZIQU11+PgwbBqdOGUP5hEhhkhCFNJuF8JOEKCQhCuEnCVEYEz1kZcGnnxrrNguRoiQhCvD5jCnBwBjbLESKkoQoDNJsFkISovAzy29Wr4b6entjEcImkhCFYfBgGDkSysuNheyFSEGSEEUzaTaLFCcJUTSThChSnCRE0eySS4z1VnbsgK+/tjsaIRJOEqJolpEBM2YYr5cvtzcWIWwgCVG0JM1mkcISlhCVUkOVUs8ppV5N1DlFJ5jlN2vWwJkz9sYiRIJFlBCVUs8rpY4rpXYEbZ+jlNqtlNqnlHow3DG01vu11rdGE6xIgLw8OP98qKqCDRvsjkaIhIr0DnERMMe6QSmVBjwJXA6MAq5XSo1SSp2vlHo76OesmEYt4kuazSJFRZQQtdbrgZNBmycA+/x3fnXAEuAarfV2rfWVQT/HYxy3iCdJiCJFKa11ZDsqNRh4W2s92v9+HjBHa73A//4HwESt9d1tfL4X8CtgJvCs1vo/2tjvduB2/9vhwO5IvwzQGzjRgf3t4pY4wT2xuiVOcE+sbokTOh7rIK11n+CN6VEEoEJsazO7aq1LgTvbO6jWeiGwsFMBKfWR1rqwM59NJLfECe6J1S1xgntidUucELtYo3nKXAwMtLzPA2QyPSGEa0WTELcCw5RSQ5RSGcB84M3YhCWEEIkXadnNS8AmYLhSqlgpdavWugG4G1gJ7ARe1lp/Eb9QI9KpprYN3BInuCdWt8QJ7onVLXFCjGKN+KGKEEIkOxm6J4QQfq5JiKFGyyileiqlViul9vr/m+vfrpRSv/GPoPlcKTXOAbH+m1KqRCn1qf9nruV3D/lj3a2Ump3AOAcqpdYqpXYqpb5QSt3r3+6o6xomTideU59S6kOl1Gf+WB/xbx+ilNriv6ZL/f3uKKW6+N/v8/9+sM1xLlJKHbBc07H+7bb+nfLHkKaU+kQp9bb/feyvqdbaFT/AVGAcsMOy7THgQf/rB4FH/a/nAssxSoMmAVscEOu/AfeF2HcU8BnQBRgCfAWkJSjO/sA4/+tsYI8/Hkdd1zBxOvGaKqCb/7UX2OK/Vi8D8/3bnwbu8r/+R+Bp/+v5wFKb41wEzAuxv61/p/wx/BT4H4x6aOJxTV1zh6hDj5a5BnjR//pF4LuW7X/Uhs1AD6VU/8RE2masbbkGWKK1PqO1PgDswxgFFHda66Na64/9ryswHo4NwGHXNUycbbHzmmqtdaX/rdf/o4HpgDmxSfA1Na/1q8BlSqlQNb6JirMttv6dUkrlAVcAz/rfK+JwTV2TENvQV2t9FIy/NIA5ZnoAYJ3htJjwf4ES5W5/c+N5sxmKQ2L1NysuxLhTcOx1DYoTHHhN/U27T4HjwGqMO9RT2qjMCI4nEKv/96eBXnbEqbU2r+mv/Nf0v5VSXYLj9Ev0n/3/A/4VaPK/70UcrqnbE2JbOjSKJkGeAr4DjAWOAv/p3257rEqpbsBfgH/SWpeH2zXEtoTFGiJOR15TrXWj1nosxmCFCcDIMPHYFmtwnEqp0cBDwAhgPNATeMDuOJVSVwLHtdbbrJvDxNPpWN2eEI+Zt+3+/5qTSDhuFI3W+pj/f8Am4A80N+FsjVUp5cVIMou11q/5NzvuuoaK06nX1KS1PgWsw+hz66GUMofKWuMJxOr/fXci726JdZxz/N0TWmt9BngBZ1zTi4GrlVIHMSaRmY5xxxjza+r2hPgm8CP/6x8Bb1i2/9D/ZGwScNpsAtolqL/lWsB8Av0mMN//ZGwIMAz4MEExKeA5YKfW+r8sv3LUdW0rTode0z5KqR7+15nADIw+z7XAPP9uwdfUvNbzgPe0/2mADXHusvxDqDD65KzX1Ja/U1rrh7TWeVrrwRgPSd7TWt9APK5pop8UdfYHeAmjWVSP8S/ArRj9Au8Ce/3/7ambn6A9idF3sx0odECsf/LH8rn/D6y/Zf+f+WPdDVyewDgvwWhKfA586v+Z67TrGiZOJ17TMcAn/ph2AL/wbx+KkZT3Aa8AXfzbff73+/y/H2pznO/5r+kO4M80P4m29e+UJe4imp8yx/yaykgVIYTwc3uTWQghYkYSohBC+ElCFEIIP0mIQgjhJwlRCCH8JCEKIYSfJEQhhPCThCiEEH7/H6Xlbj11tNXKAAAAAElFTkSuQmCC\n",
+ "image/png": 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\n",
"text/plain": [
- "<Figure size 360x360 with 1 Axes>"
+ "<Figure size 432x288 with 1 Axes>"
]
},
- "metadata": {
- "needs_background": "light"
- },
+ "metadata": {},
"output_type": "display_data"
- },
+ }
+ ],
+ "source": [
+ "scanA = np.linspace(110.0,130.0,50)\n",
+ "scanB = np.linspace(5,20,50)\n",
+ "minValue = nll(solution.x)\n",
+ "Z = [[nll([a,b]) - minValue for b in scanB] for a in scanA]\n",
+ "p1 = plt.contour(scanB, scanA, Z, [0.01,0.5, 2.0, 4.5])"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Compute numerically the error matrix of the NLL for the 2-D fit."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 301,
+ "metadata": {},
+ "outputs": [
{
- "data": {
- "text/html": [
- "<table>\n",
- "<tr style=\"background-color:#F4F4F4;\">\n",
- "<td/>\n",
- "<th title=\"Variable name\">\n",
- "Name\n",
- "</th>\n",
- "<th title=\"Value of parameter\">\n",
- "Value\n",
- "</th>\n",
- "<th title=\"Hesse error\">\n",
- "Hesse Error\n",
- "</th>\n",
- "<th title=\"Minos lower error\">\n",
- "Minos Error-\n",
- "</th>\n",
- "<th title=\"Minos upper error\">\n",
- "Minos Error+\n",
- "</th>\n",
- "<th title=\"Lower limit of the parameter\">\n",
- "Limit-\n",
- "</th>\n",
- "<th title=\"Upper limit of the parameter\">\n",
- "Limit+\n",
- "</th>\n",
- "<th title=\"Is the parameter fixed in the fit\">\n",
- "Fixed\n",
- "</th>\n",
- "</tr>\n",
- "<tr style=\"background-color:#FFFFFF;\">\n",
- "<td>\n",
- "0\n",
- "</td>\n",
- "<td>\n",
- "loc\n",
- "</td>\n",
- "<td>\n",
- "100.0\n",
- "</td>\n",
- "<td>\n",
- "1.0\n",
- "</td>\n",
- "<td>\n",
- "\n",
- "</td>\n",
- "<td>\n",
- "\n",
- "</td>\n",
- "<td>\n",
- "\n",
- "</td>\n",
- "<td>\n",
- "\n",
- "</td>\n",
- "<td>\n",
- "\n",
- "</td>\n",
- "</tr>\n",
- "<tr style=\"background-color:#F4F4F4;\">\n",
- "<td>\n",
- "1\n",
- "</td>\n",
- "<td>\n",
- "scale\n",
- "</td>\n",
- "<td>\n",
- "10.0\n",
- "</td>\n",
- "<td>\n",
- "1.0\n",
- "</td>\n",
- "<td>\n",
- "\n",
- "</td>\n",
- "<td>\n",
- "\n",
- "</td>\n",
- "<td>\n",
- "\n",
- "</td>\n",
- "<td>\n",
- "\n",
- "</td>\n",
- "<td>\n",
- "\n",
- "</td>\n",
- "</tr>\n",
- "</table>\n"
- ],
- "text/plain": [
- "-------------------------------------------------------------------------------------------\n",
- "| | Name | Value | Hesse Err | Minos Err- | Minos Err+ | Limit- | Limit+ | Fixed |\n",
- "-------------------------------------------------------------------------------------------\n",
- "| 0 | loc | 100.0 | 1.0 | | | | | |\n",
- "| 1 | scale | 10.0 | 1.0 | | | | | |\n",
- "-------------------------------------------------------------------------------------------"
- ]
- },
- "execution_count": 5,
- "metadata": {},
- "output_type": "execute_result"
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "[[11.95694692 -3.06065748]\n",
+ " [-3.06065748 5.72672173]] \n",
+ "sigma(position): 3.4578818544955507 sigma(width): 2.3930569834299082\n"
+ ]
}
],
"source": [
- "m = Minuit(blh, \n",
- " loc=100, scale= 10,\n",
- " errordef=0.5, #remember up is 0.5 for likelihood and 1 for chi^2\n",
- " pedantic=False)\n",
+ "from scipy.misc import derivative\n",
"\n",
- "# Show() is the same thing as draw(). But show the figure immediately.\n",
- "# For all parameters and return vars:\n",
- "# https://probfit.readthedocs.io/en/latest/api.html#probfit.costfunc.UnbinnedLH.draw\n",
- "plt.figure(figsize=[5,5])\n",
- "plt.yscale('log', nonposy='clip')\n",
- "plt.ylim([0.1,1000])\n",
- "blh.show(m, print_par=True)\n",
- "m.get_param_states()"
+ "# compute the error matrix\n",
+ "A = np.linalg.inv([\n",
+ " [\n",
+ " derivative(lambda x: nll([x, solution.x[1]]), solution.x[0], n=2),\n",
+ " derivative(lambda y: derivative(lambda x: nll([x, y]), solution.x[0]), solution.x[1])\n",
+ " ],\n",
+ " [\n",
+ " derivative(lambda x: derivative(lambda y: nll([x, y]), solution.x[1]), solution.x[0]),\n",
+ " derivative(lambda y: nll([solution.x[0], y]), solution.x[1], n=2)\n",
+ " ]\n",
+ "])\n",
+ "print(A, \"\\nsigma(position):\", np.sqrt(A[0,0]), \"sigma(width):\", np.sqrt(A[1,1]))"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Binned ML fit"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "With the same data as above, we now perform a binned ML fit and compare with the unbinned fit.\n",
+ "First, create a histogram of the data using np.histogram."
