{ "cells": [ { "cell_type": "code", "execution_count": 1, "metadata": { "collapsed": true }, "outputs": [], "source": [ "#Created by Kacper Lasocha, Jagiellonian University, Institute of Physics \n", "#kacper.lasocha@doctoral.uj.edu.pl\n", "\n", "import numpy as np\n", "import scipy.stats\n", "import matplotlib.pyplot as plt\n", "from matplotlib import gridspec" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Unfolding\n", "A common problem in various physical analysis is how to determine a true, unknown distribution of a certain feature being given only observed distribution, which is subject to uncertainties and limited resolution. In this notebook we will focus on histograms. The bins of an original, unknown histogram will be called **causes** and we shall speak about the probability of **cause i**: $P(C_{i})$. Alternatively, bins of an observation histogram will be called **effects**, and our starting point will be the knowledge of the **effect distribution**: $P(E_{j})$. The sets of causes and effect are often identic, but it is not always a case. We may consider completely different sets of causes and effects. We shall start however with a simple case of:\n", "\n", "$$ C_{i} = E_{i} : \\ signal \\in [i; i+1) $$\n", "$$ C_{0} = E_{0} : \\ signal < 1 $$\n", "$$ C_{99} = E_{99} : \\ signal > 99 $$" ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "collapsed": true }, "outputs": [], "source": [ "def get_signal(lam1 = 30, lam2 = 60, s = 1):\n", " \n", " choice = np.random.choice([0,1], size = s)\n", " signal = choice * np.random.normal(loc=lam1, scale = 8, size = s) + (1-choice) * np.random.normal(loc=lam2, scale = 5, size = s)\n", " return np.maximum(0,signal)\n", "\n", "def blur(signal):\n", " return signal + np.random.normal(size = len(signal))*np.sqrt(signal)" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [ { "data": { "image/png": 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "sample_size = 100000\n", "x_size = 100\n", "data = get_signal(s = sample_size)\n", "x = np.arange(x_size+1)\n", "\n", "true_dist, _, _ = plt.hist(data, bins = x, alpha = 0.75, label = \"True distribution\", density= True)\n", "\n", "observed_data = blur(data)\n", "\n", "observed_dist, _, _ = plt.hist(observed_data, bins = x, alpha = 0.75, label = \"Observed distribution\", density= True)\n", "\n", "plt.legend()\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Response matrix\n", "For our analysis it is crucial to understand what effect may be observed under a given cause. The goal is to obtain a **response matrix** $M$, for which we have: $M_{ij} = P(E_{j} \\mid C_{i})$, that is a probability of observing effect $E_{j}$ assuming the cause $C_{i}$. We have then, in matric notation:\n", "\n", "$$ C^T M = E^T, $$\n", "\n", "where $C,E$ are cause and effect vectors respectively, that is vectors $\\begin{bmatrix}\n", " P(C_{1}) \\\\\n", " \\vdots \\\\\n", " P(C_{n})\n", "\\end{bmatrix},\n", "\\begin{bmatrix}\n", " P(E_{1}) \\\\\n", " \\vdots \\\\\n", " P(E_{m})\n", "\\end{bmatrix}.\n", "$\n", "\n", "## Ex 1.\n", "a) Using functions get_signal() and blur() implemented above, approximate the response matrix basing on 1 million samples. (Monte-Carlo simulation) \n", "b) Verife the formula $ C^T M = E^T $, using calculated response matrix and vectors *true_dist*, *observed_dist* from introductory cells." ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [ { "data": { "image/png": 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hOpGSEOMzxoLEbTUiyzqZwLDeQ9yPqqCpxmV0TM7Vn5/qVTZMjyZKp2fXCl5x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\nRkII0YkaCSFEJ/8f+H6nOaetO2AAAAAASUVORK5CYII=\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "#a)\n", "\n", "#Here goes your code\n", "\n", "\n", "plt.imshow(response_M)\n", "plt.title(\"Response Matrix\")\n", "plt.xlabel(\"Effect\")\n", "plt.ylabel(\"Cause\")\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "data": { "image/png": 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SksKePXu4+uqrK2dj27ZtG1u3bsXhcNCnTx8eeOABunTpcvYP1AQ9yvbh1KWkOgY2yfY3\nOkfS//QrxjDTDvFNsg8RmOpyBTAMSNNaZ2it3cBcYEq1daYA7/oeLwDGK6WU1nqr1vqIb/lOINx3\ntXABEKW1/l4btSjeA6YSpCrKIYeHh1eWQ05ISODrr7/mscceY+3atURHR7N3715SU1O56qqrGDhw\nIM888wzZ2dmV26koyVzxuOKqYe7cudx6660/KtU8cOBAfvOb31ReQaxfv57bbrsNgJ///Oc1xrl2\n7VpuuOEGIiIiiIqKYvLkycYLHjeU5EL+YbpHluJwOLjrj8/y5WdLcYbXfsPStVNvqnzsCnMCXigx\nholWxDJ69Gjy8/N/NH/A+Vi3bh3Tpk0DjPkRunbtWpkAxo8fT3R0NE6nk7i4uBqL8ZklceaGyp84\nl1FMb7c9oUn2leS8DFSYcRUgRBV1SQCdgENVnmfzw7f4n6yjtS4H8oDqY9luArZorV2+9bOrvFbT\nNgFQSt2rlEpSSiXl5OTUIdzmFRcXV1m1s0J+fj4HDx6kZ8+eQM3lkHv37s2WLVsqm2RmzJiB1pr4\n+Hi2bdvGtm3bSElJ4auvvqp8X9VJTiZPnsyXX37J6dOnSU5OZty4cT8q1Vzxs3v37h/tt14KjoP2\nQkQMR5w9mfvVd1w9+SZWfv0lv0isvd5MxRwHAOVYjSGJhTm1/ptULYENtZfBrqvqZaXN6Dupi3jX\ndg5Yu1FgiW6S7edZWkPXkZIAxE80SyewUioeo1noN+f7Xq31TK31UK310Hbt2jV+cA00fvx4iouL\nee+99wCjauUf//hH7r777soTYE3lkI8cOUJERATTpk3jkUceYcuWLfTp04ecnBw2bDBGMpWVlbFz\n584a9xsZGckll1zCQw89xHXXXYfFYjlrqeaRI0cyd+5cwKjmWZPRo0ezePFiSkpKKCgo4NNPPwVv\nORSfAqsDnFHkFrkozM9nzJUTePJvz7FnpzEDW4vIlhQVFtS43QoF2gkeF263u/LqZd26dURHRxMd\nHU1sbGzlrGNbtmwhMzMT+Gl566pGjRpVeTz79u3j4MGDATU3gFW76ePexU7HgKbdUdwUyNkDx2v+\nexKhqS7DQA8DVRtOO/uW1bROtlLKCkQDpwCUUp2BRcCdWuv0Kut3Psc266W5J8GoKAc9ffp0/va3\nv+H1epk0aRJ///vfK9epKIecnZ3NtGnTGDp0KMuXL+eRRx4hLCwMm83GG2+8gd1uZ8GCBTz44IPk\n5eVRXl7O73//e+Lja263vfXWW7n55ptZtWpV5bIPP/yQ++67j2eeeYaysjISExMZMGAA//73v7n9\n9tt5/vnnmTKlegueYfDgwdx6660MGDCA9u3bc8kll4DLN1TUGg5AUVEhv70zEVdpKRrNE3/9BwDX\nTb2JJ/74AO/+501enfV+jdt3KwflWLBSjtPpZNCgQZSVlVX2cdx000289957xMfHM3z4cHr37g0Y\n01GOHDmSfv36cc0113D//fdXbnP69Oncd999JCQkYLVamTNnzo+++fu7nu692HGz097ECSD+Bvji\nMUhZIP0AotI5y0H7Tuj7gPEYJ+nNwO1a651V1rkfSNBa/9bXCXyj1voWpVQrYDXwV631J9W2uwl4\nkB86gV/RWn9+tlikHHQzK3cbHYcRMdDK+A5Q9U7g+mjlOUOM9yS07Q128+ftNevvp+J+lZsKPuCm\ngg/5dcePjcqfTejxU3/mwvJDtP/z3kYdbST8X73LQfva9H+HMYJnN/Cx1nqnUmqGUsrXS8gsIEYp\nlQb8AagYKvo7oCfwtFJqm++nve+16cDbQBqQTgCOAAp6hceM35EdGm2T+WHReAiDwuONts1AFu/a\nTqatZ5Of/AHWh4+hvec4ZG9u8n2JwFCnO4F938w/r7bs6SqPS4Gba3jfM8AztWwzCeh3PsGKZlTu\nMgq7RcSA1d5om/WqMPLDWtG69DSUlYLN2WjbDjQ27aKXew9ftph87pUbQZJzBG7s2FPmS20gAQTJ\nncCBNKtZwKj4hh7ZgfScwsqfxpAX1gr84CrA7L+b3u7d2Chr+g5gn5KwFmxxDoOdi8DjnyOiRPMK\n+ATgdDo5deqU6f+Zg0oTffuv4FEWaBEDJWeMfgYTaK05deoUTqd5VyDxru14CGOPvfkuhNeHj4Wi\nHMhc3Wz7FP4r4IvBde7cmezsbPzxHoGAVXwa7S7itMWD1xjM1ejcLSyQfwKOlRhVK03gdDrp3Lnz\nuVdsAnZvKQNcSWTYelMaVr/Zv+pjm/MScERB6kLoefaJ5kXwC/gEYLPZ6NatkQtohbIzWfDKZL4M\nn8Sc6OlNtpu5946AD/4CZw7AAyE0YcnR7bDpP7x5fCERupgPon7VrLsvU3boez3s/hSu/zdYbM26\nf+FfAr4JSDSyNS+AsrAk8pam31f3sXBqP+Rln3vdYFBWAu9MgtRP2OQcyV9j/pfPWtx07vc1tt4T\nwZUvo4GEJABRRe5B2P4RDLmbM5a2Tb+/7mOM3xkh0h59Yje4C2Hq67zZ+o/sdvQ3Zzx+t9FGbaD0\nlc2/b+FXJAGIH6R9a5R+GHZv8+yvQzy0aAcZoXEieutjoxbPQ6s95gYS3gouHBwy/+6idpIARKXV\n335GblgrEheeaJ4dKmVcBWSsCola9ReVZ1Ciwjlh6Wh2KMZUkYeToTTP7EiEiSQBiEq93bvYZ49r\n3maJ7r5hiSFQpCy2LIND1li08oP/dt3HGhVeM9eaHYkwkR/8JQq/UJjDBZ4j7LM3c12c7lcYvzNW\nNe9+m5vWXFSWyQFbd7MjIXHmBu5Y7qFUOaUZKMRJAhCGbGNaxn22uObdb3RniOkV/Akg9yAtdBFZ\nfpAAADzKxi57gnQEhzhJAMJwaCNl2Mi092r+ffcYCwfWG3cgB6vjxpSX/nAFUCHFMRhOpxujv0RI\nkgQgDIc2kWnradwo1AyqTolI9zFQVhzc49KPpeJFccjqPzctpjgGGQ/kKiBkSQIQxjfvw1uMDmAz\nxF4OyhLcJ6JjOzhuudA3N7J/yLZ2hZYXSD9ACJMEIODoDvC42NvcHcAVnNHQ9TJImQ9ek