{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Think Bayes\n", "\n", "Copyright 2018 Allen B. Downey\n", "\n", "MIT License: https://opensource.org/licenses/MIT" ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "# Configure Jupyter so figures appear in the notebook\n", "%matplotlib inline\n", "\n", "# Configure Jupyter to display the assigned value after an assignment\n", "%config InteractiveShell.ast_node_interactivity='last_expr_or_assign'\n", "\n", "import numpy as np\n", "import pandas as pd\n", "\n", "# import classes from thinkbayes2\n", "from thinkbayes2 import Pmf, Cdf, Suite, Joint\n", "\n", "from thinkbayes2 import MakePoissonPmf, EvalBinomialPmf, MakeMixture\n", "\n", "import thinkplot" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## The Geiger counter problem\n", "\n", "I got the idea for the following problem from Tom Campbell-Ricketts, author of the [Maximum Entropy blog](http://maximum-entropy-blog.blogspot.com). And he got the idea from E. T. Jaynes, author of the classic *Probability Theory: The Logic of Science*:\n", "\n", "> Suppose that a radioactive source emits particles toward a Geiger counter at an average rate of r particles per second, but the counter only registers a fraction, f, of the particles that hit it. If f is 10% and the counter registers 15 particles in a one second interval, what is the posterior distribution of n, the actual number of particles that hit the counter, and r, the average rate particles are emitted?\n", "\n", "\n", "\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Grid algorithm\n", "\n" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [], "source": [ "class Logistic(Suite, Joint):\n", " \n", " def Likelihood(self, data, hypo):\n", " \"\"\"\n", " \n", " data: k, number of particles detected\n", " hypo: r, emission rate in particles per second\n", " \"\"\"\n", " return 1" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "r = 160\n", "k = 15\n", "f = 0.1\n", "\n", "pmf = MakePoissonPmf(r, high=500)\n", "thinkplot.Hist(pmf)" ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "0.09921753162215896" ] }, "execution_count": 4, "metadata": {}, "output_type": "execute_result" } ], "source": [ "total = 0\n", "for n, p in pmf.Items():\n", " total += p * EvalBinomialPmf(k, n, f)\n", " \n", "total" ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [], "source": [ "def compute_likelihood(k, r, f):\n", " pmf = MakePoissonPmf(r, high=500)\n", " total = 0\n", " for n, p in pmf.Items():\n", " total += p * EvalBinomialPmf(k, n, f)\n", " \n", " return total" ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "0.09921753162215896" ] }, "execution_count": 6, "metadata": {}, "output_type": "execute_result" } ], "source": [ "compute_likelihood(k, r, f)" ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [], "source": [ "likes = pd.Series([])\n", "for kk in range(0, 40):\n", " likes[kk] = compute_likelihood(kk, r, f)" ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "likes.plot()\n", "thinkplot.decorate(xlabel='Counter