]
},
{
"cell_type": "code",
- "execution_count": 6,
+ "execution_count": 374,
"metadata": {},
"outputs": [
{
- "name": "stderr",
+ "name": "stdout",
"output_type": "stream",
"text": [
- "/Users/mauro/anaconda3/envs/fits/lib/python3.7/site-packages/ipykernel_launcher.py:1: LogWarning: x is really small return 0\n",
- " \"\"\"Entry point for launching an IPython kernel.\n"
+ "[ 1 19 26 10 7 5 5 2 0 0]\n",
+ "[ 70. 80. 90. 100. 110. 120. 130. 140. 150. 160. 170.]\n"
]
- },
+ }
+ ],
+ "source": [
+ "nBins = 10\n",
+ "histoMax = 170\n",
+ "histoMin = 70\n",
+ "binWidth = (histoMax-histoMin)/nBins\n",
+ "h0 = np.histogram(measurements, bins=nBins, range=(histoMin, histoMax))\n",
+ "print(h0[0])\n",
+ "print(h0[1])"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Compute the binned NLL:"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 375,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "def nll_binned(params):\n",
+ " # params is a list of [position, sigma]\n",
+ " expected = [likelihood_point(x+binWidth/2, params[0], params[1])*(binWidth/2)*sum(h0[0]) for x in h0[1]]\n",
+ " return sum([-np.log(expected[i]**h0[0][i]) for i in range(nBins)])"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Minimize the binned NLL:"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 376,
+ "metadata": {},
+ "outputs": [
{
- "data": {
- "image/png": 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\n",
- "text/plain": [
- "<Figure size 360x360 with 1 Axes>"
- ]
- },
- "metadata": {
- "needs_background": "light"
- },
- "output_type": "display_data"
- },
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ " fun: -138.93433719876123\n",
+ " jac: array([-1.90734863e-06, 1.90734863e-06])\n",
+ " message: 'Optimization terminated successfully.'\n",
+ " nfev: 60\n",
+ " nit: 6\n",
+ " njev: 15\n",
+ " status: 0\n",
+ " success: True\n",
+ " x: array([116.43876363, 15.33581135])\n"
+ ]
+ }
+ ],
+ "source": [
+ "solution_binned=minimize(nll_binned, [120.0, 10], method='CG')\n",
+ "print(solution_binned)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Make a contour plot of the 1,2, and 3 $\\sigma$ contours for the binned NLL and overlay it with the unbinned contours."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 377,
+ "metadata": {},
+ "outputs": [
{
"data": {
- "text/html": [
- "<table>\n",
- "<tr style=\"background-color:#F4F4F4;\">\n",
- "<td/>\n",
- "<th title=\"Variable name\">\n",
- "Name\n",
- "</th>\n",
- "<th title=\"Value of parameter\">\n",
- "Value\n",
- "</th>\n",
- "<th title=\"Hesse error\">\n",
- "Hesse Error\n",
- "</th>\n",
- "<th title=\"Minos lower error\">\n",
- "Minos Error-\n",
- "</th>\n",
- "<th title=\"Minos upper error\">\n",
- "Minos Error+\n",
- "</th>\n",
- "<th title=\"Lower limit of the parameter\">\n",
- "Limit-\n",
- "</th>\n",
- "<th title=\"Upper limit of the parameter\">\n",
- "Limit+\n",
- "</th>\n",
- "<th title=\"Is the parameter fixed in the fit\">\n",
- "Fixed\n",
- "</th>\n",
- "</tr>\n",
- "<tr style=\"background-color:#FFFFFF;\">\n",
- "<td>\n",
- "0\n",
- "</td>\n",
- "<td>\n",
- "loc\n",
- "</td>\n",
- "<td>\n",
- "100.25\n",
- "</td>\n",
- "<td>\n",
- "0.25\n",
- "</td>\n",
- "<td>\n",
- "\n",
- "</td>\n",
- "<td>\n",
- "\n",
- "</td>\n",
- "<td>\n",
- "\n",
- "</td>\n",
- "<td>\n",
- "\n",
- "</td>\n",
- "<td>\n",
- "\n",
- "</td>\n",
- "</tr>\n",
- "<tr style=\"background-color:#F4F4F4;\">\n",
- "<td>\n",
- "1\n",
- "</td>\n",
- "<td>\n",
- "scale\n",
- "</td>\n",
- "<td>\n",
- "25.07\n",
- "</td>\n",
- "<td>\n",
- "0.25\n",
- "</td>\n",
- "<td>\n",
- "\n",
- "</td>\n",
- "<td>\n",
- "\n",
- "</td>\n",
- "<td>\n",
- "\n",
- "</td>\n",
- "<td>\n",
- "\n",
- "</td>\n",
- "<td>\n",
- "\n",
- "</td>\n",
- "</tr>\n",
- "</table>\n"
- ],
+ "image/png": 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\n",
"text/plain": [
- "-------------------------------------------------------------------------------------------\n",
- "| | Name | Value | Hesse Err | Minos Err- | Minos Err+ | Limit- | Limit+ | Fixed |\n",
- "-------------------------------------------------------------------------------------------\n",
- "| 0 | loc | 100.25 | 0.25 | | | | | |\n",
- "| 1 | scale | 25.07 | 0.25 | | | | | |\n",
- "-------------------------------------------------------------------------------------------"
+ "<Figure size 432x288 with 1 Axes>"
]
},
- "execution_count": 6,
"metadata": {},
- "output_type": "execute_result"
+ "output_type": "display_data"
}
],
"source": [
- "m.migrad()\n",
- "plt.figure(figsize=[5,5])\n",
- "plt.yscale('log', nonposy='clip')\n",
- "plt.ylim([0.1,1000])\n",
- "blh.show(m)\n",
- "m.get_param_states()"
+ "scanA = np.linspace(110.0,130.0,50)\n",
+ "scanB = np.linspace(5,20,50)\n",
+ "Z_binned = [[nll_binned([a,b]) - solution_binned.fun for b in scanB] for a in scanA]\n",
+ "\n",
+ "fig1, ax2 = plt.subplots(constrained_layout=True)\n",
+ "\n",
+ "p1 = ax2.contour(scanB, scanA, Z, [0.01,0.5, 2.0, 4.5])\n",
+ "p2 = ax2.contour(scanB, scanA, Z_binned, [0.01,0.5, 2.0, 4.5], linestyles=\"dotted\")\n",
+ "plt.show()"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Repeat the same for 50 bins:"
]
},
{
"cell_type": "code",
- "execution_count": 7,
+ "execution_count": 373,
"metadata": {},
"outputs": [
- {
- "name": "stderr",
- "output_type": "stream",
- "text": [
- "/Users/mauro/anaconda3/envs/fits/lib/python3.7/site-packages/ipykernel_launcher.py:1: LogWarning: x is really small return 0\n",
- " \"\"\"Entry point for launching an IPython kernel.\n"
- ]
- },
{
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\n",
"text/plain": [
- "-------------------------------------------------------------------------------------------\n",
- "| | Name | Value | Hesse Err | Minos Err- | Minos Err+ | Limit- | Limit+ | Fixed |\n",
- "-------------------------------------------------------------------------------------------\n",
- "| 0 | loc | 100.25 | 0.25 | -0.25 | 0.25 | | | |\n",
- "| 1 | scale | 25.07 | 0.25 | -0.25 | 0.25 | | | |\n",
- "-------------------------------------------------------------------------------------------"
+ "<Figure size 432x288 with 1 Axes>"
]
},
- "execution_count": 7,
"metadata": {},
- "output_type": "execute_result"
+ "output_type": "display_data"
}
],
"source": [
- "m.minos()\n",
- "m.get_param_states()"
+ "scanA = np.linspace(110.0,130.0,50)\n",
+ "scanB = np.linspace(5,20,50)\n",
+ "Z_binned = [[nll_binned([a,b]) - solution_binned.fun for b in scanB] for a in scanA]\n",
+ "\n",
+ "fig1, ax2 = plt.subplots(constrained_layout=True)\n",
+ "\n",
+ "p1 = ax2.contour(scanB, scanA, Z, [0.01,0.5, 2.0, 4.5])\n",
+ "p2 = ax2.contour(scanB, scanA, Z_binned, [0.01,0.5, 2.0, 4.5], linestyles=\"dotted\")\n",
+ "plt.show()"
]
},
{
@@ -532,7 +449,7 @@
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython3",
- "version": "3.7.7"
+ "version": "3.8.5"
}
},
"nbformat": 4,
diff --git a/notebooks/binnedLikelihood_probfit.ipynb b/notebooks/binnedLikelihood_probfit.ipynb
new file mode 100644
index 0000000..c82fdcf
--- /dev/null
+++ b/notebooks/binnedLikelihood_probfit.ipynb
@@ -0,0 +1,540 @@
+{
+ "cells": [
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "# Binned Likelihood\n",
+ "\n",
+ "\n",
+ "In this notebook we will be using probfit together with iminuit to perform a Binned Likelihood fit.\n",
+ "\n",
+ "probfit:\n",
+ "https://probfit.readthedocs.io/en/latest/\n",
+ "\n",
+ "iMinuit:\n",
+ "https://iminuit.readthedocs.io/en/latest/index.html#\n",
+ "\n",
+ " "
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "### Fit an exponential"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 1,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "import numpy as np\n",
+ "%matplotlib inline\n",
+ "import matplotlib.pyplot as plt\n",
+ "from math import exp, pi, sqrt\n",
+ "import probfit\n",
+ "from probfit import BinnedLH\n",
+ "from iminuit import Minuit, describe\n",
+ "from scipy.stats import norm, chi2, lognorm\n",
+ "import scipy.stats"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 2,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "# Generate data\n",
+ "# set the seed to always get the same samples\n",
+ "np.random.seed(seed=123456)\n",
+ "\n",
+ "# Generate a toy dataset on an exponential distribution (background)\n",
+ "# pdf = lambda * exp(-lambda * x) ; scale = 1/lambda\n",
+ "data = scipy.stats.expon.rvs(loc= 100, scale = 25, size=10000)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 3,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "image/png": "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\n",
+ "text/plain": [
+ "<Figure size 360x360 with 1 Axes>"
+ ]
+ },
+ "metadata": {
+ "needs_background": "light"
+ },
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "plt.figure(figsize=[5,5])\n",
+ "plt.subplot(111)\n",
+ "plt.hist(data, bins=150, range=[100,400], color='blue', alpha=0.5)\n",
+ "plt.xlabel(r'x [units]')\n",
+ "plt.ylabel(r'Entries / bins size = 2')\n",
+ "plt.yscale('log', nonposy='clip')"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 4,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "['loc', 'scale']"
+ ]
+ },
+ "execution_count": 4,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "def exp_func(x, loc, scale):\n",
+ " return scipy.stats.expon.pdf(x, loc, scale)\n",
+ "\n",
+ "blh = BinnedLH(exp_func, data, bins=150, bound=(100,400))\n",
+ "describe(blh)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 5,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "image/png": 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+ "text/plain": [
+ "<Figure size 360x360 with 1 Axes>"
+ ]
+ },
+ "metadata": {