8fIN5Xj\nqRyw+c+3f6DKMNzVUGUuZhE6JAEIOLQRgP1mJQAwbj7LPQB7zzopXGAqzYczWWTZepgdyU+8ldUe\nSk7z0JuLzA5FmEASgDASQKuu5FpizIvh4muh1UXw/RvmxdBUTuwC4KAfdQBXqOiUvqgsw+RIhBkk\nAYS4xLe+48zetax1mfftNHHmBhLf3sR73gnGaKAj20yLpbElztzA7IVGCQh/GgFU4ZAtFi9hdC3L\nNDsUYQJJACGunec4rb1nzOsArmJlxESwR8LGN80OpVF1LcukUEVyKqwZCuydpzLl4Ki1E13L5Qog\nFEkCCHHx7u0A7PWDBFAS1oIvbOMo3z6f37yxzOxwGk3Xsgyj/d+Myp91cMDana7SBBSSJAGEuEtK\nviPH0p6DfjI+fXmLKYTh4eqiz8wOpVFYdDldyrP8sv2/wgFbN9p7jkNJrtmhiGYmCSCUuQpIcG1h\ns3Ok33w7PWbtxDbHJYwr/gI8ZWaH02CjSr7FoV3scAw2O5RaVfZNhEBBPvFjkgBCWdo32Cljs3OE\n2ZH8yLctrqG19wzsW252KA3jKWdKwTwybT3Y5hhqdjS1+iEBpJobiGh2kgBC2e7PyA+LZo893uxI\nfmSrYxinw2IgeY7ZoTTMzkVc4DnCJ5G3+c0VVk3OhMWQHxYFx1LMDkU0M0kAoarcDfu/Itk5HK0s\nZkfzI15lYVXE1ZD2DeQeMjuc+vF6Ye0LHLJ2Jcl5mdnRnJ1SHLR2lyuAECQJIFRlrQFXvtH+74dW\nRkwwHmz9wNxA6mvPp5Czh0WRif4xAcw5HLB1M+Ys9pSbHYpoRv7/lymaxu7PwB75Q0VIP5Nj7Qg9\nxsHW9wOvPpDWsOaf0KYHG8JHmx1NnRywdYfyUqM8tAgZkgBCkddr1NzpeWWzlX+ulyF3Qf5hoyko\ngPz75efhWAqve6f6XfNabSrrFEk/QEiRBBCKsjdB4XHoe73ZkZzVHWtbkxvWis2fvGTMGxAIykq5\nLX82B6zdWBs+zuxo6uywtQuE2aQfIMRIAghFm2eBvSX0utrsSM7Ko2ysibiKwaUbaeU5ZXY4dbNp\nJu09x/kg6tcB8+0fjH9r2vWBY5IAQokkgFCTlw2pC43mFWeU2dGc08qIq7HgZXTxt2aHcm7Fp2HN\nC2x1XEKK039v/KpVh35yBRBiJAGEmopyy8N/a24cdXTU2oU99njGFC83Olf92ernwV3Ah1G/NDuS\nenkvKwoKjvLg65+YHYpoJpIAQklpHiS/C/E3QKsuZkdTZysiJnKh5zAc9ON+gMITsPltGPRzsm2x\nZkdTL9+Hj8JLGOOKvzQ7FNFMJAGEkuR3wV0Al/3O7EjOy0bnKIpVBGx5z+xQavXvWbPBW84TB4eY\nHUq9nba0Y4tzGGOKvzJuFBRBTxJAqPCUGXX2Y0eR+FmpMQlLgIyscYU5+S78Cti52LiK8UMXu1Io\nUeF+Oe3j+fgm4lpaec/A3uApxy1qJwkgVOxZZoypv+wBsyOplxURE6G8xOjA9kN93anstcfhDaCR\nPzXZ7hhMjqU9JL1jdiiiGUgCCBXZm8HigB7jzY6kXjJsvTlgjWX/8rf878ql+DQXlWexx97P7Ega\nTCsL30ZMgszVcEruCg52kgBCxbEd0CEOLFazI6kfpVgfPpZeZXuI8eSYHc2PHfwegD32BJMDaRwr\nI66GMCsky1VAsKtTAlBKTVRK7VVKpSmlHq/hdYdSap7v9Y1KqVjf8hil1EqlVKFS6tVq71nl2+Y2\n30/7xjggUQOtjRt8Ogb2CWpzuFG4bmjJdyZHUs2B9bixkW7vbXYkjSLP0gYuvha2fgjlLrPDEU3o\nnAlAKWUBXgOuAeKA25RS1SeQ/SVwRmvdE3gJeN63vBR4Cni4ls3fobUe6Ps5UZ8DEHWQfwRKTkPH\n/mZH0iBHrZ05ZL2IYaXrzQ7lxw58R5r9Yv+uq3S+Em42/maObjc7EtGE6nIFMAxI01pnaK3dwFxg\nSrV1pgDv+h4vAMYrpZTWukhrvQ4jEQizVBT4CvArAIDNzpH0dafy6ze+9I+RTK5COLrd7ybVabBO\nvuGsR7aaG4doUnVJAJ2AqrNyZPuW1biO1rocyANi6rDtd3zNP08pVfOUSUqpe5VSSUqppJwcP2v7\nDRTHfQmgQ+CfpDaFjyQML0Nc35sdiiF7E2hP0LT/V4q6ECI7wuEtZkcimpCZncB3aK0TgFG+n5/X\ntJLWeqbWeqjWemi7du2aNcCgcSyFY5YLSHw31fxvzA2UZe3BCUsHhpX4STPQge9AWdhn72t2JI2v\n02A4IgkgmNUlARwGqtYN6OxbVuM6SikrEA2ctXyj1vqw73cB8F+MpibRFI6lcCDAb1CqpBSbnCNJ\ncG0l3FtkdjRGArhgAKVhEWZH0vguHAQn90NpvtmRiCZSlwSwGeillOqmlLIDicDSaussBe7yPf4Z\nsELr2it3KaWsSqm2vsc24DpAyhA2BVcBnM4gy9bd7EgazSbnSGyUMdC12dxAyl2QnQRd/XzO33pI\nnLmBf2wPBzQc3WZ2OKKJnDMB+Nr0fwcsB3YDH2utdyqlZiilJvtWmwXEKKXSgD8AlUNFlVJZwIvA\n3UqpbN8IIgewXCm1A9iGcQXxn8Y7LFHp+C7AN+VfkNhv78uZsNYML1lnbiBZa8HjgthR5sbRRDJs\nvYwH0g8QtOp0V5DW+nPg82rLnq7yuBS4uZb3xtay2cCtmhVIju0ACJ4mIECrMDY7R3JFydc4vCXm\nBZKyEBzR0GMsrA6+k2SBJZrjlo50kH6AoCV3Age7YykQ3ppTYW3NjqRRrQ8fg0O7GFpqUqd2WSns\n+cyYVtPqMCeGZpBh6yVDQYOYJIBgd9x3B3DNo2wD1j57HDmW9lxestKcANK+Blc+JNxkzv6bSbq9\nN+QehKKTZocimoAkgCB2+1vrcB9O4bMTwfXtH4xmoO/Cx9DflWzOySllAblhrbj9G3vAD609mwyb\nr7yFXAUEJUkAQaxj+WHsuIOqA7iq9eFjsOCFnYuad8euAti3nI3OUQFf/vlcjI5gJR3BQUoSQBDr\nWp4BBNcIoKoO2rpz0BoLKQuad8d7v4DyEmOSmiBXGhZBtrULyRu+DeornVAlCSCIXexKpVQ5OWy9\nyOxQmsz68DFw6HseeH1R87hHyoMAABt9SURBVJ2gUhZAVGf22avXRAxOGbZe9CjbZ1SVFUFFEkAQ\n6+/ayi57fzwqQOcAqIPvwscAcFnJqmbZ36/eXE75/m/41DMcrULjv0+6rTetvGf8bx4G0WCh8Rcc\ninIPcoHnMCmOwWZH0qRyrB3Za4tjVMmKZvmGenXRp1jxsCbiyibfl7+ouNK52L3T5EhEYwver4ah\nLt0YHrnDMcjkQJreihYTuS/3Rfq7kkmc+cNw17n3jmjcHZXmM6lwEZudIzhk69a42/ZjWbbuFKsI\n+rp3mB2KaGRyBRCsMlZyOiwmqNv/K6wLH8vpsBiuL2zizuBNbxGpC/kk8vam3Y+f0crCHns8fd