particles (n)',\n", " ylabel='PMF')" ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [], "source": [ "# Solution\n", "\n", "class Logistic(Suite, Joint):\n", " f = 0.1\n", " \n", " def Likelihood(self, data, hypo):\n", " \"\"\"\n", " \n", " data: k, number of particles detected\n", " hypo: r, emission rate in particles per second\n", "\n", " \"\"\"\n", " k = data\n", " r = hypo\n", " return compute_likelihood(k, r, self.f)" ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [], "source": [ "rs = np.linspace(0, 300, 51);" ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [], "source": [ "suite = Logistic(rs);" ] }, { "cell_type": "code", "execution_count": 12, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "0.03262565933783285" ] }, "execution_count": 12, "metadata": {}, "output_type": "execute_result" } ], "source": [ "suite.Update(15)" ] }, { "cell_type": "code", "execution_count": 13, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "thinkplot.Pdf(suite)\n", "thinkplot.decorate(xlabel='Emission rate (particles/second)',\n", " ylabel='PMF',\n", " title='Posterior marginal distribution')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### MCMC\n", "\n", "Implement this model using MCMC. As a starting place, you can use this example from [the PyMC3 docs](https://docs.pymc.io/notebooks/GLM-logistic.html#The-model).\n", "\n", "As a challege, try writing the model more explicitly, rather than using the GLM module." ] }, { "cell_type": "code", "execution_count": 14, "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "/home/downey/anaconda3/lib/python3.6/site-packages/h5py/__init__.py:36: FutureWarning: Conversion of the second argument of issubdtype from `float` to `np.floating` is deprecated. In future, it will be treated as `np.float64 == np.dtype(float).type`.\n", " from ._conv import register_converters as _register_converters\n" ] } ], "source": [ "import pymc3 as pm" ] }, { "cell_type": "code", "execution_count": 15, "metadata": {}, "outputs": [], "source": [ "# Solution\n", "\n", "f = 0.1\n", "model = pm.Model()\n", "\n", "with model:\n", " r = pm.Uniform('r', 0, 500)\n", " n = pm.Poisson('n', r)\n", " k = pm.Binomial('k', n, f, observed=15)\n", " trace = pm.sample_prior_predictive(1000)" ] }, { "cell_type": "code", "execution_count": 16, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "thinkplot.Cdf(Cdf(trace['n']));" ] }, { "cell_type": "code", "execution_count": 18, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "thinkplot.Cdf(Cdf(trace['k']));" ] }, { "cell_type": "code", "execution_count": 19, "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "Multiprocess sampling (4 chains in 4 jobs)\n", "CompoundStep\n", ">NUTS: [r]\n", ">Metropolis: [n]\n", "Sampling 4 chains: 100%|██████████| 16000/16000 [00:04<00:00, 3852.03draws/s]\n", "The acceptance probability does not match the target. It is 0.46421389596339574, but should be close to 0.8. Try to increase the number of tuning steps.