+ "needs_background": "light"
+ },
+ "output_type": "display_data"
+ },
+ {
+ "data": {
+ "text/html": [
+ "<table>\n",
+ "<tr style=\"background-color:#F4F4F4;\">\n",
+ "<td/>\n",
+ "<th title=\"Variable name\">\n",
+ "Name\n",
+ "</th>\n",
+ "<th title=\"Value of parameter\">\n",
+ "Value\n",
+ "</th>\n",
+ "<th title=\"Hesse error\">\n",
+ "Hesse Error\n",
+ "</th>\n",
+ "<th title=\"Minos lower error\">\n",
+ "Minos Error-\n",
+ "</th>\n",
+ "<th title=\"Minos upper error\">\n",
+ "Minos Error+\n",
+ "</th>\n",
+ "<th title=\"Lower limit of the parameter\">\n",
+ "Limit-\n",
+ "</th>\n",
+ "<th title=\"Upper limit of the parameter\">\n",
+ "Limit+\n",
+ "</th>\n",
+ "<th title=\"Is the parameter fixed in the fit\">\n",
+ "Fixed\n",
+ "</th>\n",
+ "</tr>\n",
+ "<tr style=\"background-color:#FFFFFF;\">\n",
+ "<td>\n",
+ "0\n",
+ "</td>\n",
+ "<td>\n",
+ "loc\n",
+ "</td>\n",
+ "<td>\n",
+ "100.0\n",
+ "</td>\n",
+ "<td>\n",
+ "1.0\n",
+ "</td>\n",
+ "<td>\n",
+ "\n",
+ "</td>\n",
+ "<td>\n",
+ "\n",
+ "</td>\n",
+ "<td>\n",
+ "\n",
+ "</td>\n",
+ "<td>\n",
+ "\n",
+ "</td>\n",
+ "<td>\n",
+ "\n",
+ "</td>\n",
+ "</tr>\n",
+ "<tr style=\"background-color:#F4F4F4;\">\n",
+ "<td>\n",
+ "1\n",
+ "</td>\n",
+ "<td>\n",
+ "scale\n",
+ "</td>\n",
+ "<td>\n",
+ "10.0\n",
+ "</td>\n",
+ "<td>\n",
+ "1.0\n",
+ "</td>\n",
+ "<td>\n",
+ "\n",
+ "</td>\n",
+ "<td>\n",
+ "\n",
+ "</td>\n",
+ "<td>\n",
+ "\n",
+ "</td>\n",
+ "<td>\n",
+ "\n",
+ "</td>\n",
+ "<td>\n",
+ "\n",
+ "</td>\n",
+ "</tr>\n",
+ "</table>\n"
+ ],
+ "text/plain": [
+ "-------------------------------------------------------------------------------------------\n",
+ "| | Name | Value | Hesse Err | Minos Err- | Minos Err+ | Limit- | Limit+ | Fixed |\n",
+ "-------------------------------------------------------------------------------------------\n",
+ "| 0 | loc | 100.0 | 1.0 | | | | | |\n",
+ "| 1 | scale | 10.0 | 1.0 | | | | | |\n",
+ "-------------------------------------------------------------------------------------------"
+ ]
+ },
+ "execution_count": 5,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "m = Minuit(blh, \n",
+ " loc=100, scale= 10,\n",
+ " errordef=0.5, #remember up is 0.5 for likelihood and 1 for chi^2\n",
+ " pedantic=False)\n",
+ "\n",
+ "# Show() is the same thing as draw(). But show the figure immediately.\n",
+ "# For all parameters and return vars:\n",
+ "# https://probfit.readthedocs.io/en/latest/api.html#probfit.costfunc.UnbinnedLH.draw\n",
+ "plt.figure(figsize=[5,5])\n",
+ "plt.yscale('log', nonposy='clip')\n",
+ "plt.ylim([0.1,1000])\n",
+ "blh.show(m, print_par=True)\n",
+ "m.get_param_states()"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 6,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stderr",
+ "output_type": "stream",
+ "text": [
+ "/Users/mauro/anaconda3/envs/fits/lib/python3.7/site-packages/ipykernel_launcher.py:1: LogWarning: x is really small return 0\n",
+ " \"\"\"Entry point for launching an IPython kernel.\n"
+ ]
+ },
+ {
+ "data": {
+ "image/png": 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\n",
+ "text/plain": [
+ "<Figure size 360x360 with 1 Axes>"
+ ]
+ },
+ "metadata": {
+ "needs_background": "light"
+ },
+ "output_type": "display_data"
+ },
+ {
+ "data": {
+ "text/html": [
+ "<table>\n",
+ "<tr style=\"background-color:#F4F4F4;\">\n",
+ "<td/>\n",
+ "<th title=\"Variable name\">\n",
+ "Name\n",
+ "</th>\n",
+ "<th title=\"Value of parameter\">\n",
+ "Value\n",
+ "</th>\n",
+ "<th title=\"Hesse error\">\n",
+ "Hesse Error\n",
+ "</th>\n",
+ "<th title=\"Minos lower error\">\n",
+ "Minos Error-\n",
+ "</th>\n",
+ "<th title=\"Minos upper error\">\n",
+ "Minos Error+\n",
+ "</th>\n",
+ "<th title=\"Lower limit of the parameter\">\n",
+ "Limit-\n",
+ "</th>\n",
+ "<th title=\"Upper limit of the parameter\">\n",
+ "Limit+\n",
+ "</th>\n",
+ "<th title=\"Is the parameter fixed in the fit\">\n",
+ "Fixed\n",
+ "</th>\n",
+ "</tr>\n",
+ "<tr style=\"background-color:#FFFFFF;\">\n",
+ "<td>\n",
+ "0\n",
+ "</td>\n",
+ "<td>\n",
+ "loc\n",
+ "</td>\n",
+ "<td>\n",
+ "100.25\n",
+ "</td>\n",
+ "<td>\n",
+ "0.25\n",
+ "</td>\n",
+ "<td>\n",
+ "\n",
+ "</td>\n",
+ "<td>\n",
+ "\n",
+ "</td>\n",
+ "<td>\n",
+ "\n",
+ "</td>\n",
+ "<td>\n",
+ "\n",
+ "</td>\n",
+ "<td>\n",
+ "\n",
+ "</td>\n",
+ "</tr>\n",
+ "<tr style=\"background-color:#F4F4F4;\">\n",
+ "<td>\n",
+ "1\n",
+ "</td>\n",
+ "<td>\n",
+ "scale\n",
+ "</td>\n",
+ "<td>\n",
+ "25.07\n",
+ "</td>\n",
+ "<td>\n",
+ "0.25\n",
+ "</td>\n",
+ "<td>\n",
+ "\n",
+ "</td>\n",
+ "<td>\n",
+ "\n",
+ "</td>\n",
+ "<td>\n",
+ "\n",
+ "</td>\n",
+ "<td>\n",
+ "\n",
+ "</td>\n",
+ "<td>\n",
+ "\n",
+ "</td>\n",
+ "</tr>\n",
+ "</table>\n"
+ ],
+ "text/plain": [
+ "-------------------------------------------------------------------------------------------\n",
+ "| | Name | Value | Hesse Err | Minos Err- | Minos Err+ | Limit- | Limit+ | Fixed |\n",
+ "-------------------------------------------------------------------------------------------\n",
+ "| 0 | loc | 100.25 | 0.25 | | | | | |\n",
+ "| 1 | scale | 25.07 | 0.25 | | | | | |\n",
+ "-------------------------------------------------------------------------------------------"
+ ]
+ },
+ "execution_count": 6,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "m.migrad()\n",
+ "plt.figure(figsize=[5,5])\n",
+ "plt.yscale('log', nonposy='clip')\n",
+ "plt.ylim([0.1,1000])\n",
+ "blh.show(m)\n",
+ "m.get_param_states()"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 7,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stderr",
+ "output_type": "stream",
+ "text": [
+ "/Users/mauro/anaconda3/envs/fits/lib/python3.7/site-packages/ipykernel_launcher.py:1: LogWarning: x is really small return 0\n",
+ " \"\"\"Entry point for launching an IPython kernel.\n"
+ ]
+ },
+ {
+ "data": {
+ "text/html": [
+ "<table>\n",
+ "<tr style=\"background-color:#F4F4F4;\">\n",
+ "<td/>\n",
+ "<th title=\"Variable name\">\n",
+ "Name\n",
+ "</th>\n",
+ "<th title=\"Value of parameter\">\n",
+ "Value\n",
+ "</th>\n",
+ "<th title=\"Hesse error\">\n",
+ "Hesse Error\n",
+ "</th>\n",
+ "<th title=\"Minos lower error\">\n",
+ "Minos Error-\n",
+ "</th>\n",
+ "<th title=\"Minos upper error\">\n",
+ "Minos Error+\n",
+ "</th>\n",
+ "<th title=\"Lower limit of the parameter\">\n",
+ "Limit-\n",
+ "</th>\n",
+ "<th title=\"Upper limit of the parameter\">\n",
+ "Limit+\n",
+ "</th>\n",
+ "<th title=\"Is the parameter fixed in the fit\">\n",
+ "Fixed\n",
+ "</th>\n",
+ "</tr>\n",
+ "<tr style=\"background-color:#FFFFFF;\">\n",
+ "<td>\n",
+ "0\n",
+ "</td>\n",
+ "<td>\n",
+ "loc\n",
+ "</td>\n",
+ "<td>\n",
+ " 100.25\n",
+ "</td>\n",
+ "<td>\n",
+ " 0.25\n",
+ "</td>\n",
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+ "-0.25\n",
+ "</td>\n",
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+ " 0.25\n",
+ "</td>\n",
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+ "\n",
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+ " 25.07\n",
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+ " 0.25\n",
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+ "<td>\n",
+ "-0.25\n",
+ "</td>\n",
+ "<td>\n",
+ " 0.25\n",
+ "</td>\n",
+ "<td>\n",
+ "\n",
+ "</td>\n",
+ "<td>\n",
+ "\n",
+ "</td>\n",
+ "<td>\n",
+ "\n",
+ "</td>\n",
+ "</tr>\n",
+ "</table>\n"
+ ],
+ "text/plain": [
+ "-------------------------------------------------------------------------------------------\n",
+ "| | Name | Value | Hesse Err | Minos Err- | Minos Err+ | Limit- | Limit+ | Fixed |\n",
+ "-------------------------------------------------------------------------------------------\n",
+ "| 0 | loc | 100.25 | 0.25 | -0.25 | 0.25 | | | |\n",
+ "| 1 | scale | 25.07 | 0.25 | -0.25 | 0.25 | | | |\n",
+ "-------------------------------------------------------------------------------------------"
+ ]
+ },
+ "execution_count": 7,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "m.minos()\n",
+ "m.get_param_states()"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": []
+ }
+ ],
+ "metadata": {
+ "kernelspec": {
+ "display_name": "Python 3",
+ "language": "python",
+ "name": "python3"
+ },
+ "language_info": {
+ "codemirror_mode": {
+ "name": "ipython",
+ "version": 3
+ },
+ "file_extension": ".py",
+ "mimetype": "text/x-python",
+ "name": "python",
+ "nbconvert_exporter": "python",
+ "pygments_lexer": "ipython3",
+ "version": "3.8.5"
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+ "nbformat": 4,
+ "nbformat_minor": 2
+}
diff --git a/notebooks/ubinnedLikelihood.ipynb b/notebooks/ubinnedLikelihood.ipynb
new file mode 100644
index 0000000..080fc3a
--- /dev/null
+++ b/notebooks/ubinnedLikelihood.ipynb
@@ -0,0 +1,457 @@
+{
+ "cells": [
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "# Solutions 7\n",
+ "Maximum Likelihood method"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 205,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "from __future__ import print_function\n",
+ "import numpy as np\n",
+ "%matplotlib inline\n",
+ "import matplotlib.pyplot as plt\n",
+ "from scipy.optimize import curve_fit, minimize, fsolve\n",
+ "from scipy.stats import norm, chi2, lognorm"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 151,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "measurements = np.array([97.8621, 114.105, 87.7593, 93.2134, 86.6624, 87.4629, 79.7712, \\\n",
+ "91.5024, 87.7737, 89.6926, 133.506, 91.4124, 94.4401, 97.3968, \\\n",
+ "108.424, 103.197, 88.2166, 142.217, 89.0393, 102.438, 95.7987, \\\n",
+ "94.5177, 96.8171, 90.903, 132.463, 92.3394, 84.1451, 87.3447, \\\n",
+ "92.2861, 84.4213, 124.017, 90.4941, 95.7992, 92.3484, 95.9813, \\\n",