0p\nZociGpkkgGDk9ULGalIcg4LuBrCaeJSNL1tMIcG9jdiytKbZiasANrxGsmM4mfZeTbMPP7bb3p9O\n5dlQcNzsUEQjkgQQjI5th5LT7Ajy9v+qvmkxiRIVznWFC5tmB5v+AyVn+KRlaH37r7Db4Zvw5qCf\nzccsGkQSQDDytf+nhkD7f4XisEi+jbiGESWraVveuN9S73pzJfkr/8U2x1DS7X0adduBItPWk1Ll\nhCw/mYhHNApJAMEoYyV06EeepbXZkTSrL1pMBWBS0eJG3e6EoqVEefNYGKLf/gE8yspeexwckAQQ\nTCQBBBt3MRz8HrqPMTuSZnfK2p714WOZULSEn+W/D57yhm+0NJ/rC+ez1XEJ+0Pkxq/a7Lb3hxO7\noOisk/2JACIJIMj8/c1Z4HHz970dzQ7FFO9ET2d9+Fh+VvghzJ4Ap9IbtsGNb9FSFzC/5bTGCTCA\n7bJLP0CwkQQQZPq6UynHwh57P7NDMUVJWAteb/0I/279Jzi1H94eD4X1vIO1JBc2vEKSYzgZIdr2\nX1WGvRdYpR8gmEgCCDLdytLItnbFHeY0OxRTbQi/An6x3Bi+ufKZ+m3k+9ehNI8FUT9v3OACVLmy\nQ+dL4IDJU3GKRiMJIJhoTWxZGpm2nmZH4h/a94Vh90Lyu3D0PO9iLToJG16HvteTJf+eP4i9HI6l\nQskZsyMRjUASQDApOEYrby5ZQTT/b4Nd8RhEtGH3O/eR+NZ3dasYmncY5lxrTPg+5ommjzGQxI4C\nNByQfoBgILWAgsnR7QByBeBTcbIfb7uDXxe/zKWla/k+fHSN64CvdlDOXnj/RmO6x2kLoUMcIHXw\nK3W+BGwRkLEKLr7W7GhEA0kCCCbHduBFBe0EMPW1ImICVxYt4xd5r9LTvQfSS6HrZT+azD3Kkwvf\nvQprX4AwG9y9DC7ob2LUfspqh64jK282FIFNEkAwObqdo9ZOuMLCzY7Er2hl4fXWD/PzvJlMKPoU\n3v/EOMm3juXRQuNmuf6uZPjKA12Gww1vkbjgGPLNvxbdx8BXT0JeNkR3Njsa0QCSAILJ0R3S/l+L\nQ7Zu/L3tP3B4S3l3nBsOboBT6bTJSyVcF/Nli6lcd9cjRscxAMdMjddfJc7cQJeyNvwTIGM1DLrD\n7JBEA0gCCBbFpyHvIJlRV5kdiV9zhTmh91joPQGAx6v0AVxXefIXZ3PIGktuWGtaZayUBBDgJAEE\nC18HsFwBnJtMbt5ASpHiGMiojFXGLGwhUHI8WEkCCBbHjHHuMma9/iQx1F2qYxCjclfC8Z3QMTTv\nOg8Gch9AsDi6HaK7UBgWZXYkIgSkVJQaz1hlahyiYSQBBIujO+CCAWZHIULEaUs7aNtbEkCAkwQQ\nDFyFcCoNOsq4ddGMuo8x5gcod5kdiagnSQDB4HgqoOUKQDSv7mOgrBgOJ5sdiagnSQDBwDcCSBKA\naFZdhhu/s5PMjUPUmySAILB+1eecDmtD4keZZociQkmLttCqKxyWBBCoJAEEOq3p69rBbkd/GY8t\nmlXizA2sd8WSs1eGzwYqSQCB7nQGbbynf5iuT4hmlG7rQzvPCSg4bnYooh4kAQS6rLUA7HLICCDR\n/NLsFxsPpCM4IEkCCHRZ68kNa81Ri1RlFM0v09aDcizSDxCgJAEEMq0hax277NL+L8xRphwctHWT\nK4AAVacEoJSaqJTaq5RKU0o9XsPrDqXUPN/rG5VSsb7lMUqplUqpQqXUq9XeM0QpleJ7z8tKyRns\nvJ3JhIIj7HZI+78wT7qtDxzeAl6v2aGI83TOBKCUsgCvAdcAccBtSqm4aqv9Ejijte4JvAQ871te\nCjwFPFzDpt8Afg308v1MrM8BhLSsdQDstEv7vzBPmr0PuPL5wxsLpKBegKnLFcAwIE1rnaG1dgNz\ngSnV1pkCvOt7vAAYr5RSWusirfU6jERQSSl1ARCltf5ea62B94CpDTmQkJS1Hlq044i1i9mRiBCW\nZusDQM+yPSZHIs5XXRJAJ+BQlefZvmU1rqO1LgfygJhzbDP7HNsEQCl1r1IqSSmVlJOTU4dwQ4Sv\n/Z+uI6X9X5jqiLUzxSqCHu69ZocizpPfdwJrrWdqrYdqrYe2a9fO7HD8xgNvLIb8bGYfvtDsUESI\n08pChq03PcskAQSauiSAw0DVNobOvmU1rqOUsgLRwKlzbLPquMWatinOIs5tTACzS9r/hR9Is/em\na1kGNu02OxRxHuqSADYDvZRS3ZRSdiARWFptnaXAXb7HPwNW+Nr2a6S1PgrkK6Uu9Y3+uRNYct7R\nh7A41w7yw6LJtnY1OxQhSLNdjBUP3crSzA5FnIdzTgmptS5XSv0OWA5YgNla651KqRlAktZ6KTAL\neF8plQacxkgSACilsoAowK6UmgpcrbXeBUwH5gDhwBe+H1EXWpPg2spO+wBp/xd+YZ/dGBh4sSvF\n5EjE+ajTnMBa68+Bz6ste7rK41Lg5lreG1vL8iRAJhOtj5P7aeM99cO0fEKYLN/SikPWrsS7t5sd\nijgPft8JLGrgm4Yv1THQ3DiEqGKXvT993DvBU2Z2KKKO6nQFIPxM5mqOWzpywnqB2ZEIUWmnYwAT\nij/l6Tfeq2wSmnvvCJOjEmcjVwCBxlMOmWvl27/wO7t9JcnjXNIMFCgkAQSao9vBlUeqtP8LP1Ng\nieaAtRvxkgAChiSAQJOxEoBUu8z/K/zPTscA+rh3YZX7AQKCJIBAk7kaOiRQYGlldiRC/MRO+wDs\nuOkpZSECgiSAQFJWAgc3QvcrzI5EiBrtcfTDi5LhoAFCEkAAeebN2eBx8dzeDmaHIkSNisJakmXr\nIf0AAUISQABJcG2jHCu77XL/nPBfu+wD6OXeg027zA5FnIMkgADSz7WV/faLcYWFmx2KELXa6eiP\njTL6uHeZHYo4B0kAgaL4NN3K0mT8v/B7u+0JlGFjYOlms0MR5yAJIFBkrSMMTYpdxv8L/1YaFsFO\nxwCGlm4wJi4SfksSQKDIWEWJCifd3sfsSIQ4pyTnCDp6jkKODAf1Z5IAAkXmanbb++FRUr5J+L8t\nzmHGg72fn31FYSpJAIEgLxtOpUn5BxEwTlvakW7rBXtlmg9/JgkgEGSsBqT8swgsyc5LIXszFJ4w\nOxRRC0kAgSBzNUS05ZA11uxIhKizJOcIQMO+L80ORdRCEoC/09qYAKb7FWglH5cIHAet3SC6izQD\n+TE5o/i7nL1QeBy6Sf0fEWCUgj7XQPpKcBebHY2ogSQAf5dptP9LATgRkPpMgvKSyjLmwr9IAvBz\nm1cu4rilI4nzj5odihDn7Y5vrBSqSNYuedvsUEQNJAH4M6+HONcOGf0jApZHWdkcfhlDSr+HslKz\nwxHVSALwZ0e300IXsVNm/xIB7HvnaCJ0MaSvMDsUUY0kAH+WuQYwptkTIlClOgZSqCJh12KzQxHV\nSALwZ5lrOGS9iDxLG7MjEaLePMrKpvCRsOdzaQbyM5IA/FW5Gw5uYKe0/4sg8L1zFLgLIP1bs0MR\nVUgC8FeHk6GsWNr/RVDY6RgI4a1hpzQD+RNJAP4qcw2g2OXob3YkQjSYR1mh7/VGddCyErPDET6S\nAPxV5hq4oD9FYS3NjkSIxhE3FdyFkCbNQP5CEoA/chdD9iboNtrsSIRoPN1GgyMa9i83OxLhIwnA\nHx3aCB631P8RwcViM0qapH0rU0X6CUkA/ihzDYRZ4aJLzY5EiMbV80rIPwwndpsdiUASgH/a9yV0\nvgQc0v4vgkzPK43fad+YG4cAJAH4n2OpcGIXs/MGkThzg9nRCNG4ojtB+zhI+9rsSAQgM4z7m5T5\neAhjg1M6gEVwqfhCc3tRHJNPLgFXITgiTY4qtMkVgD/xeiFlAdsdQyiwtDI7GiGaxHbnUPCWVda6\nEuaRBOBPDm6A/GzWh481OxIhmsweezzYWkg/gB+QBOBPUuaDLcI3mbYQwcmjKoaDfi3DQU1WpwSg\nlJqolNqrlEpTSj1ew+sOpdQ83+sblVKxVV77k2/5XqXUhCrLs5RSKUqpbUqppMY4mIBW7jbK5V58\nLa6wcLOjEaJJzTrWHXIP8j9vzDc7lJB2zgSglLIArwHXAHHAbUqpuGqr/RI4o7XuCbwEPO97bxyQ\nCMQDE4HXfdurMFZrPVBrPbTBRxLo0r+FkjOQcLPZkQjR5LY5jP/yl5TISDcz1eUKYBiQprXO0Fq7\ngbnAlGrrTAHe9T1eAIxXSinf8rlaa5fWOhNI821PVJcyHyJioMc4syMRosnlWDuSah/AxKIlUO4y\nO5yQVZcE0Ak4VOV5tm9ZjetorcuBPCDmHO/VwFdKqWSl1L217Vwpda9SKkkplZSTk1OHcANQWQns\n/dKolmixmR2NEM1iaeQttPGegh0fmx1KyDKzE/hyrfVgjKal+5VSNQ5811rP1FoP1VoPbdeuXfNG\n2FzSV0BZEcRVv7ASInjtcAwm09YD1v8bvB6zwwlJdUkAh4EuVZ539i2rcR2llBWIBk6d7b1a64rf\nJ4BFhHLT0K6l4GwFsaPMjkSI5qMUSyJvhVP7Yc8ys6MJSXVJAJuBXkqpbkopO0an7tJq6ywF7vI9\n/hmwQmutfcsTfaOEugG9gE1KqRZKqZYASqkWwNVAasMPJwCVuylK+ZRV6hISZyVJ+QcRUjY6R0Lr\nbrDuRRkSaoJzJgBfm/7vgOXAbuBjrfVOpdQMpdRk32qzgBilVBrwB+Bx33t3Ah8Du4Avgfu11h6g\nA7BOKbUd2AQs01p/2biHFiAyV9NCF7Ep/HKzIxGi2WllgZEPwZGtkLna7HBCTp1qAWmtPwc+r7bs\n6SqPS4Eaxy9qrZ8Fnq22LAOQyW4Bdi2hWEWwwzHI7EiEMMeA22Dls7DxLeg+xuxoQorcCWwmTzns\nWcZW5zDKld3saIQwh80Jg35ulEHPyzY7mpAiCcBMB9ZDyWk2OqX5R4S4IXcZfQBb3jc7kpAiCcBM\nu5eCNZztDrkRWoSuxJkbSJx/lK2OobDlXePKWDQLSQBm8ZQbwz97XYUrzGl2NEKY7psWk6DgqNEU\nJJqFJACzZKyEohPQ/1azIxHCL2x1DIOoTpA02+xQQoYkAJOs/+RVClRL7lgTZXYoQvgFr7LA4DuN\nO+NPZ5odTkiQBGAGVwFDSzewIfwKoza6EMIw+E5QYXIV0EwkAZhh96c4tIu1EVL5U4gfibrQqImV\nPAdK882OJuhJAjDD9rkcs1zAfltfsyMRwv+MfBBc+UYSEE1KEkBzyzsMmWtYFz4OlDI7GiH8SuLM\nDSR+VkqKfSB8/7oxU55oMpIAmlvKfECzNmK82ZEI4bc+jbzZGBKaIlNGNiVJAM3J64GtH0DnYRy3\nXmh2NEL4rR2OwdAhAb57Gbxes8MJWpIAmtEbLz8Dp/bzYtHVZocihH9TyugLyNkD+5ebHU3QkgTQ\nXMpd/KzgA9JtvdjkHGl2NEL4v/gboNVF8O0M8JSZHU1QkgTQXJLeoZ3nBHNb3iOdv0LUQeKsJP6p\n7oETu4wOYdHo6jQfgKi/xJkbcHhLePnE3zlkH0CK1P0Xos6Sw0eQVHIpQ1c998MVgWg0cgXQDCYV\nLSLam8fcqLvl278Q52lO1H3Ggy8eNzeQICQJoIm19ORyfeECNjtHkGaXG7+EOF8nrR3gisdg7zKZ\nPL6RSQJoYjcWfoRTl/JRy3vMDkWIwDXifmgfD58+BAXHzY4maEgCaEqnM7iqaBkrIiZwxCZtl0LU\nV+KsJB7WD+AqzodPfmXcUyMaTBJAU/r2b5QrCwtaTjM7EiECXrYtlneip0PmGlj7f2aHExQkATSV\n7GTY+QnLWtxEriXG7GiECAqrwq9mbfhYvCv/wV9fecvscAKeJICm4PXAV09CRFs+jfyZ2dEIETyU\nYlb0AxyzXMBDZ/5hFFcU9SYJoCl8OwMOboCrZlAaFmF2NEIEldKwCF5s8xQOXQrzpkFZqdkhBSxJ\nAI0t9RNY/y++jphE4ubuZkcjRFDKtsXyWqtH4MgW+Oz3oLXZIQUkSQCN6VgKLLmfPfY45kTfZ3Y0\nQgS1pPDLWBB5B2z/iA9e+qPZ4QQkSQCNpeA4zL0dnNG81PrPMtevEM1gYcs72OAcxbT8WbDqObkS\nOE+SABqDq4CMlydRmnecJxyPk2dpY3ZEQoQErcJ4pfXjrA6/Elb9A754VOYPOA+SABqq3A0f30nX\nsgz+1fpJMux9zI5IiJDiVRbebPUHGPE72DQTltwvVwJ1JAmgIbxeWPoApK/gP60eYptzmNkRCRGS\ntAojMetaX5/Af5n/4u/MDikgSAKoL6+HVf+8BXbMZV7LO1kVMcHsiIQIbUqxoOU0Vodfyc0FH8CO\nj82OyO/JfAD14SmHJdMZU/I181tOY1HL282OSAgBoBQzWz1EO89xen0ynX+sPs0uxwDm3jvC7Mj8\nklwBnC93MXzya9gxj7kt72Kh1PkRwq94lI3/a/M0OZb2PH3qMZ46+SikLIByl9mh+R1JAOfjyDaY\neQXs/ASumsHilreZHZEQogZFYS15ut1L/LflPbT15MDCX8K/+kPSbJlfuApJAHXhKTOqD749HlyF\ncOcSGPmQ2VEJIc6iMCyKpS1v5fftZ8G0T6B1LHz2P/DacNi5SEYKAUoH0D/C0KFDdVJSUvPuNGs9\nfP6wMTF13FR+efoOisJaNm8MQoiG05rBro3clv8OXcoPkGbrTc/bX4Ruo8yOrMkppZK11kOrL5dO\n4Fo8/NpHTC2cx+UlK8mxtGdO6/9H8plLIUzm9BUiICnFFuelbHVcwuiSb7kl/z149zroOhK6j4Wu\nl0GnIWBzmh1ps5ErgKrcxZCxEja+BZmrcWPns8gbWRyZiDssdP4ohAgFNu1iQtGnjC7+hovKswAo\nx0qWrQc9B4+Diy6F7mMgvJWZYTaK2q4A6pQAlFITgX8DFuBtrfVz1V53AO8BQ4BTwK1a6yzfa38C\nfgl4gAe11svrss2aNHoCKD4NR7bC4WTIWA3Zm8DjhpYX8hFXsyLiGgos0Y23PyGEX2rhLaCPeycX\nu3fSy72