\n", "The estimated number of effective samples is smaller than 200 for some parameters.\n" ] } ], "source": [ "with model:\n", " trace = pm.sample(1000, tune=3000)" ] }, { "cell_type": "code", "execution_count": 20, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "pm.traceplot(trace);" ] }, { "cell_type": "code", "execution_count": 21, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "{'xscale': 'linear', 'yscale': 'linear'}" ] }, "execution_count": 21, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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+ywCX1FRFwj36nOsdkRdpQ0TsA/YBbNu2rcCvXjsDXFIbFQn3RWBr1/EW4OSANosRcTbwHuC/ez8oMw8ABwBmZmZKKdkY3pK0UpFwPwrsiIgLgJeA3cB1PW0OAb8OPAZ8CDgyrnr7Q3d8ZBwfK0mNMjLcOzX0/cAjLE2FvCczj0fELcB8Zh4C7ga+GBELLI3Yd4+z05Kk4QrNc8/Mw8DhnnM3db3+NvDL5XZNknSm3IlJkhrIcJekBjLcJamBDHdJaiDDXZIaKMa8/MvgXxxxGvhGJb98dTYxhmUUGsZrVIzXaTSv0Wjvy8zNoxpVFu51ERHzmekC7kN4jYrxOo3mNSqPZRlJaiDDXZIayHAf7UDVHagBr1ExXqfRvEYlseYuSQ3kyF2SGqjV4R4R90TEqYh4uuvcD0bEP0TEf3b+/IHO+YiIz0bEQkQ8FREXVdfzyRpwnW6OiJci4mudn6u73vtU5zo9GxE/X02vJysitkbEoxHxTEQcj4iPdc77feoy5Dr5fSpbZrb2B/gZ4CLg6a5ztwE3dl7fCHym8/pq4GGWdp26FHii6v5XfJ1uBj7Zp+1O4BiwEbgA+C9gXdX/DhO4RucBF3VenwP8R+da+H0qdp38PpX80+qRe2Z+lZU7Rs0C93Ve3wf8Qtf5+3PJ48C5EXHeZHparQHXaZBZ4GBmvpGZXwcWWNpkvdEy8+XM/NfO6/8FnmFpb2G/T12GXKdBWvl9KkOrw32AH87Ml2Hpiwi8t3O+30bhw76UbbC/U1K4Z7ncgNeJiNgOXAg8gd+ngXquE/h9KpXhXlyhTcBb5HPAjwDvB14G/rhzvtXXKSLeDTwE/G5m/s+wpn3Otfk6+X0qmeG+0jeX/3rc+fNU53yRjcJbIzO/mZnfzcz/A77A9/6q3NrrFBHrWQqsv8zMv+6c9vvUo9918vtUPsN9peXNvun8Odd1/vrOLIdLgdeW/7rdRj314V8ElmfSHAJ2R8TGzqbqO4B/mXT/Ji0igqW9hJ/JzD/pesvvU5dB18nvU/kK7aHaVBHxJeAKYFNELAKfBm4FHoyIvcALfG9v2MMszXBYAF4HPjzxDldkwHW6IiLez9JfkZ8HfgsglzZPfxA4AbwFfDQzv1tFvyfscuDXgH+PiK91zv0+fp96DbpOe/w+lcsnVCWpgSzLSFIDGe6S1ECGuyQ1kOEuSQ1kuEtSAxnuktRAhrskNZDhLkkN9P+ohQ9Ro6k7xAAAAABJRU5ErkJggg==\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "n_sample = trace['n']\n", "thinkplot.Cdf(Cdf(n_sample))" ] }, { "cell_type": "code", "execution_count": 22, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "{'xscale': 'linear', 'yscale': 'linear'}" ] }, "execution_count": 22, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "r_sample = trace['r']\n", "thinkplot.Cdf(Cdf(r_sample))" ] }, { "cell_type": "code", "execution_count": 23, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "{'xscale': 'linear', 'yscale': 'linear'}" ] }, "execution_count": 23, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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vPr03q/2BdyyJphCRM6BwFxnBjv3D8+vTvJ+6Gv26SPnQu1Ukjx37uzl4bHh+fZauRpUyo3AXydE/mOQf1r2Ubtd6kjqSEVYkMn4Kd5EcD2/al9U+z49HVInImVO4i+TYsL0jvV3nCY3apSwp3EUy/Orl7Fv/zvGeiCoROTsKd5FQEDjfeHJ4gbD62hhTGIywIpEzp4uYREitIbPq0RfoCIavSJ0fdNEwyveIlDKN3EVIrSGTGey1nqSBRLqtNWSk3CjcRYD9OWvIZJ4hozVkpBxpWkaqXtuhHnoz1pD51H95Cx9455LoChIpAo3cpaq5Ow/+MvveqAp2qQQKd6lqG9uO8tqR4VvmzfETo+wtUj4U7lK13LNPfaz1JNMZiLAikeJRuEvVeuy5g1ntc7Q4mFQQhbtUpUQy4Ps5a8g00h9RNSLFp3CXqvTM7q6s9qLgyAh7ipSngsLdzK4zs51m1mZmd46y301m5mamk4KlpD2xozO93dxYTy1BhNWIFN+Y4W5mcWAVcD1wMXCLmV2cZ79G4OPAr4tdpEgxdXSfou3Q8IJgK95yfoTViEyMQi5iugJoc/ddAGa2BlgBbM/Z72+AzwN/XtQKRYrokQ1b+dyjL9EbDI9rjj7fikVYk8hEKGRaZj6Qeafg9rAvzcyWAwvd/UdFrE2k6B5c90xWsM8JerKCXWvISKUoJNzzDWo8/aBZDPhH4M/GfCKz28ys1cxaOzs7x9pdpKjcnV2JaVl9M+hLb2sNGakkhUzLtAMLM9oLgP0Z7UbgUuCnZgZwHrDWzG5099bMJ3L31cBqgJaWFkdkEm3Y3sGgDb/l73zfW1n5m4sirEhk4hQyct8ELDOzpWZWB6wE1g496O7H3X2Ouy9x9yXARuC0YBeJ2o82H8hq33TFgogqEZl4Y4a7uyeAO4D1wA7gO+6+zczuNrMbJ7pAkWIZSA6f7jgr6KEmrss8pHIVtOSvu68D1uX03TXCvledfVkixdV+tJf+weFwb8qYaxepRBq6SFX4yQsd6e2pPqBTH6XiKdyl4iUD5+cvHU63p7hWfpTKp3CXivfQxr1Z7elaIEyqgMJdKl7mzTgAarSOjFQBhbtUtNx1ZM4PjkVYjcjkUbhLRXts6/ANOc5ramAKgxFWIzJ5CjoVUqTcPLJhKw891sr2RFO6b07Qw8wIaxKZTBq5S0V66LFWjg9kr3DRyKn0thYIk0qncJeK1D8wSJdNTbdjHhAL17vTAmFSDTQtIxVpgDi9Vg9AyyWL+cjVF/DWC2ZFXJXI5NHIXSrSEZue3p5aF6dl6TkRViMy+RTuUnH2He2j1+rS7Y9cfQHhctQiVUPhLhXn8e2H0tu1nuSSBTpHRqqPwl0qSm9/gqdeHF5HZqZr9UepTgp3qSgP/uq19LbhNGppX6lSCnepGL39CTa2HU23Z3qf3uBStfTel4rx5IvZN12f5ScjqkQkejrPXcra0DIDpwYG2RVrTvc3+indkEOqmkbuUtYeeqyV/oFBeqnL6p/pqWV+tcyAVCuFu5S1/oHUKo+d1pjuq/Uk9SS1zIBUNU3LSNnrpoGkxWi5ZDEAn3jPMt64UOe2S3XTyF3KXk+4hgzA+ec0KNhFULhLmRskRl/GUgMr374owmpESofCXcraCWtIb89rauDi+TMirEakdCjcpWz19ifosmnp9rt+o3mUvUWqi8Jdytb654cXCDOcd12kcBcZonCXsjSQCHh0y4F0e7qfojaut7PIEP02SFn63tPtWe05WmpAJIvOc5eyMLTMQP/AIAGwO2OpgTpPpO+PKiIpGrlLWRgKdoCjGbfQi+Es8C4tMyCSQ+EuZWEo2Hup5bhNSffP8D4atMyAyGkKmpYxs+uAe4A48HV3/2zO458CPgwkgE7gj9z91SLXKlUuiXHIZqSXGQD48gcvp65GYxSRXGP+VphZHFgFXA9cDNxiZhfn7LYZaHH3NwHfAz5f7EJFjtsUAht+y9789oUKdpERFPKbcQXQ5u673H0AWAOsyNzB3Z9wD9dYhY3AguKWKdXOgW6Gp2N+r2U+77703OgKEilxhYT7fGBvRrs97BvJh4DH8j1gZreZWauZtXZ2dubbRSSvU9SSDEftZnDtJXMjrkiktBUS7vluaJP3vDMz+wOgBfhCvsfdfbW7t7h7S3OzriaUwu2PNaW3Z0+vo742HmE1IqWvkA9U24GFGe0FwP7cnczsWuDTwLvcvb845YnAuq0HstrvXX5+RJWIlI9CRu6bgGVmttTM6oCVwNrMHcxsOfBV4EZ37yh+mVKtXmg/zvc37cvq+83XzY6oGpHyMebI3d0TZnYHsJ7UqZD3uvs2M7sbaHX3taSmYaYD3zUzgNfc/cYJrFsqVOaVqAPE2RublfX44uAwsZhufS0yloLOc3f3dcC6nL67MravLXJdUqUyr0TNvFgJoDk4wbQ6rZghUgidJCwlZSjY+6mhO+NGHDO9l+a6pK5EFSmQhkFSchzYbzNpuWQJALOm1/G5m99IOOUnIgXQyF1KzmGbnnUl6oevWqpgFxknhbuUlAQxujPm2i9b3MTrz2uMsCKR8qRwl5Lh7uyzpqy+m9+2cIS9RWQ0CncpGV987CUSNnzl6W8tm03zjPoIKxIpX/pAVSKReT47QA/1HIrNyNrnj961NIrSRCqCRu4SicxgT2J0xLLn1ZfFj0dRlkjFULhLJIaCHeCITccz1qdbGD/JH9zwlijKEqkYmpaRSJ2ihjdc+oZ0+3cum8fvtoy2orSIFEIjd4lUpw1Px0ypi3Pj5VrxUaQYFO4SmR7qGLDhPx4/+M4lWhRMpEgU7hIJBw7FZqbbs6fX8Zal50RXkEiFUbhLJI7atKz2re9YHFElIpVJH6jKhMo9nx3gJHUcyxi1NzbUcOmCmfm+XUTOkEbuMqFyg32AOAczgr3G4LM3vzGK0kQqmkbuMqEygz2JsT9j7ZiYGbdeuUA3uxaZAAp3mRQBsLjlCub0J9N9v/2GOXzgnUsiq0mkkmlaRiZcAmN3rJmTGcG+fHGTgl1kAmnkLkWR74NTgONM4XBselZffW2Mj1574WSWJ1J1NHKXosgX7N00pIM9lnEnpf9763LdWUlkgmnkLkWRGewOHLCZ9FkdkAr28+c20bL0HG6/RiN2kcmgcJeicmDWG1uYldP/h+9czDvf0BxFSSJVSeEuRePArlhzVrDXxo3br7mQNy9qGunbRGQCKNxlXEb64DSJsSc257T9v/zByzW/LhIBhbuMS75gP2SN9FgDkP3BqYJdJDoKdxmX3KUE9lsTSUuddDX0wSnA39/yJupqdDKWSFQU7pLXSNMvDvRRS6c1ctmlF3BuzvdddVEz/+23FmnELhIxhbvklS/Ye6hLr8EeyxPef/e+S5k7o2FS6hOR0SncJa+hYB8kxglroCtj/fXM6ReANy+ayUevfR1x3UVJpGQUFO5mdh1wDxAHvu7un815vB74JvAW4Ahws7vvKW6pMhFyp18cGCTOUZvBSasHoOWS/DfSeO/yeVxzyblMb9AYQaTUjPlbaWZxYBXwbqAd2GRma919e8ZuHwK63P11ZrYS+Bxw80QULGcmM8QdcIwg/NdLHSdtGqes9rTvyzf98rFrL2T5Et0ST6SUFTLkugJoc/ddAGa2BlgBZIb7CuAz4fb3gC+Zmbm7F7FWGUUiGfDki52s/eXLbHmxne6ghrgHJCxOzAMww5mJxwAKmz7JnH5pWXoO77qomYvOnzFxByEiRVNIuM8H9ma024G3jbSPuyfM7DgwGzhcjCIz/f4nvlLsp6wImR92QmoEnrDUTTACG/2UxKEQP2/OcHDHY8ZvzGvk969YwKLZUyekZhGZOIWEe75hXu6IvJB9MLPbgNsAFi1aVMCPlkIN2tgvZWaIm4E7zGmso64mRsyMlqXncNniJs6b2UBNXOeoi5SzQsK9HViY0V4A7B9hn3YzqwFmAkdzn8jdVwOrAVpaWjRlU0RTfYCYB/RZHVPisOLKZVz11tczp7GOafU11NfEiMWMuBkxndUiUvEKCfdNwDIzWwrsA1YC78/ZZy3wh8CvgJuADRM13/7wPbdPxNOKiFSUMcM9nEO/A1hP6lTIe919m5ndDbS6+1rgG8ADZtZGasS+ciKLFhGR0RV0grK7rwPW5fTdlbF9CvivxS1NRETOlD41ExGpQAp3EZEKpHAXEalACncRkQqkcBcRqUAW1fIvZtYJvHqG3z6HCVjaIAI6jtKi4ygtOo78Frt781g7RRbuZ8PMWt29Jeo6zpaOo7ToOEqLjuPsaFpGRKQCKdxFRCpQuYb76qgLKBIdR2nRcZQWHcdZKMs5dxERGV25jtxFRGQUZRfuZnadme00szYzuzPqesbDzPaY2fNmtsXMWsO+WWb2YzN7OfxacjcnNbN7zazDzF7I6Mtbt6X8c/j6PGdml0dXebYRjuMzZrYvfE22mNkNGY/9ZXgcO83sPdFUfTozW2hmT5jZDjPbZmafCPvL5jUZ5RjK8fVoMLOnzWxreCx/HfYvNbNfh6/HQ2ZWF/bXh+228PElE1KYu5fNP1JLDr8CXADUAVuBi6Ouaxz17wHm5PR9Hrgz3L4T+FzUdeap+7eBy4EXxqobuAF4jNTdud4O/Drq+sc4js8Af55n34vD91c9sDR838WjPoawtnnA5eF2I/BSWG/ZvCajHEM5vh4GTA+3a4Ffh/+dvwOsDPu/AvxJuP1R4Cvh9krgoYmoq9xG7umbdbv7ADB0s+5ytgK4P9y+H/jdCGvJy92f4vQ7a41U9wrgm56yEWgys3mTU+noRjiOkawA1rh7v7vvBtpIvf8i5+4H3P3ZcPsEsIPUfYzL5jUZ5RhGUsqvh7t7T9isDf85cDXwvbA/9/UYep2+B1xjZkW/PVq5hXu+m3WP9oYoNQ78h5k9E95PFuBcdz8AqTc8MDey6sZnpLrL8TW6I5yuuDdjWqwsjiP8k345qdFiWb4mOccAZfh6mFnczLYAHcCPSf1lcczdE+EumfWmjyV8/Dgwu9g1lVu4F3Qj7hJ2pbtfDlwPfMzMfjvqgiZAub1G/wJcCFwGHAD+Iewv+eMws+nAw8Cfunv3aLvm6SuJY8lzDGX5erh70t0vI3WP6SuAi/LtFn6dlGMpt3Av5GbdJcvd94dfO4AfkHoTHBr6Ezn82hFdheMyUt1l9Rq5+6HwFzMAvsbwn/olfRxmVksqFL/l7t8Pu8vqNcl3DOX6egxx92PAT0nNuTeZ2dDd7jLrTR9L+PhMCp8uLFi5hXv6Zt3hJ88rSd2cu+SZ2TQzaxzaBv4T8ALDNxcn/PpINBWO20h1rwU+EJ6h8Xbg+NBUQSnKmXv+PVKvCaSOY2V4ZsNSYBnw9GTXl084P/sNYIe7fzHjobJ5TUY6hjJ9PZrNrCncngJcS+ozhCeAm8Ldcl+PodfpJmCDh5+uFlXUnzSfwSfTN5D6ZP0V4NNR1zOOui8g9Wn/VmDbUO2k5toeB14Ov86KutY8tX+b1J/Ig6RGHR8aqW5Sf3KuCl+f54GWqOsf4zgeCOt8jtQv3byM/T8dHsdO4Pqo68+o6x2k/ox/DtgS/ruhnF6TUY6hHF+PNwGbw5pfAO4K+y8g9X9AbcB3gfqwvyFst4WPXzARdekKVRGRClRu0zIiIlIAhbuISAVSuIuIVCCFu4hIBVK4i4hUIIW7iEgFUriLiFQghbuISAX6/76Hklhd/trDAAAAAElFTkSuQmCC\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "thinkplot.Cdf(suite.MakeCdf())\n", "thinkplot.Cdf(Cdf(r_sample))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Grid algorithm, version 2" ] }, { "cell_type": "code", "execution_count": 24, "metadata": {}, "outputs": [], "source": [ "# Solution\n", "\n", "class Logistic(Suite, Joint):\n", " f = 0.1\n", " \n", " def Likelihood(self, data, hypo):\n", " \"\"\"\n", " \n", " data: k, number of particles detected\n", " hypo: r, n\n", " \"\"\"\n", " k = data\n", " r, n = hypo\n", " return EvalBinomialPmf(k, n, self.f)" ] }, { "cell_type": "code", "execution_count": 25, "metadata": {}, "outputs": [], "source": [ "rs = np.linspace(0, 300, 51);" ] }, { "cell_type": "code", "execution_count": 26, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "50.99999999999964" ] }, "execution_count": 26, "metadata": {}, "output_type": "execute_result" } ], "source": [ "suite = Logistic()\n", "\n", "for r in rs:\n", " pmf = MakePoissonPmf(r, high=500)\n", " for n, p in pmf.Items():\n", " suite[r, n] += p\n", " \n", "suite.Normalize()" ] }, { "cell_type": "code", "execution_count": 27, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "0.03262565933783306" ] }, "execution_count": 27, "metadata": {}, "output_type": "execute_result" } ], "source": [ "suite.Update(15)" ] }, { "cell_type": "code", "execution_count": 28, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "pmf_r = suite.Marginal(0)\n", "thinkplot.Pdf(pmf_r)\n", "thinkplot.decorate(xlabel='Emission rate (particles/second)',\n", " ylabel='PMF',\n", " title='Posterior marginal distribution')" ] }, { "cell_type": "code", "execution_count": 29, "metadata": {}, "outputs": [ { "data": { "image/png": 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pFTXziXR8SlDSbhomJwTSNnpEc86PJKhlZRW0MMSjiGQpJShpN2WRLt/nFGfm/lODkjGD6dG9GwB7DxylcteBjJ5PRNJPCUraRX19Pes2NzbxTcxwDSovrwvnTWx8CFjNfCIdjxKUtIuKnfupPlkDQP8+PSnq3zvj55ye1MwnIh2LEpS0i7JN0ea9IQTTeWXWeec0zm25esPOxASJItIxKEFJuyjf2ti819AFPNOGDCxkUFhTqz5Zw8bKPe1yXhFJDyUoaRcbKhqTw4TR7ZOgzKzJaOkr1ut5KJGORAlKMq6mpo6KnfsS6+NGDWq3c0+NDKe0ct32FkqKSLZRgpKM27J9b2Lai6GD+tCrR0G7nXtKSWOCWrtJ96FEOhIlKMm46L2fsSMzM7xRcwYPKGTwgEIATtbUUr61ql3PLyJnTglKMi7aQWJ8OzbvNdB9KJGOSQlKMi6ODhJRUyPNfKvKdR9KpKNQgpKMirODRIPovFNrN+6kpkb3oUQ6AiUoyag4O0g0GNS/N0MH9QGgpraOdVs0DbxIR6AEJRkVZweJqGgtavWGHbHFISJtpwQlGbV5297E8riR7d+816B0/LDE8holKJEOQQlKMmrz9sYEVTxiYGxxTI4kqLWbdiWaHUUkeylBSca4O1uyJEENHlDIgL69gGBcvmjNTkSykxKUZMzufYc5UR1MsdG7ZwH9+/SMLRYza1KLWrNRzXwi2S6jCcrMZplZmZmVm9l9KV4vMLOnwtcXmFlx5LX7w+1lZnZ9ZPs/mdkqM1tpZk+aWfdMvgc5c9FaSvGIge0yxUZLSsfpPpRIR5KxBGVmecAPgRuAUuA2MytNKnYnsN/dJwAPAw+F+5YCtwJTgFnAj8wsz8xGAPcCM9x9KpAXlpMs1CRBDY+vg0SDyeMbp5lfvXEn7h5jNCLSmkzWoGYC5e6+0d1PAnOA2UllZgO/CJefBq614GP2bGCOu1e7+yagPDweQD7Qw8zygZ6AhgbIUluz5P5Tg9HDBtCzezcADh05zvaqgzFHJCItyWSCGgFE59muDLelLOPutcBBYGBz+7r7NuDfga3ADuCgu7+Q6uRmdpeZLTazxVVVGiA0DtnSg6+BmTE50sy3VvehRLJaJhNUqhsOyW0qzZVJud3M+hPUrsYCw4FeZvaRVCd390fcfYa7zygqiu8B0Vx1/MRJdu45BEAXM0YM6RdzRIFJ4yLNfBt2xhiJiLQmkwmqEhgVWR/Jqc1xiTJhk11fYF8L+14HbHL3KnevAZ4BLstI9HJWtu5oHH9vxJB+dOuaH2M0jfTArkjHkckEtQgoMbOxZtaNoDPDvKQy84A7wuVbgJc8uHM9D7g17OU3FigBFhI07V1iZj3De1XXAmsy+B7kDEU7SIweHn/zXoPxo4romp8HwK69h9h38GjMEYlIczKWoMJ7SvcA8wmSyFx3X2VmD5jZTWGxR4GBZlYOfBG4L9x3FTAXWA08D9zt7nXuvoCgM8XbwIow/kcy9R7kzG3Z3liDKs6iBNW1ax4lYxqn/FizUc18Itkqo+0u7v4c8FzStq9Glk8AH2xm3weBB1Ns/xrwtfRGKumWbR0koiaPG5YYMHbNhh1cfv74mCMSkVQ0koSkXTYNcZRKdEQJjWwukr2UoCTtqvYfyZohjlI5p3hIopvo1u17OXq8OtZ4RCQ1JShJu4pID75RQwfEPsRRsp49ulEcTv3hBLPsikj2UYKStKvcdSCxPGpY/xgjaV60u3nZJs2wK5KNlKAk7aLPQI0ckp0JKvrArkY2F8lOSlCSdpU79yeWRw8bEGMkzZs0tjFBrduym5qauhijEZFUlKAkrdydikiCytYmvgF9ezF0UB8Aamvr2FCh8RpFso0SlKTVnv1HqD7Z2IOvb+8eMUfUvEnjNIGhSDZTgpK0alJ7ysIefFGTI/eh1JNPJPsoQUlaRRPUyKHZMYJ5c6IdJdZu0gSGItlGCUrSqmJn02egstmIwf0o7NUdgCPHqpt0jxeR+ClBSVpV7Ig28WVnB4kGwQSGke7mGvZIJKsoQUnanNqDL7trUKCOEiLZTAlK0ibag69XjwL6FWZvD74GTWtQ6ighkk2UoCRtkp9/yuYefA3GjRyUmMCwav9h9uw/EnNEItJACUrSpmkX8+y+/9