+ "88.0641, 101.002, 97.7268, 137.379, 96.213, 140.795, 99.9332, \\\n",
+ "130.087, 108.839, 90.0145, 100.313, 87.5952, 92.995, 114.457, \\\n",
+ "90.7526, 112.181, 117.857, 95.2804, 115.922, 117.043, 104.317, \\\n",
+ "126.728, 87.8592, 89.9614, 100.377, 107.38, 88.8426, 93.3224, \\\n",
+ "138.947, 102.288, 123.431, 114.334, 88.5134, 124.7, 87.7316, 84.7141, \\\n",
+ "91.1646, 87.891, 121.257, 92.9314])"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## 1-D Maximum likelihood fit"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "We have a set of measurements which are distributed according to the sum of two Gaussians (e.g. this can be signal and background).\n",
+ "\n",
+ "$\\rho = \\frac{1}{3}\\frac{1}{\\sqrt{2\\pi \\sigma^2}} e^{-\\frac{1}{2}\\left(\\frac{x-p}{\\sigma}\\right)^2} + \\frac{2}{3}\\frac{1}{\\sqrt{2\\pi \\sigma_b^2}} e^{-\\frac{1}{2}\\left(\\frac{x-p_b}{\\sigma_b}\\right)^2}$ \n",
+ "\n",
+ "where for one of the two peaks the parameters are known already\n",
+ "\n",
+ "$p_b = 91.0$ \n",
+ "$\\sigma_b = 5.0$ \n",
+ " "
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 228,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "def likelihood_point(x, position, width):\n",
+ " return 1.0/3/np.sqrt(2*np.pi*width**2)*np.exp(-0.5*((x-position)/(width))**2.0) + 2.0/3/np.sqrt(2*np.pi*5**2)*np.exp(-0.5*((x-91)/(5))**2.0)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "First, we assume the width of the peak we want to fit is already known: $\\sigma = 15.0$.\n",
+ "Perform a 1-D Maximum Likelihood fit for the position of the peak $p$.\n",
+ "\n",
+ "Complete the functions below which return the likelihood and negative log likelihood (NLL)."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 347,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "def likelihood_1d(params):\n",
+ " return np.prod([likelihood_point(x, params[0], 15.0) for x in measurements])\n",
+ "\n",
+ "def nll_1d(params):\n",
+ " return -np.log(likelihood_1d(params))"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Minimize the NLL and give the best-fit result, including asymetric errors and plot the NLL."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 355,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "position: 117.72333147980623\n",
+ "negative error: [3.31211666]\n",
+ "positive error: [3.39091994]\n"
+ ]
+ },
+ {
+ "data": {
+ "image/png": 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\n",
+ "text/plain": [
+ "<Figure size 432x288 with 1 Axes>"
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "solution = minimize(nll_1d, [100.0], method='CG')\n",
+ "min_pos = solution.x[0]\n",
+ "min0 = solution.fun\n",
+ "scan_points = np.linspace(110.0,126.0,50)\n",
+ "plt.plot(scan_points, [nll_1d([x]) - min0 for x in scan_points])\n",
+ "\n",
+ "nll_1sigma = lambda x: nll_1d([x]) - min0 - 0.5\n",
+ "print(\"position:\", min_pos)\n",
+ "print(\"negative error:\", min_pos - fsolve(nll_1sigma, min_pos-0.5))\n",
+ "print(\"positive error:\", fsolve(nll_1sigma, min_pos+0.5) - min_pos)\n",
+ "plt.show()"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## 2-D Likelihood fit"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Now we perform the 2-D Maximum Likelihood fit, fitting for both $\\sigma$ and $p$ at the same time."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 350,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "def likelihood(params):\n",
+ " return np.prod([likelihood_point(x, params[0], params[1]) for x in measurements])\n",
+ "\n",
+ "def nll(params):\n",
+ " return -np.log(likelihood(params))"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Minimize the NLL and find the best-fit result."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 353,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "position: 118.31548192622421 width: 13.629783202046086\n"
+ ]
+ }
+ ],
+ "source": [
+ "solution = minimize(nll, [120.0, 10], method='CG')\n",
+ "print(\"position:\", solution.x[0], \"width:\", solution.x[1])"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Create a 2D contour plot of the 1, 2 and 3 $\\sigma$ contours of the NLL and plot the best-fit solution."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 354,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "image/png": 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\n",
+ "text/plain": [
+ "<Figure size 432x288 with 1 Axes>"
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "scanA = np.linspace(110.0,130.0,50)\n",
+ "scanB = np.linspace(5,20,50)\n",
+ "minValue = nll(solution.x)\n",
+ "Z = [[nll([a,b]) - minValue for b in scanB] for a in scanA]\n",
+ "p1 = plt.contour(scanB, scanA, Z, [0.01,0.5, 2.0, 4.5])"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Compute numerically the error matrix of the NLL for the 2-D fit."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 301,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "[[11.95694692 -3.06065748]\n",
+ " [-3.06065748 5.72672173]] \n",
+ "sigma(position): 3.4578818544955507 sigma(width): 2.3930569834299082\n"
+ ]
+ }
+ ],
+ "source": [
+ "from scipy.misc import derivative\n",
+ "\n",
+ "# compute the error matrix\n",
+ "A = np.linalg.inv([\n",
+ " [\n",
+ " derivative(lambda x: nll([x, solution.x[1]]), solution.x[0], n=2),\n",
+ " derivative(lambda y: derivative(lambda x: nll([x, y]), solution.x[0]), solution.x[1])\n",
+ " ],\n",
+ " [\n",
+ " derivative(lambda x: derivative(lambda y: nll([x, y]), solution.x[1]), solution.x[0]),\n",
+ " derivative(lambda y: nll([solution.x[0], y]), solution.x[1], n=2)\n",
+ " ]\n",
+ "])\n",
+ "print(A, \"\\nsigma(position):\", np.sqrt(A[0,0]), \"sigma(width):\", np.sqrt(A[1,1]))"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Binned ML fit"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "With the same data as above, we now perform a binned ML fit and compare with the unbinned fit.\n",
+ "First, create a histogram of the data using np.histogram."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 374,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "[ 1 19 26 10 7 5 5 2 0 0]\n",
+ "[ 70. 80. 90. 100. 110. 120. 130. 140. 150. 160. 170.]\n"
+ ]
+ }
+ ],
+ "source": [
+ "nBins = 10\n",
+ "histoMax = 170\n",
+ "histoMin = 70\n",
+ "binWidth = (histoMax-histoMin)/nBins\n",
+ "h0 = np.histogram(measurements, bins=nBins, range=(histoMin, histoMax))\n",
+ "print(h0[0])\n",
+ "print(h0[1])"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Compute the binned NLL:"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 375,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "def nll_binned(params):\n",
+ " # params is a list of [position, sigma]\n",
+ " expected = [likelihood_point(x+binWidth/2, params[0], params[1])*(binWidth/2)*sum(h0[0]) for x in h0[1]]\n",
+ " return sum([-np.log(expected[i]**h0[0][i]) for i in range(nBins)])"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Minimize the binned NLL:"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 376,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ " fun: -138.93433719876123\n",
+ " jac: array([-1.90734863e-06, 1.90734863e-06])\n",
+ " message: 'Optimization terminated successfully.'\n",
+ " nfev: 60\n",
+ " nit: 6\n",
+ " njev: 15\n",
+ " status: 0\n",
+ " success: True\n",
+ " x: array([116.43876363, 15.33581135])\n"
+ ]
+ }
+ ],
+ "source": [
+ "solution_binned=minimize(nll_binned, [120.0, 10], method='CG')\n",
+ "print(solution_binned)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Make a contour plot of the 1,2, and 3 $\\sigma$ contours for the binned NLL and overlay it with the unbinned contours."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 377,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "image/png": 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\n",
+ "text/plain": [
+ "<Figure size 432x288 with 1 Axes>"
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "scanA = np.linspace(110.0,130.0,50)\n",
+ "scanB = np.linspace(5,20,50)\n",
+ "Z_binned = [[nll_binned([a,b]) - solution_binned.fun for b in scanB] for a in scanA]\n",
+ "\n",
+ "fig1, ax2 = plt.subplots(constrained_layout=True)\n",
+ "\n",
+ "p1 = ax2.contour(scanB, scanA, Z, [0.01,0.5, 2.0, 4.5])\n",
+ "p2 = ax2.contour(scanB, scanA, Z_binned, [0.01,0.5, 2.0, 4.5], linestyles=\"dotted\")\n",
+ "plt.show()"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Repeat the same for 50 bins:"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 373,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "image/png": 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\n",
+ "text/plain": [
+ "<Figure size 432x288 with 1 Axes>"
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "scanA = np.linspace(110.0,130.0,50)\n",
+ "scanB = np.linspace(5,20,50)\n",
+ "Z_binned = [[nll_binned([a,b]) - solution_binned.fun for b in scanB] for a in scanA]\n",
+ "\n",
+ "fig1, ax2 = plt.subplots(constrained_layout=True)\n",
+ "\n",
+ "p1 = ax2.contour(scanB, scanA, Z, [0.01,0.5, 2.0, 4.5])\n",
+ "p2 = ax2.contour(scanB, scanA, Z_binned, [0.01,0.5, 2.0, 4.5], linestyles=\"dotted\")\n",
+ "plt.show()"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": []
+ }
+ ],
+ "metadata": {
+ "kernelspec": {
+ "display_name": "Python 3",
+ "language": "python",
+ "name": "python3"
+ },
+ "language_info": {
+ "codemirror_mode": {
+ "name": "ipython",
+ "version": 3
+ },
+ "file_extension": ".py",
+ "mimetype": "text/x-python",
+ "name": "python",
+ "nbconvert_exporter": "python",
+ "pygments_lexer": "ipython3",
+ "version": "3.8.5"
+ }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 2
+}