b7mX7cWgX5Viwxl4G3a6Alh0gvDVEtIWoC6DlBWB1mB16ndQ7ASilLMA+4CogG9gM3Ka1\n3lVlnelAf631b5VSicANWutblVJxwEfAMOBC4Bugt+9tZ91mTRqUAPZ/bQzftDg4UaIJw2uMDgC8\nKA7YupNqH0iqYxCpjoF4lLSOCRGqLLqcHu69DHZtYlDpJrqWZ9a8YkRbiGwPLdoZP/YWYIsAe4Tx\nWot20CIGbC2MpiWrE1CA77xrsRnLrE4IsxrPw6zgLTeGrXrcxmvOqAYdT0P6AIYBaVrrDN+G5gJT\ngKon6ynAX3yPFwCvKqWUb/lcrbULyFRKpfm2Rx222age/eoE49VIrN5ybPYyFJpD1lgy7L3IsPWi\nOCyyqXYthAgwHmVlnyOefY545kbdg8NbSqQ3n5Y6nyhPHq29p4jx5NDGc5Lo/FyizxwnyrsPhy7F\noV04dSlhNFJRuiseg7FPNM62qqlLAugEHKryPBsYXts6WutypVQeEONb/n2193byPT7XNgFQSt0L\n3Ot7WqiU2luHmGvS9p9wsp7vDVRtkWMOBaF2zCF2vE8CTzb0mLvWtNDv2zm01jOBmQ3djlIqqaZL\noGAmxxwaQu2YQ+14oemOuS43gh0GulR53tm3rMZ1lFJWIBqjM7i299Zlm0IIIZpQXRLAZqCXUqqb\nUsoOJAJLq62zFLjL9/hnwApt9C4vBRKVUg6lVDegF7CpjtsUQgjRhM7ZBORr0/8dsBxjyOZsrfVO\npdQMIElrvRSYBbzv6+Q9jXFCx7fexxidu+XA/VprD0BN22z8w/uRBjcjBSA55tAQasccascLTXTM\nAXUjmBBCiMYjxeCEECJESQIQQogQFfQJQCk1USm1VymVppR63Ox4moJSqotSaqVSapdSaqdS6iHf\n8jZKqa+VUvt9v1ubHWtjU0pZlFJblVKf+Z53U0pt9H3e83yDDIKGUqqVUmqBUmqPUmq3UmpEsH/O\nSqn/8f1dpyqlPlJKOYPtc1ZKzVZKnVB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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# b)\n", "\n", "#Here goes your code. \n", "\n", "#Hint: Think what should be the values of x axis." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Basic Unfolding\n", "\n", "After verifying the validity of equation $ C^T M = E^T $, we may try to restore the original distribution by a simple linear algebra. We should have \n", "\n", "$$ E^T M^{-1} = C^T M M^{-1} = C^T,$$ \n", "\n", "what means that all we need to solve an unfolding problem is the effect vector $E$ and precise knowledge of response matrix $M$.\n", "\n", "As we will soon see, there is a fundamental problem bound with this approach. We do not know the response matrix nor the effect vector **exactly**, and we must rely on (usually MC) approximations. It will be often the case, that small perturbations lead to chaotic and significant changes in $C$. We call such equations **ill posed problems**.\n", "\n", "## Ex 2\n", "a) Inverce matrix $M$ and calculate true distribution according to $ E^T M^{-1} = C,$ \n", "b) Suprising results of the **Ex 2a)** may suggest numerical errors. For obtained solution verify, if it is in fact the solution of equation $ C^T M = E^T $." ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [ "#a)\n", "\n", "#Here goes your code.\n", "\n", "#Hint: np.linalg.inv()" ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "data": { "image/png": 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "#b)\n", "\n", "#Here goes your code." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Playing with binning\n", "We know now, that solution of the equation $ C^T M = E^T $ may be nowhere near to the true distribution due to random fluctuations and an ill-posedness of the problem. One of the possible ways to reduce an impact of these limitations is to artificially increase the number of ** effects ** by reducing the width of histogram bins. As the result, response matrix will no longer be square, so that it will be impossible to calculate it's inverse. On the other hand, we still will be able to determine most suitable solution of the equation $ C^T M = E^T $ with least square method.