diff --git a/notebooks/unbinnedLikelihood.ipynb b/notebooks/unbinnedLikelihood.ipynb
deleted file mode 100644
index 1b3f6c6..0000000
--- a/notebooks/unbinnedLikelihood.ipynb
+++ /dev/null
@@ -1,854 +0,0 @@
-{
- "cells": [
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "# Unbinned Likelihood fits\n",
- "\n",
- "In this notebook we will be using probfit together with iminuit to perform an Unbinned Likelihood fit.\n",
- " \n",
- "probfit: \n",
- "https://probfit.readthedocs.io/en/latest/ \n",
- " \n",
- "iMinuit: \n",
- "https://iminuit.readthedocs.io/en/latest/index.html# \n",
- "\n",
- "Here below a quick summary of: \n",
- "http://piti118.github.io/babar_python_tutorial/notebooks/04_Fitting.html \n"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 1,
- "metadata": {},
- "outputs": [],
- "source": [
- "import numpy as np\n",
- "%matplotlib inline\n",
- "import matplotlib.pyplot as plt\n",
- "import scipy.stats\n",
- "from math import exp, pi, sqrt\n",
- "from probfit import UnbinnedLH\n",
- "from iminuit import Minuit, describe"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 2,
- "metadata": {},
- "outputs": [],
- "source": [
- "# Generate data\n",
- "# set the seed to always get the same samples\n",
- "np.random.seed(seed=12345)\n",
- "\n",
- "# Generate a toy dataset on an gaussian distribution (signal)\n",
- "#mu = 125, sigma = 1\n",
- "gdata = scipy.stats.norm.rvs(loc=0, scale=1, size=10)"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 18,
- "metadata": {},
- "outputs": [
- {
- "name": "stdout",
- "output_type": "stream",
- "text": [
- "3.0\n"
- ]
- },
- {
- "data": {
- "text/plain": [
- "Text(0, 0.5, 'Entries / bins size = 0.4')"
- ]
- },
- "execution_count": 18,
- "metadata": {},
- "output_type": "execute_result"
- },
- {
- "data": {
- "image/png": "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\n",
- "text/plain": [
- "<Figure size 360x360 with 1 Axes>"
- ]
- },
- "metadata": {
- "needs_background": "light"
- },
- "output_type": "display_data"
- }
- ],
- "source": [
- "plt.figure(figsize=[5,5])\n",
- "plt.subplot(111)\n",
- "n, bins, patches = plt.hist(gdata, bins=25, range=[-5,5], color='blue', alpha=0.5)\n",
- "max = np.amax(n)\n",
- "plt.xlabel(r'x [units]')\n",
- "plt.ylabel(r'Entries / bins size = 0.4')"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 4,
- "metadata": {},
- "outputs": [
- {
- "data": {
- "text/plain": [
- "['mean', 'sigma']"
- ]
- },
- "execution_count": 4,
- "metadata": {},
- "output_type": "execute_result"
- }
- ],
- "source": [
- "from probfit import gaussian\n",
- "ulh = UnbinnedLH(gaussian, gdata)\n",
- "describe(ulh)"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 20,
- "metadata": {
- "scrolled": false
- },
- "outputs": [
- {
- "data": {
- "image/png": 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\n",
- "text/plain": [
- "<Figure size 360x360 with 1 Axes>"
- ]
- },
- "metadata": {
- "needs_background": "light"
- },
- "output_type": "display_data"
- },
- {
- "data": {
- "text/html": [
- "<table>\n",
- "<tr style=\"background-color:#F4F4F4;\">\n",
- "<td/>\n",
- "<th title=\"Variable name\">\n",
- "Name\n",
- "</th>\n",
- "<th title=\"Value of parameter\">\n",
- "Value\n",
- "</th>\n",
- "<th title=\"Hesse error\">\n",
- "Hesse Error\n",
- "</th>\n",
- "<th title=\"Minos lower error\">\n",
- "Minos Error-\n",
- "</th>\n",
- "<th title=\"Minos upper error\">\n",
- "Minos Error+\n",
- "</th>\n",
- "<th title=\"Lower limit of the parameter\">\n",
- "Limit-\n",
- "</th>\n",
- "<th title=\"Upper limit of the parameter\">\n",
- "Limit+\n",
- "</th>\n",
- "<th title=\"Is the parameter fixed in the fit\">\n",
- "Fixed\n",
- "</th>\n",
- "</tr>\n",
- "<tr style=\"background-color:#FFFFFF;\">\n",
- "<td>\n",
- "0\n",
- "</td>\n",
- "<td>\n",
- "mean\n",
- "</td>\n",
- "<td>\n",
- "1.00\n",
- "</td>\n",
- "<td>\n",
- "0.10\n",
- "</td>\n",
- "<td>\n",
- "\n",
- "</td>\n",
- "<td>\n",
- "\n",
- "</td>\n",
- "<td>\n",
- "\n",
- "</td>\n",
- "<td>\n",
- "\n",
- "</td>\n",
- "<td>\n",
- "\n",
- "</td>\n",
- "</tr>\n",
- "<tr style=\"background-color:#F4F4F4;\">\n",
- "<td>\n",
- "1\n",
- "</td>\n",
- "<td>\n",
- "sigma\n",
- "</td>\n",
- "<td>\n",
- "2.00\n",
- "</td>\n",
- "<td>\n",
- "0.10\n",
- "</td>\n",
- "<td>\n",
- "\n",
- "</td>\n",
- "<td>\n",
- "\n",
- "</td>\n",
- "<td>\n",
- "\n",
- "</td>\n",
- "<td>\n",
- "\n",
- "</td>\n",
- "<td>\n",
- "\n",
- "</td>\n",
- "</tr>\n",
- "</table>\n"
- ],
- "text/plain": [
- "-------------------------------------------------------------------------------------------\n",
- "| | Name | Value | Hesse Err | Minos Err- | Minos Err+ | Limit- | Limit+ | Fixed |\n",
- "-------------------------------------------------------------------------------------------\n",
- "| 0 | mean | 1.00 | 0.10 | | | | | |\n",
- "| 1 | sigma | 2.00 | 0.10 | | | | | |\n",
- "-------------------------------------------------------------------------------------------"
- ]
- },
- "execution_count": 20,
- "metadata": {},
- "output_type": "execute_result"
- }
- ],
- "source": [
- "m = Minuit(ulh, \n",
- " mean=1, sigma=2,\n",
- " error_mean=0.1, error_sigma=0.1,\n",
- " errordef=0.5)#remember up is 0.5 for likelihood and 1 for chi^2\n",
- "\n",
- "# Show() is the same thing as draw(). But show the figure immediately.\n",
- "# For all parameters and return vars:\n",
- "# https://probfit.readthedocs.io/en/latest/api.html#probfit.costfunc.UnbinnedLH.draw\n",
- "plt.figure(figsize=[5,5])\n",
- "plt.ylim([0.1,max*1.5])\n",
- "ulh.show(m, bins=25, bound=[-5,5],print_par=True)\n",
- "m.get_param_states()"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 22,
- "metadata": {},
- "outputs": [
- {
- "data": {
- "image/png": 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\n",
- "text/plain": [
- "<Figure size 360x360 with 1 Axes>"
- ]
- },
- "metadata": {
- "needs_background": "light"
- },
- "output_type": "display_data"
- },
- {
- "data": {
- "text/html": [
- "<table>\n",
- "<tr style=\"background-color:#F4F4F4;\">\n",
- "<td/>\n",
- "<th title=\"Variable name\">\n",
- "Name\n",
- "</th>\n",
- "<th title=\"Value of parameter\">\n",
- "Value\n",
- "</th>\n",
- "<th title=\"Hesse error\">\n",
- "Hesse Error\n",
- "</th>\n",
- "<th title=\"Minos lower error\">\n",
- "Minos Error-\n",
- "</th>\n",
- "<th title=\"Minos upper error\">\n",
- "Minos Error+\n",
- "</th>\n",
- "<th title=\"Lower limit of the parameter\">\n",
- "Limit-\n",
- "</th>\n",
- "<th title=\"Upper limit of the parameter\">\n",
- "Limit+\n",
- "</th>\n",
- "<th title=\"Is the parameter fixed in the fit\">\n",
- "Fixed\n",
- "</th>\n",
- "</tr>\n",
- "<tr style=\"background-color:#FFFFFF;\">\n",
- "<td>\n",
- "0\n",
- "</td>\n",
- "<td>\n",
- "mean\n",
- "</td>\n",
- "<td>\n",
- "0.49\n",
- "</td>\n",
- "<td>\n",
- "0.25\n",
- "</td>\n",
- "<td>\n",
- "\n",
- "</td>\n",
- "<td>\n",
- "\n",
- "</td>\n",
- "<td>\n",
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- "<td>\n",
- "\n",
- "</td>\n",
- "<td>\n",
- "\n",
- "</td>\n",
- "</tr>\n",
- "<tr style=\"background-color:#F4F4F4;\">\n",
- "<td>\n",
- "1\n",
- "</td>\n",
- "<td>\n",
- "sigma\n",
- "</td>\n",
- "<td>\n",
- "0.80\n",
- "</td>\n",
- "<td>\n",
- "0.18\n",
- "</td>\n",
- "<td>\n",
- "\n",
- "</td>\n",
- "<td>\n",
- "\n",
- "</td>\n",
- "<td>\n",
- "\n",
- "</td>\n",
- "<td>\n",
- "\n",
- "</td>\n",
- "<td>\n",
- "\n",
- "</td>\n",
- "</tr>\n",
- "</table>\n"
- ],
- "text/plain": [
- "-------------------------------------------------------------------------------------------\n",
- "| | Name | Value | Hesse Err | Minos Err- | Minos Err+ | Limit- | Limit+ | Fixed |\n",
- "-------------------------------------------------------------------------------------------\n",
- "| 0 | mean | 0.49 | 0.25 | | | | | |\n",
- "| 1 | sigma | 0.80 | 0.18 | | | | | |\n",
- "-------------------------------------------------------------------------------------------"
- ]
- },
- "execution_count": 22,
- "metadata": {},
- "output_type": "execute_result"
- }
- ],
- "source": [
- "m.migrad()\n",
- "\n",
- "plt.figure(figsize=[5,5])\n",
- "plt.ylim([0.1,max*1.5])\n",
- "ulh.show(m, bins=25, bound=[-5,5],print_par=True)\n",
- "m.get_param_states()"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 23,
- "metadata": {},
- "outputs": [
- {
- "data": {
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- "sigma\n",
- "</th>\n",
- "</tr>\n",
- "<tr>\n",
- "<th>\n",
- "mean\n",
- "</th>\n",
- "<td>\n",
- "0.644E-1\n",
- "</td>\n",
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- ],
- "text/plain": [
- "-----------------------------\n",
- "| | mean sigma |\n",
- "-----------------------------\n",
- "| mean | 0.644E-1 0.000E-1 |\n",
- "| sigma | 0.000E-1 0.322E-1 |\n",
- "-----------------------------"
- ]
- },
- "execution_count": 23,
- "metadata": {},
- "output_type": "execute_result"
- }
- ],
- "source": [
- "m.matrix()"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 24,
- "metadata": {},
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- "text/plain": [
- "-------------------------------------------------\n",
- "| mean | Valid |\n",
- "-------------------------------------------------\n",
- "| Error | -0.26 | 0.26 |\n",
- "| Valid | True | True |\n",
- "| At Limit | False | False |\n",
- "| Max FCN | False | False |\n",
- "| New Min | False | False |\n",
- "-------------------------------------------------\n",
- "-------------------------------------------------\n",
- "| sigma | Valid |\n",
- "-------------------------------------------------\n",
- "| Error | -0.15 | 0.22 |\n",
- "| Valid | True | True |\n",
- "| At Limit | False | False |\n",
- "| Max FCN | False | False |\n",
- "| New Min | False | False |\n",
- "-------------------------------------------------"
- ]
- },
- "execution_count": 24,
- "metadata": {},
- "output_type": "execute_result"
- }
- ],
- "source": [
- "m.minos()"
- ]
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- {
- "cell_type": "code",
- "execution_count": 25,
- "metadata": {},
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- "data": {
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- "<th title=\"Value of parameter\">\n",
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- "<th title=\"Hesse error\">\n",
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- "-------------------------------------------------------------------------------------------\n",
- "| | Name | Value | Hesse Err | Minos Err- | Minos Err+ | Limit- | Limit+ | Fixed |\n",
- "-------------------------------------------------------------------------------------------\n",
- "| 0 | mean | 0.49 | 0.25 | -0.26 | 0.26 | | | |\n",
- "| 1 | sigma | 0.80 | 0.18 | -0.15 | 0.22 | | | |\n",
- "-------------------------------------------------------------------------------------------"
- ]
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- "execution_count": 25,
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- }
- ],
- "source": [
- "m.get_param_states()"
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- {
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- "execution_count": 26,
- "metadata": {},
- "outputs": [
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\n",
- "text/plain": [
- "<Figure size 432x288 with 1 Axes>"
- ]
- },
- "metadata": {
- "needs_background": "light"
- },
- "output_type": "display_data"
- }
- ],
- "source": [
- "m.draw_profile('mean');"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 27,
- "metadata": {},
- "outputs": [
- {
- "data": {
- "image/png": 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\n",
- "text/plain": [
- "<Figure size 432x288 with 1 Axes>"
- ]
- },
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- "needs_background": "light"
- },
- "output_type": "display_data"
- }
- ],
- "source": [
- "m.draw_profile('sigma');"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 28,
- "metadata": {},
- "outputs": [
- {
- "data": {
- "image/png": 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\n",
- "text/plain": [
- "<Figure size 432x288 with 1 Axes>"
- ]
- },
- "metadata": {
- "needs_background": "light"
- },
- "output_type": "display_data"
- }
- ],
- "source": [
- "px, py = m.profile('mean', subtract_min=True)\n",
- "plt.plot(px, py);"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 29,
- "metadata": {},
- "outputs": [
- {
- "data": {
- "text/plain": [
- "<matplotlib.contour.ContourSet at 0x1a1a52c850>"
- ]
- },
- "execution_count": 29,
- "metadata": {},
- "output_type": "execute_result"
- },
- {
- "data": {
- "image/png": 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\n",
- "text/plain": [
- "<Figure size 360x360 with 1 Axes>"
- ]
- },
- "metadata": {
- "needs_background": "light"
- },
- "output_type": "display_data"
- }
- ],
- "source": [
- "plt.figure(figsize=[5,5])\n",
- "m.draw_mncontour('mean', 'sigma', nsigma=4, numpoints=100) # nsigma=4 says: draw four contours from sigma=1 to 4"
- ]
- }
- ],
- "metadata": {
- "kernelspec": {
- "display_name": "Python 3",
- "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": "3.7.7"
- }
- },
- "nbformat": 4,
- "nbformat_minor": 2
-}
diff --git a/notebooks/unbinnedLikelihood_probfit.ipynb b/notebooks/unbinnedLikelihood_probfit.ipynb
new file mode 100644
index 0000000..87953d1
--- /dev/null
+++ b/notebooks/unbinnedLikelihood_probfit.ipynb
@@ -0,0 +1,720 @@
+{
+ "cells": [
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "# Unbinned Likelihood fits\n",
+ "\n",
+ "In this notebook we will be using probfit together with iminuit to perform an Unbinned Likelihood fit.\n",
+ " \n",
+ "probfit: \n",
+ "https://probfit.readthedocs.io/en/latest/ \n",
+ " \n",
+ "iMinuit: \n",
+ "https://iminuit.readthedocs.io/en/latest/index.html# \n",
+ "\n",
+ "Here below a quick summary of: \n",
+ "http://piti118.github.io/babar_python_tutorial/notebooks/04_Fitting.html \n"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 1,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "import numpy as np\n",
+ "%matplotlib inline\n",
+ "import matplotlib.pyplot as plt\n",
+ "import scipy.stats\n",
+ "from math import exp, pi, sqrt\n",
+ "#from probfit import UnbinnedLH\n",
+ "from argparse import Namespace\n",
+ "import math\n",
+ "\n",
+ "from iminuit import Minuit, describe\n",
+ "from iminuit.cost import UnbinnedNLL"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 2,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "# Generate data\n",
+ "# set the seed to always get the same samples\n",
+ "np.random.seed(seed=12345)\n",
+ "\n",
+ "# Generate a toy dataset on an gaussian distribution (signal)\n",
+ "#mu = 125, sigma = 1\n",
+ "gdata = scipy.stats.norm.rvs(loc=0, scale=1, size=10)\n",
+ "truth = Namespace(mu=0, sigma=1)\n",
+ "\n",
+ "def norm_pdf(x, mu, sigma):\n",
+ " invs = 1.0 / sigma\n",
+ " z = (x - mu) * invs\n",
+ " invnorm = 1 / np.sqrt(2 * np.pi) * invs\n",
+ " return np.exp(-0.5 * z ** 2) * invnorm\n",
+ "\n",
+ "def nb_erf(x):\n",
+ " y = np.empty_like(x)\n",
+ " for i in range(len(x)):\n",
+ " y[i] = math.erf(x[i])\n",
+ " return y\n",
+ "\n",
+ "def norm_cdf(x, mu, sigma):\n",
+ " invs = 1.0 / (sigma * np.sqrt(2))\n",
+ " z = (x - mu) * invs\n",
+ " return 0.5 * (1 + nb_erf(z))\n",
+ "\n",
+ "def norm_delta(xrange, mu, sigma):\n",
+ " c = norm_cdf(xrange, mu, sigma)\n",
+ " return c[1] - c[0]\n"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 3,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "Text(0, 0.5, 'Entries / bins size = 0.4')"
+ ]
+ },
+ "execution_count": 3,
+ "metadata": {},
+ "output_type": "execute_result"
+ },
+ {
+ "data": {
+ "image/png": "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\n",
+ "text/plain": [
+ "<Figure size 360x360 with 1 Axes>"
+ ]
+ },
+ "metadata": {
+ "needs_background": "light"
+ },
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "plt.figure(figsize=[5,5])\n",
+ "plt.subplot(111)\n",
+ "xrange = [-5,5]\n",
+ "n, bins, patches = plt.hist(gdata, bins=25, range=xrange, color='blue', alpha=0.5)\n",
+ "max = np.amax(n)\n",
+ "plt.xlabel(r'x [units]')\n",
+ "plt.ylabel(r'Entries / bins size = 0.4')"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 19,
+ "metadata": {
+ "scrolled": false
+ },
+ "outputs": [],
+ "source": [
+ "m = Minuit(UnbinnedNLL(gdata,\n",
+ " lambda x, mu, sigma: (norm_pdf(x, mu, sigma) / norm_delta(xrange, mu, sigma)),\n",
+ " ),\n",
+ " mu=truth.mu,\n",
+ " sigma=truth.sigma,\n",
+ " )\n",
+ "\n"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 28,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/html": [
+ "<table>\n",
+ " <tr>\n",
+ " <td colspan=\"2\" style=\"text-align:left\" title=\"Minimum value of function\"> FCN = 23.98 </td>\n",
+ " <td colspan=\"3\" style=\"text-align:center\" title=\"No. of function evaluations in last call and total number\"> Nfcn = 85 </td>\n",
+ " </tr>\n",
+ " <tr>\n",
+ " <td colspan=\"2\" style=\"text-align:left\" title=\"Estimated distance to minimum and goal\"> EDM = 1.28e-23 (Goal: 0.0002) </td>\n",
+ " <td colspan=\"3\" style=\"text-align:center\" title=\"No. of gradient evaluations in last call and total number\"> </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\"> Valid Parameters </td>\n",
+ " <td colspan=\"3\" style=\"text-align:center;background-color:#92CCA6;color:black\"> No Parameters at limit </td>\n",
+ " </tr>\n",
+ " <tr>\n",
+ " <td colspan=\"2\" style=\"text-align:center;background-color:#92CCA6;color:black\"> Below EDM threshold (goal x 10) </td>\n",
+ " <td colspan=\"3\" style=\"text-align:center;background-color:#92CCA6;color:black\"> Below call limit </td>\n",
+ " </tr>\n",
+ " <tr>\n",
+ " <td style=\"text-align:center;background-color:#92CCA6;color:black\"> Covariance </td>\n",
+ " <td style=\"text-align:center;background-color:#92CCA6;color:black\"> Hesse ok </td>\n",
+ " <td style=\"text-align:center;background-color:#92CCA6;color:black\" title=\"Is covariance matrix accurate?\"> Accurate </td>\n",
+ " <td style=\"text-align:center;background-color:#92CCA6;color:black\" title=\"Is covariance matrix positive definite?\"> Pos. def. </td>\n",
+ " <td style=\"text-align:center;background-color:#92CCA6;color:black\" title=\"Was positive definiteness enforced by Minuit?\"> Not forced </td>\n",
+ " </tr>\n",
+ "</table><table>\n",
+ " <tr>\n",
+ " <td></td>\n",
+ " <th title=\"Variable name\"> Name </th>\n",
+ " <th title=\"Value of parameter\"> Value </th>\n",
+ " <th title=\"Hesse error\"> Hesse Error </th>\n",
+ " <th title=\"Minos lower error\"> Minos Error- </th>\n",
+ " <th title=\"Minos upper error\"> Minos Error+ </th>\n",
+ " <th title=\"Lower limit of the parameter\"> Limit- </th>\n",
+ " <th title=\"Upper limit of the parameter\"> Limit+ </th>\n",
+ " <th title=\"Is the parameter fixed in the fit\"> Fixed </th>\n",
+ " </tr>\n",
+ " <tr>\n",
+ " <th> 0 </th>\n",
+ " <td> mu </td>\n",
+ " <td> 0.49 </td>\n",
+ " <td> 0.25 </td>\n",
+ " <td> </td>\n",
+ " <td> </td>\n",
+ " <td> </td>\n",
+ " <td> </td>\n",
+ " <td> </td>\n",
+ " </tr>\n",
+ " <tr>\n",
+ " <th> 1 </th>\n",
+ " <td> sigma </td>\n",
+ " <td> 0.80 </td>\n",
+ " <td> 0.18 </td>\n",
+ " <td> </td>\n",
+ " <td> </td>\n",
+ " <td> </td>\n",
+ " <td> </td>\n",
+ " <td> </td>\n",
+ " </tr>\n",
+ "</table><table>\n",
+ " <tr>\n",
+ " <td></td>\n",
+ " <th> mu </th>\n",
+ " <th> sigma </th>\n",