\n", "\n", "## Ex 3\n", "Solve equation $ C^T M = E^T $ for number of effects increased (widths of histogram bins decreased) by the factor of: \n", "a) 1, \n", "b) 2, \n", "c) 10, \n", "d) 30, \n", "e) 100 (if you have enough memory). \n", "\n", "\n", "\n", "\n", "*Hint:* \n", "\n", "Firstly, generate data using the *get_signal()* function. Then, choose denser binning for effects, that is instead of having \n", "\n", "$$ \\dots, [n:n+1), [n+1:n+2), \\dots$$ \n", "\n", "you shall have for example $$\\dots, [n:n+0.1), [n+0.1:n+0.2), \\dots$$ \n", "\n", "Using this binning calculate a histogram of observations. Compute the response matrix combining two binnings (it will be 100 x 1000 matrix in the above case).\n", "\n", "Finally, solve the equation $ C^T M = E^T $ using function *np.linalg.lstsq()*.\n", "\n", "Remember, that as the number of effects rise, you may need to use more samples for your analysis." ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [ { "data": { "image/png": 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Q7zJyOt0vdSUPDP6JVljJj5lFt7lIvopdM8gwd8iK2uCA1xvgySdSePKtu6it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\njCcvCIIgJFNKSl4QBEHwIEFeEAShhCmJIK+UOlMp9YZSaqt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FT3mzCNpV6qgeiB08t6mZStlGgFhSoFjT4htBjcs1VBFXFkabr4pYTkKwx3YL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\nMsohEIRPdv2YF3LMydECaVmuD1XpU42g44ighxoBdC4UQ+s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8jU8n/55126CgAgor1GtnweASendZ4og+hXn01gbhhcE22myF4Z2lo3REr9FC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\nQ7DTOYWhwQZceHm4/Nu6zEEv8Yi8iIg+Lsd2w/E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clm9e54wxu0Q113V5mjfW3FCOB4eZzPXF9mB7Eu+PRfoxhz4YKhy5JtVVat7E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\nSq0NxLsL3wxpLeaITMQGZH/iBJ7O+qZ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FRX2lycGSOahnuG7S+oBSx/5aSoXcgFVtyxShF8R1IwBul0k0lpIDoy+EvLGB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\nRpsNLvkLNB6GdW9FcHZCRxChP9bs/NI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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "for ratio in [1, 2,10,30,100]:\n", "\n", " #Here goes your code." ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Regularization\n", "As we've seen in the previous exercise, although derived solutions match true distribution quite well, we can still see some defects. In order to smoothen calculated distributions it is common to introduce a regularization in the form of a penalty for unrealistic shape. \n", "\n", "## Ex 4\n", "Take a response matrix for with 3000 effect columns and 100 cause rows (from previous exercise). Append 99 columns of the form:\n", "\n", "$$\\begin{bmatrix}\n", " p \\\\\n", " -p \\\\\n", " 0 \\\\\n", " 0 \\\\\n", " \\vdots \\\\\n", " 0\n", "\\end{bmatrix},\n", "\\begin{bmatrix}\n", " 0 \\\\\n", " p \\\\\n", " -p \\\\\n", " 0 \\\\\n", " \\vdots \\\\\n", " 0\n", "\\end{bmatrix}\n", "\\dots\n", "\\begin{bmatrix}\n", " 0 \\\\\n", " \\vdots \\\\\n", " 0\\\\\n", " p \\\\\n", " -p \\\\\n", " 0 \n", "\\end{bmatrix}\n", "\\begin{bmatrix}\n", " 0 \\\\\n", " \\vdots \\\\\n", " 0\\\\\n", " 0\\\\\n", " p \\\\\n", " -p \\\\\n", "\\end{bmatrix}\n", ".$$\n", "\n", "Append 99 zeros to the effect vector. Calculate and plot source vector using leastsq() function for p = [0.01, 0.1, 1, 10]. Explain results." ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [ { "data": { "image/png": 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6T7K7kjq2uYeR7eoKm96xuxRlEw36tij9MzCVMHiGT3a3InoK2a6uzC6YD7Th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\nnH0PdB14bJvsDPjPJKtVX3gYBPjl10H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sVcM06P3INdlvMTb7BbaGdubxhn/hZEBdu0vyTGAwtOhi/TDZmlZYCNm/QtY+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\nDZgFfGGMedU1/QVgtTFmWYn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kkUfYvXs3EydO5OKLL6aiooJu3bpx5513Mnz4cFatWsV5551XE8Qg6GkzJyeHyZMnU1RU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\nKvg+wr7P4EABfLkDDuyAgzu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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "for p in [0.01, 0.1, 1, 10]:\n", " \n", " #Here goes your code." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Explanation: \n", "Extra columns force adjacent points in the distribution to be as equal as possible. Apart from fitting the distribution, we are trying to minimize 99 expressions in the form $p^{2}[P(C_{i}) - P(C_{i+1})]^{2}$ The bigger $p$, the more impact has this extra \"smoothness\" regularization." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Bayesian (D'Agostini) unfolding\n", "\n", "Another unfolding approach comes from the theory of Bayesian inference. Let $P_{0}(C_{i})$ be our initial knowledge of true distribution. Let's also assume, that we know the response matrix $M$. Then, instead of inversing the response matrix, we can get the probability that cause $C_{i}$ was responsible for effect $E_{j}$ using the Bayes theorem:\n", "\n", "$$ P(C_{i} \\mid E_{j}) = \\dfrac{P(E_{j} \\mid C_{i}) P_{0}(C_{i})}{\\sum_{k=1}^{n}P(E_{j} \\mid C_{k}) P_{0}(C_{k})}.$$\n", "\n", "Quick reminder: we read $P(E_{j} \\mid C_{i})$ from the response matrix.\n", "\n", "To get the probability of the cause $C_{i}$, that is the original distribution, we just need to use the integral probability formula:\n", "\n", "$$ P(C_{i}) = \\sum_{j=1}^{m} P(C_{i} \\mid E_{j}) P(E_{j}). $$\n", "\n", "Quick reminder: we read $P(E_{j})$ from the observation vector. \n", "If we now denote tha matrix $M_{ij} = P(C_{i} \\mid E_{j})$ as $M_{B}$, we can write:\n", "\n", "$$ C = M_{B} E, $$\n", "\n", "where $C$ and $E$ are cause and effect vector, defined as in previous exercises.\n", "\n", "As usually in the case of Bayesian methods, the procedure is iterative, with every next step using a result of the previous one as a prior.\n", "\n", "More details in the original paper: \n", "https://lib-extopc.kek.jp/preprints/PDF/1994/9408/9408011.pdf\n", "\n", "## Ex 5\n", "Calculate the distribution of $C_{i}$ using a method described above and: \n", "a) Flat prior, \n", "b) Prior equal to the observed distribution. \n", "\n", "Compare rms difference between real and calculated distributions. Plot results after the few iterations." ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Loss: 0.9657319999999999\n", "Loss: 0.31471495935597427\n", "Loss: 0.1648517892657277\n", "Loss: 0.07981750389988693\n", "Loss: 0.05362148548094371\n" ] }, { "data": { "image/png": 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s2DEmTZrE3r17AcjKymLDhg1YrVYcDgerVq3C39+fgwcPcuutt5Kens4LL7zA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\n8zBHvi7B1ubf5KVNSiR2yRLaPv4Y+6Fz+/gfmPgAubG5/G7r72i0KzE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"text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "#a) \n", "\n", "\n", "#Here goes your code." ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Loss: 0.3676331590063602\n", "Loss: 0.21715442388276718\n", "Loss: 0.1354876758929421\n", "Loss: 0.07262983134008812\n", "Loss: 0.052220148103284965\n" ] }, { "data": { "image/png": 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Qo0cPgoKCmDRpEpMmTTrj8yQnJzN79mxCQ0P5zW9+A8DNN9/MQw89xJgxYzh6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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "#b)\n", "\n", "#Here goes your code." ] } ], "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": "3.6.1" } }, "nbformat": 4, "nbformat_minor": 2 }