+ " </tr>\n",
+ " <tr>\n",
+ " <th> mu </th>\n",
+ " <td> 0.0644 </td>\n",
+ " <td style=\"background-color:rgb(250,250,250);color:black\"> -4.21e-07 </td>\n",
+ " </tr>\n",
+ " <tr>\n",
+ " <th> sigma </th>\n",
+ " <td style=\"background-color:rgb(250,250,250);color:black\"> -4.21e-07 </td>\n",
+ " <td> 0.0322 </td>\n",
+ " </tr>\n",
+ "</table>"
+ ],
+ "text/plain": [
+ "┌──────────────────────────────────┬──────────────────────────────────────â”\n",
+ "│ FCN = 23.98 │ Nfcn = 85 │\n",
+ "│ EDM = 1.28e-23 (Goal: 0.0002) │ │\n",
+ "├───────────────┬──────────────────┼──────────────────────────────────────┤\n",
+ "│ Valid Minimum │ Valid Parameters │ No Parameters at limit │\n",
+ "├───────────────┴──────────────────┼──────────────────────────────────────┤\n",
+ "│ Below EDM threshold (goal x 10) │ Below call limit │\n",
+ "├───────────────┬──────────────────┼───────────┬─────────────┬────────────┤\n",
+ "│ Covariance │ Hesse ok │ Accurate │ Pos. def. │ Not forced │\n",
+ "└───────────────┴──────────────────┴───────────┴─────────────┴────────────┘\n",
+ "┌───┬───────┬───────────┬───────────┬────────────┬────────────┬─────────┬─────────┬───────â”\n",
+ "│ │ Name │ Value │ Hesse Err │ Minos Err- │ Minos Err+ │ Limit- │ Limit+ │ Fixed │\n",
+ "├───┼───────┼───────────┼───────────┼────────────┼────────────┼─────────┼─────────┼───────┤\n",
+ "│ 0 │ mu │ 0.49 │ 0.25 │ │ │ │ │ │\n",
+ "│ 1 │ sigma │ 0.80 │ 0.18 │ │ │ │ │ │\n",
+ "└───┴───────┴───────────┴───────────┴────────────┴────────────┴─────────┴─────────┴───────┘\n",
+ "┌───────┬─────────────────────â”\n",
+ "│ │ mu sigma │\n",
+ "├───────┼─────────────────────┤\n",
+ "│ mu │ 0.0644 -4.21e-07 │\n",
+ "│ sigma │ -4.21e-07 0.0322 │\n",
+ "└───────┴─────────────────────┘"
+ ]
+ },
+ "execution_count": 28,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "m.migrad()"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 36,
+ "metadata": {},
+ "outputs": [
+ {
+ "ename": "TypeError",
+ "evalue": "unsupported operand type(s) for -: 'list' and 'float'",
+ "output_type": "error",
+ "traceback": [
+ "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
+ "\u001b[0;31mTypeError\u001b[0m Traceback (most recent call last)",
+ "\u001b[0;32m<ipython-input-36-9268e6007dfb>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m\u001b[0m\n\u001b[1;32m 9\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 10\u001b[0m \u001b[0;31m#plt.plot(gdata, norm_pdf(gdata, m.values[0], m.values[1])/norm_delta(xrange, m.values[0], m.values[1]) , label=\"fit\")\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 11\u001b[0;31m \u001b[0mplt\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mplot\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mgdata\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mnorm_pdf\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mgdata\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mm\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mvalues\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m0\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mm\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mvalues\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m/\u001b[0m\u001b[0mnorm_delta\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mxrange\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mm\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mvalues\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m0\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mm\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mvalues\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;34m,\u001b[0m \u001b[0mlabel\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;34m\"fit\"\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m 12\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 13\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n",
+ "\u001b[0;32m<ipython-input-2-c6ed65eb7b5e>\u001b[0m in \u001b[0;36mnorm_delta\u001b[0;34m(xrange, mu, sigma)\u001b[0m\n\u001b[1;32m 27\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 28\u001b[0m \u001b[0;32mdef\u001b[0m \u001b[0mnorm_delta\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mxrange\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mmu\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0msigma\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 29\u001b[0;31m \u001b[0mc\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mnorm_cdf\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mxrange\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mmu\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0msigma\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m 30\u001b[0m \u001b[0;32mreturn\u001b[0m \u001b[0mc\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m]\u001b[0m \u001b[0;34m-\u001b[0m \u001b[0mc\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m0\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
+ "\u001b[0;32m<ipython-input-2-c6ed65eb7b5e>\u001b[0m in \u001b[0;36mnorm_cdf\u001b[0;34m(x, mu, sigma)\u001b[0m\n\u001b[1;32m 23\u001b[0m \u001b[0;32mdef\u001b[0m \u001b[0mnorm_cdf\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mx\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mmu\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0msigma\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 24\u001b[0m \u001b[0minvs\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;36m1.0\u001b[0m \u001b[0;34m/\u001b[0m \u001b[0;34m(\u001b[0m\u001b[0msigma\u001b[0m \u001b[0;34m*\u001b[0m \u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0msqrt\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m2\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 25\u001b[0;31m \u001b[0mz\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;34m(\u001b[0m\u001b[0mx\u001b[0m \u001b[0;34m-\u001b[0m \u001b[0mmu\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;34m*\u001b[0m \u001b[0minvs\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m 26\u001b[0m \u001b[0;32mreturn\u001b[0m \u001b[0;36m0.5\u001b[0m \u001b[0;34m*\u001b[0m \u001b[0;34m(\u001b[0m\u001b[0;36m1\u001b[0m \u001b[0;34m+\u001b[0m \u001b[0mnb_erf\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mz\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 27\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n",
+ "\u001b[0;31mTypeError\u001b[0m: unsupported operand type(s) for -: 'list' and 'float'"
+ ]
+ },
+ {
+ "data": {
+ "image/png": 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\n",
+ "text/plain": [
+ "<Figure size 360x360 with 1 Axes>"
+ ]
+ },
+ "metadata": {
+ "needs_background": "light"
+ },
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "# Show() is the same thing as draw(). But show the figure immediately.\n",
+ "plt.figure(figsize=[5,5])\n",
+ "plt.subplot(111)\n",
+ "xrange = [-5,5]\n",
+ "n, bins, patches = plt.hist(gdata, bins=25, range=xrange, color='blue', alpha=0.5)\n",
+ "max = np.amax(n)\n",
+ "plt.xlabel(r'x [units]')\n",
+ "plt.ylabel(r'Entries / bins size = 0.4')\n",
+ "\n",
+ "#plt.plot(gdata, norm_pdf(gdata, m.values[0], m.values[1])/norm_delta(xrange, m.values[0], m.values[1]) , label=\"fit\")\n",
+ "plt.plot(gdata, norm_pdf(gdata, m.values[0], m.values[1])/norm_delta(xrange, m.values[0], m.values[1]) , label=\"fit\")\n",
+ "\n",
+ "\n",
+ "# plt.figure(figsize=[5,5])\n",
+ "# plt.ylim([0.1,max*1.5])\n",
+ "# ulh.show(m, bins=25, bound=[-5,5],print_par=True)\n",
+ "# m.get_param_states()"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 7,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/html": [
+ "<table>\n",
+ " <tr>\n",
+ " <td></td>\n",
+ " <th> mu </th>\n",
+ " <th> sigma </th>\n",
+ " </tr>\n",
+ " <tr>\n",
+ " <th> mu </th>\n",
+ " <td> 0.0644 </td>\n",
+ " <td style=\"background-color:rgb(250,250,250);color:black\"> 2.43e-05 </td>\n",
+ " </tr>\n",
+ " <tr>\n",
+ " <th> sigma </th>\n",
+ " <td style=\"background-color:rgb(250,250,250);color:black\"> 2.43e-05 </td>\n",
+ " <td> 0.0322 </td>\n",
+ " </tr>\n",
+ "</table>"
+ ],
+ "text/plain": [
+ "┌───────┬───────────────────â”\n",
+ "│ │ mu sigma │\n",
+ "├───────┼───────────────────┤\n",
+ "│ mu │ 0.0644 2.43e-05 │\n",
+ "│ sigma │ 2.43e-05 0.0322 │\n",
+ "└───────┴───────────────────┘"
+ ]
+ },
+ "execution_count": 7,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "m.covariance"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 8,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/html": [
+ "<table>\n",
+ " <tr>\n",
+ " <td colspan=\"2\" style=\"text-align:left\" title=\"Minimum value of function\"> FCN = 23.98 </td>\n",
+ " <td colspan=\"3\" style=\"text-align:center\" title=\"No. of function evaluations in last call and total number\"> Nfcn = 140 </td>\n",
+ " </tr>\n",
+ " <tr>\n",
+ " <td colspan=\"2\" style=\"text-align:left\" title=\"Estimated distance to minimum and goal\"> EDM = 7.37e-10 (Goal: 0.0002) </td>\n",
+ " <td colspan=\"3\" style=\"text-align:center\" title=\"No. of gradient evaluations in last call and total number\"> </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\"> Valid Parameters </td>\n",
+ " <td colspan=\"3\" style=\"text-align:center;background-color:#92CCA6;color:black\"> No Parameters at limit </td>\n",
+ " </tr>\n",
+ " <tr>\n",
+ " <td colspan=\"2\" style=\"text-align:center;background-color:#92CCA6;color:black\"> Below EDM threshold (goal x 10) </td>\n",
+ " <td colspan=\"3\" style=\"text-align:center;background-color:#92CCA6;color:black\"> Below call limit </td>\n",
+ " </tr>\n",
+ " <tr>\n",
+ " <td style=\"text-align:center;background-color:#92CCA6;color:black\"> Covariance </td>\n",
+ " <td style=\"text-align:center;background-color:#92CCA6;color:black\"> Hesse ok </td>\n",
+ " <td style=\"text-align:center;background-color:#92CCA6;color:black\" title=\"Is covariance matrix accurate?\"> Accurate </td>\n",
+ " <td style=\"text-align:center;background-color:#92CCA6;color:black\" title=\"Is covariance matrix positive definite?\"> Pos. def. </td>\n",
+ " <td style=\"text-align:center;background-color:#92CCA6;color:black\" title=\"Was positive definiteness enforced by Minuit?\"> Not forced </td>\n",
+ " </tr>\n",
+ "</table><table>\n",
+ " <tr>\n",
+ " <td></td>\n",
+ " <th title=\"Variable name\"> Name </th>\n",
+ " <th title=\"Value of parameter\"> Value </th>\n",
+ " <th title=\"Hesse error\"> Hesse Error </th>\n",
+ " <th title=\"Minos lower error\"> Minos Error- </th>\n",
+ " <th title=\"Minos upper error\"> Minos Error+ </th>\n",
+ " <th title=\"Lower limit of the parameter\"> Limit- </th>\n",
+ " <th title=\"Upper limit of the parameter\"> Limit+ </th>\n",
+ " <th title=\"Is the parameter fixed in the fit\"> Fixed </th>\n",
+ " </tr>\n",
+ " <tr>\n",
+ " <th> 0 </th>\n",
+ " <td> mu </td>\n",
+ " <td> 0.49 </td>\n",
+ " <td> 0.25 </td>\n",
+ " <td> -0.26 </td>\n",
+ " <td> 0.26 </td>\n",
+ " <td> </td>\n",
+ " <td> </td>\n",
+ " <td> </td>\n",
+ " </tr>\n",
+ " <tr>\n",
+ " <th> 1 </th>\n",
+ " <td> sigma </td>\n",
+ " <td> 0.80 </td>\n",
+ " <td> 0.18 </td>\n",
+ " <td> -0.15 </td>\n",
+ " <td> 0.22 </td>\n",
+ " <td> </td>\n",
+ " <td> </td>\n",
+ " <td> </td>\n",
+ " </tr>\n",
+ "</table><table>\n",
+ " <tr>\n",
+ " <td></td>\n",
+ " <th colspan=\"2\" style=\"text-align:center\" title=\"Parameter name\"> mu </th>\n",
+ " <th colspan=\"2\" style=\"text-align:center\" title=\"Parameter name\"> sigma </th>\n",
+ " </tr>\n",
+ " <tr>\n",
+ " <th title=\"Lower and upper minos error of the parameter\"> Error </th>\n",
+ " <td> -0.26 </td>\n",
+ " <td> 0.26 </td>\n",
+ " <td> -0.15 </td>\n",
+ " <td> 0.22 </td>\n",
+ " </tr>\n",
+ " <tr>\n",
+ " <th title=\"Validity of lower/upper minos error\"> Valid </th>\n",
+ " <td style=\"background-color:#92CCA6;color:black\"> True </td>\n",
+ " <td style=\"background-color:#92CCA6;color:black\"> True </td>\n",
+ " <td style=\"background-color:#92CCA6;color:black\"> True </td>\n",
+ " <td style=\"background-color:#92CCA6;color:black\"> True </td>\n",
+ " </tr>\n",
+ " <tr>\n",
+ " <th title=\"Did scan hit limit of any parameter?\"> At Limit </th>\n",
+ " <td style=\"background-color:#92CCA6;color:black\"> False </td>\n",
+ " <td style=\"background-color:#92CCA6;color:black\"> False </td>\n",
+ " <td style=\"background-color:#92CCA6;color:black\"> False </td>\n",
+ " <td style=\"background-color:#92CCA6;color:black\"> False </td>\n",
+ " </tr>\n",
+ " <tr>\n",
+ " <th title=\"Did scan hit function call limit?\"> Max FCN </th>\n",
+ " <td style=\"background-color:#92CCA6;color:black\"> False </td>\n",
+ " <td style=\"background-color:#92CCA6;color:black\"> False </td>\n",
+ " <td style=\"background-color:#92CCA6;color:black\"> False </td>\n",
+ " <td style=\"background-color:#92CCA6;color:black\"> False </td>\n",
+ " </tr>\n",
+ " <tr>\n",
+ " <th title=\"New minimum found when doing scan?\"> New Min </th>\n",
+ " <td style=\"background-color:#92CCA6;color:black\"> False </td>\n",
+ " <td style=\"background-color:#92CCA6;color:black\"> False </td>\n",
+ " <td style=\"background-color:#92CCA6;color:black\"> False </td>\n",
+ " <td style=\"background-color:#92CCA6;color:black\"> False </td>\n",
+ " </tr>\n",
+ "</table><table>\n",
+ " <tr>\n",
+ " <td></td>\n",
+ " <th> mu </th>\n",
+ " <th> sigma </th>\n",
+ " </tr>\n",
+ " <tr>\n",
+ " <th> mu </th>\n",
+ " <td> 0.0644 </td>\n",
+ " <td style=\"background-color:rgb(250,250,250);color:black\"> 2.43e-05 </td>\n",
+ " </tr>\n",
+ " <tr>\n",
+ " <th> sigma </th>\n",
+ " <td style=\"background-color:rgb(250,250,250);color:black\"> 2.43e-05 </td>\n",
+ " <td> 0.0322 </td>\n",
+ " </tr>\n",
+ "</table>"
+ ],
+ "text/plain": [
+ "┌──────────────────────────────────┬──────────────────────────────────────â”\n",
+ "│ FCN = 23.98 │ Nfcn = 140 │\n",
+ "│ EDM = 7.37e-10 (Goal: 0.0002) │ │\n",
+ "├───────────────┬──────────────────┼──────────────────────────────────────┤\n",
+ "│ Valid Minimum │ Valid Parameters │ No Parameters at limit │\n",
+ "├───────────────┴──────────────────┼──────────────────────────────────────┤\n",
+ "│ Below EDM threshold (goal x 10) │ Below call limit │\n",
+ "├───────────────┬──────────────────┼───────────┬─────────────┬────────────┤\n",
+ "│ Covariance │ Hesse ok │ Accurate │ Pos. def. │ Not forced │\n",
+ "└───────────────┴──────────────────┴───────────┴─────────────┴────────────┘\n",
+ "┌───┬───────┬───────────┬───────────┬────────────┬────────────┬─────────┬─────────┬───────â”\n",
+ "│ │ Name │ Value │ Hesse Err │ Minos Err- │ Minos Err+ │ Limit- │ Limit+ │ Fixed │\n",
+ "├───┼───────┼───────────┼───────────┼────────────┼────────────┼─────────┼─────────┼───────┤\n",
+ "│ 0 │ mu │ 0.49 │ 0.25 │ -0.26 │ 0.26 │ │ │ │\n",
+ "│ 1 │ sigma │ 0.80 │ 0.18 │ -0.15 │ 0.22 │ │ │ │\n",
+ "└───┴───────┴───────────┴───────────┴────────────┴────────────┴─────────┴─────────┴───────┘\n",
+ "┌──────────┬───────────────────────┬───────────────────────â”\n",
+ "│ │ mu │ sigma │\n",
+ "├──────────┼───────────┬───────────┼───────────┬───────────┤\n",
+ "│ Error │ -0.26 │ 0.26 │ -0.15 │ 0.22 │\n",
+ "│ Valid │ True │ True │ True │ True │\n",
+ "│ At Limit │ False │ False │ False │ False │\n",
+ "│ Max FCN │ False │ False │ False │ False │\n",
+ "│ New Min │ False │ False │ False │ False │\n",
+ "└──────────┴───────────┴───────────┴───────────┴───────────┘\n",
+ "┌───────┬───────────────────â”\n",
+ "│ │ mu sigma │\n",
+ "├───────┼───────────────────┤\n",
+ "│ mu │ 0.0644 2.43e-05 │\n",
+ "│ sigma │ 2.43e-05 0.0322 │\n",
+ "└───────┴───────────────────┘"
+ ]
+ },
+ "execution_count": 8,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "m.minos()"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 9,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/html": [
+ "<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> mu </td>\n",
+ " <td> 0.49 </td>\n",
+ " <td> 0.25 </td>\n",
+ " <td> -0.26 </td>\n",
+ " <td> 0.26 </td>\n",
+ " <td> </td>\n",
+ " <td> </td>\n",
+ " <td> </td>\n",
+ " </tr>\n",
+ " <tr>\n",
+ " <th> 1 </th>\n",
+ " <td> sigma </td>\n",
+ " <td> 0.80 </td>\n",
+ " <td> 0.18 </td>\n",
+ " <td> -0.15 </td>\n",
+ " <td> 0.22 </td>\n",
+ " <td> </td>\n",
+ " <td> </td>\n",
+ " <td> </td>\n",
+ " </tr>\n",
+ "</table>"
+ ],
+ "text/plain": [
+ "┌───┬───────┬───────────┬───────────┬────────────┬────────────┬─────────┬─────────┬───────â”\n",
+ "│ │ Name │ Value │ Hesse Err │ Minos Err- │ Minos Err+ │ Limit- │ Limit+ │ Fixed │\n",
+ "├───┼───────┼───────────┼───────────┼────────────┼────────────┼─────────┼─────────┼───────┤\n",
+ "│ 0 │ mu │ 0.49 │ 0.25 │ -0.26 │ 0.26 │ │ │ │\n",
+ "│ 1 │ sigma │ 0.80 │ 0.18 │ -0.15 │ 0.22 │ │ │ │\n",
+ "└───┴───────┴───────────┴───────────┴────────────┴────────────┴─────────┴─────────┴───────┘"
+ ]
+ },
+ "execution_count": 9,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "m.params"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 10,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
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\n",
+ "text/plain": [
+ "<Figure size 432x288 with 1 Axes>"
+ ]
+ },
+ "metadata": {
+ "needs_background": "light"
+ },
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "m.draw_profile('mu');"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 11,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "image/png": 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\n",
+ "text/plain": [
+ "<Figure size 432x288 with 1 Axes>"
+ ]
+ },
+ "metadata": {
+ "needs_background": "light"
+ },
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "m.draw_profile('sigma');"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 12,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "image/png": 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\n",
+ "text/plain": [
+ "<Figure size 432x288 with 1 Axes>"
+ ]
+ },
+ "metadata": {
+ "needs_background": "light"
+ },
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "px, py = m.profile('mu', subtract_min=True)\n",
+ "plt.plot(px, py);"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 13,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "<matplotlib.contour.ContourSet at 0x7fdbdd543af0>"
+ ]
+ },
+ "execution_count": 13,
+ "metadata": {},
+ "output_type": "execute_result"
+ },
+ {
+ "data": {
+ "image/png": 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\n",
+ "text/plain": [
+ "<Figure size 360x360 with 1 Axes>"
+ ]
+ },
+ "metadata": {
+ "needs_background": "light"
+ },
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "plt.figure(figsize=[5,5])\n",
+ "m.draw_mncontour('mu', 'sigma', cl=(0.68, 0.9, 0.99), size=100) # nsigma=4 says: draw four contours from sigma=1 to 4"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": []
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": []
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": []
+ }
+ ],
+ "metadata": {
+ "kernelspec": {
+ "display_name": "Python 3",
+ "language": "python",
+ "name": "python3"
+ },
+ "language_info": {
+ "codemirror_mode": {
+ "name": "ipython",
+ "version": 3
+ },
+ "file_extension": ".py",
+ "mimetype": "text/x-python",
+ "name": "python",
+ "nbconvert_exporter": "python",
+ "pygments_lexer": "ipython3",
+ "version": "3.8.5"
+ }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 2
+}
--
GitLab