QgPz+PicVDEutrN6kWJZItlKAkbSqTnoHqKPQ8lEh2UoKStIl2MR/ZQWpQ0HQCQ00BL5I9lKAkLU7pwdeBEtTEMY0TGG7ZtkcTGIpkCSUoSYu9B44mZtHt2b1b1s2i25KePboxZkTjBIbrNu+ONyARAZSgJE2Sn3/qCD34okrHR+9D6XkokWygBCVp0XSIo47TvNcg+sDuao0oIZIVlKAkLTrSEEepRHvyrd+ym9paTWAoEjclKEmLJjWoDjDEUbIBfXsxZGAwgWFNbR0bK/fEHJGIKEHJWXP3JiOBd8QaFDSdfkPdzUXipwQlZ23vgaMcP3ES6Hg9+KI0srlIdlGCkrNWuatj9+BrkDyyuSYwFImXEpSctY7eQaLByCH96N2zAAgmMNy2WxMYisQpownKzGaZWZmZlZvZfSleLzCzp8LXF5hZceS1+8PtZWZ2fWR7PzN72szWmtkaM7s0k+9BWrd1R2SIoyEdN0EFExg21qI0Lp9IvDKWoMwsD/ghcANQCtxmZqVJxe4E9rv7BOBh4KFw31LgVmAKMAv4UXg8gO8Bz7v7JGAasCZT70HaJtrEN3p4x+vBFxXtKKHnoUTilcka1Eyg3N03uvtJYA4wO6nMbOAX4fLTwLUW3MCYDcxx92p33wSUAzPNrA9wJfAogLufdHe1w8QoeQy+kUP6xRjN2SsdrxqUSLbIZIIaAVRE1ivDbSnLuHstcBAY2MK+44Aq4Odm9o6Z/dTMeqU6uZndZWaLzWxxVVVVOt6PpLDvYNMefAP6pvxxdBjRCQx37T3EvoNHY45IJHdlMkGl6sqV3C2quTLNbc8HLgB+7O7nA0eBU+5tAbj7I+4+w91nFBUVtT1qOS1Nak9DO8Ysui3Jz8+jZMzgxLqehxKJTyYTVCUwKrI+EtjeXBkzywf6Avta2LcSqHT3BeH2pwkSlsSks/Tgi2raUUL3oUTikskEtQgoMbOxZtaNoNPDvKQy84A7wuVbgJc8ePhkHnBr2MtvLFACLHT3nUCFmZ0T7nMtsDqD70Fa0XSQ2I7dQaKBRpQQyQ4tJigzeyyyfEcLRU8R3lO6B5hP0NNurruvMrMHzOymsNijwEAzKwe+SNhc5+6rgLkEyed54G53bxi983PAE2a2HJgOfON04pL0ajLE0bDOUYM6Z2zjBIabK/ck7rGJSPvKb+X1aZHlz9PY465N3P054LmkbV+NLJ8APtjMvg8CD6bYvhSYcTpxSGa4OxWd5BmoqF49Chg9fCBbtu8NJjDcsptp54yMOyyRnNNaE5/GepFm7T90jGNh7aJH924M7Nexe/BFRbub63kokXi0VoMaaWbfJ+hV17Cc4O73ZiwyyXrJzz919B58UZPGDeVPr60E1FFCJC6tJaj/HllenMlApOOJNu91lg4SDSaNbewoUbZpF7W1deTn57Wwh4ikW4sJyt1P656T5JZoDaqzdJBoMKh/b4r6F1K1/zA1tXVs2raHkjFD4g5LJKe0mKDMLLlbeBPuflNLr0vn1iRBdbIaFMDk8UOpWnwYgFXlO5SgRNpZa018lxIMOfQksIDUIzxIDkruwddZHtKNmjJhOH9dvB6AVeXb+cC102OOSCS3tJaghgLvAW4DPgw8CzwZPqckOawz9+BrMGXC8MTy6g07qKurJy9PU6iJtJcW/9rcvc7dn3f3O4BLCEYVf8XMPtcu0UnW6sw9+BoMHdQnkXhPVNewoUKDDou0p1Y/DobDDd0MPA7cDXwfeCbTgUl227q98/bga2BmTWpRK9cnDyUpIpnU2lBHvwD+RjAg67+5+0Xu/r/cfVu7RCdZKzoG3+hhnTNBAZxb0jhDzKpyJSiR9tTaPaiPEkxpMRH4vJk1jCxhgLt7n0wGJ9mrM3cxj5o6sTFBrdm4U89DibSj1u5BdXH3wshXn/CrUMkpd7k7lTs73zQbqQweUEhR/0IAqk/qPpRIe2qtia+7mX3BzH4QzlDbWo1LcsC+g0eb9ODr6LPotmZKSeN9qBW6DyXSblrrJPELgpHDVwDvA76d8Ygk61Uk1Z46Yw++qHMjCWqVEpRIu2mtRlTq7ucCmNmjwMLMhyTZrjPOotuSaE++NRt36D6USDtprQZV07AQTkAo0iln0W1J0YBChgwMbrnW1NaxfsvumCMSyQ2tJahpZnYo/DoMnNewbGaH2iNAyT650oMvKlqLWrFeT1mItIfWevHlJfXcy1cvvtzm7qfcg8oF506MJKh1SlAi7UEDi8lp2XvgKMfDHnw9c6AHX4NzJzZO+V62eVfiGohI5ihByWmp3BVt3hvQ6XvwNejfp2dixIy6unpWaRp4kYxTgpLTkms9+KKmTxqVWF62tiLGSERygxKUnJatkTmgRg7JrQQ1bVJjM9+ytZUxRiKSG5Sg5LQ0GSR2eOfvYh5VOn5Y4vmnbbsPsGf/kZgjEunclKCkzdydyl0HEuu51sTXrWs+peOGJdaXlamZTySTlKCkzZJ78PXv0zPmiNpfk2a+MnU3F8kkJShps6YP6OZOD76o6U3uQ1Xg7i2UFpGzoQQlbRbtIJFrzXsNxgwfSJ/ePQA4cqyajRV7Yo5IpPNSgpI2iyaoMTnWQaKBmTHtnGgzn3rziWRKRhOUmc0yszIzKzez+1K8XmBmT4WvLzCz4shr94fby8zs+qT98szsHTP7Yybjl6Y2b9ubWB4zfGCMkcSraYJSRwmRTMlYgjKzPOCHwA1AKXCbmZUmFbsT2O/uE4CHgYfCfUuBW4EpwCzgR+HxGnweWJOp2OVUdXX1TbqY53SCityHWrNxJ8eOa9gjkUzIZA1qJlDu7hvd/SQwB5idVGY2waSIAE8D11pw5302MMfdq919E1AeHg8zGwm8H/hpBmOXJNurDlJXVw/AwH696N2zIOaI4jOgby+KRwwCgsStZj6RzMhkghoBRNs/KsNtKcuE800dBAa2su93gS8D9S2dPJyifrGZLa6qqjrT9yChLdvVvBc1Y8roxPKS1VtijESk88pkgkrVBzm5T25zZVJuN7Mbgd3uvqS1k7v7I+4+w91nFBUVtR6ttGjr9kjz3rDc7CARdeGUMYnlt1dvVXdzkQzIZIKqBEZF1kcC25srY2b5QF9gXwv7Xg7cZGabCZoMrzGzxzMRvDQV7SDR0LyVyyaMLqKwV3cADh4+zoatqqWLpFsmE9QioMTMxppZN4JOD/OSyswD7giXbwFe8uCj6Dzg1rCX31igBFjo7ve7+0h3Lw6P95K7fySD70FCW3Y0JqhcG4MvlS5dunBBaWMz32I184mkXcYSVHhP6R5gPkGPu7nuvsrMHjCzm8JijwIDzawc+CJwX7jvKmAusBp4Hrjb3esyFau07Ojx6sTAqHl5XRhe1DfmiLJDk2a+VVtjjESkc8rP5MHd/TnguaRtX40snwA+2My+DwIPtnDsV4BX0hGntGzL9ugIEgMSI3rnuumTRtLFjHp3NlRUsf/QsZwcn1AkUzSShLSqSQcJNe8l9OpRwOTxjaObv61mPpG0UoKSVm3e3jjenLqYNxVt5lu4fHN8gYh0QkpQ0qotqkE1a+a5xYnlpWWVielIROTsKUFJi9w9KUGpBhU1rKhv4prU1tbx9hqNzSeSLkpQ0qIdVQepPlkDQJ/ePehX2CPmiLLPJdPGJpbfWrYxxkhEOhclKGlRdL6j8aMG5eQkha25+LxxieUlq7ZysqY2xmhEOg8lKGnRxsrGERLGjdSQUamMHtafYeGzYdUna1i+TlPBi6SDEpS0aGNlYw1q7EgNcZSKmXHxeY3NfAuWbYoxGpHOQwlKmuXuTZv4RqsG1Zxoglq4YlNiahIROXNKUNKs3fsOc/R4NQC9exZQ1L93zBFlr5IxgxnQtxcAR45Vq5lPJA2UoKRZGyqa3n9SB4nmmRmXnz8+sf7akvUxRiPSOShBSbM2RZr3xo3S/afWXHHBhMTyguWb1JtP5CwpQUmz1EHi9IwfXZQxfYFaAAAWgUlEQVTozXeiuobFqzQ2n8jZUIKSlDwcobvB+FHqINEaM+PySC3qjSXlMUYj0vEpQUlKew8c5fDREwD06N6NoYP6xBxRx/CuCxsT1OLVWxOdTETk9ClBSUpNmvdGDFQHiTYaOaQ/xSOC5tDa2jqNcC5yFpSgJCU17525K2eUJJZfWVQWYyQiHZsSlKS0YevuxLJ68J2eKy4YT0N9c+X67eyoOhhrPCIdlRKUnMLdWbe5MUGVjBkSYzQdz8B+vTm/dHRi/eUFqkWJnAklKDnF9qqDiZv7hb26q4PEGbjm4kmJ5ZcXllFfr6GPRE6XEpScYt2mXYnliWOGqIPEGbho6hj69A7mztp38CjvaCJDkdOmBCWnWLclkqDGqnnvTOTn53H1RRMT6y+9tTbGaEQ6JiUoOUX0/tPEMYNjjKRju+aSxma+hSu3cPDw8RijEel4lKCkiRPVNWzZFjwDZcCE0UpQZ2rU0P5MLA5qoPX19bz45pqYIxLpWJSgpIkNFVV4uDxy2AB69ugWazwd3awrpiSW57++itrauhijEelYlKCkibImHSRUezpbl00fT9/Cxs4SC1ZsjjcgkQ5ECUqaWLtxZ2L5HHWQOGtdu+bx3stLE+vPvroixmhEOhYlKEmor69n9cYdifXS8cNjjKbzeO9lpeTlBX9qZZt2smFrVSt7iAhkOEGZ2SwzKzOzcjO7L8XrBWb2VPj6AjMrjrx2f7i9zMyuD7eNMrOXzWyNma0ys89nMv5cs3nbXo6fOAlA/z499YBumgzo24vLpjfOtvvsX1WLEmmLjCUoM8sDfgjcAJQCt5lZaVKxO4H97j4BeBh4KNy3FLgVmALMAn4UHq8W+Gd3nwxcAtyd4phyhlaVR2pPE4brAd00ev9VUxPLry0pp2rf4RijEekYMlmDmgmUu/tGdz8JzAFmJ5WZDfwiXH4auNaC/4qzgTnuXu3um4ByYKa773D3twHc/TCwBhiRwfeQU1Zv2J5YnjJ+WIyRdD4lY4YweVxwTevr6/ndX5bGHJFI9stkghoBRMd3qeTUZJIo4+61wEFgYFv2DZsDzwcWpDq5md1lZovNbHFVldr8W+PurN7QtAYl6XXL9Rcklv/81lr2HzoWYzQi2S+TCSpV+5C3sUyL+5pZb+A3wBfc/VCqk7v7I+4+w91nFBVpPqPWbN2xjyPHggFi+/Tuwcgh/WKOqPOZds7IxNxatbV1zHtpWcwRiWS3TCaoSmBUZH0ksL25MmaWD/QF9rW0r5l1JUhOT7j7MxmJPAetKm/80ZSOH6b7TxlgZtxy/YWJ9flvrObw0RMxRiSS3TKZoBYBJWY21sy6EXR6mJdUZh5wR7h8C/CSu3u4/dawl99YoARYGN6fehRY4+7fyWDsOWd52bbE8tQSNe9lykVTxzB62AAAqk/W6F6USAsylqDCe0r3APMJOjPMdfdVZvaAmd0UFnsUGGhm5cAXgfvCfVcBc4HVwPPA3e5eB1wOfBS4xsyWhl/vy9R7yBW1tXUsX9eYoKZPGtVCaTkbybWoP766gj37j8QYkUj2ys/kwd39OeC5pG1fjSyfAD7YzL4PAg8mbXud1Pen5Cys2biT6pM1AAwd1IdhRX1jjqhzu2z6OH4/qogNFVXU1tbx5HOL+Nzt7447LJGso5EkhKVrGztMTjtHtadMMzM+NvuSxPqrC8vYsn1vjBGJZCclKGky2+v5pUpQ7WFqyQguLB0DBN1Tf/n7t+INSCQLKUHluH0HjyY+vefldeHcEj333F5u/7uLE+3VS9dWsGD5pljjEck2SlA5bmmk9jR53FC6F3SNMZrcMmb4AK67bHJi/dHfvJ4YC1FElKBy3lvLGj+1nz95dIyR5Kbbb7yYPr2D+aL2HjjKU39aHHNEItlDCSqHHTt+kqVljTWoi88bG2M0uamwV3c+/oFLE+vPvrqCTZV7YoxIJHsoQeWwJau2UFdXD0DxiEHqXh6TK2eUJB6Ornfn+4+/xMma2pijEomfElQOe3PZxsTypdPHxRhJbjMz7vqHK+manwcE4yI+8YeFMUclEj8lqBx1orqGt1dvTawrQcVrxOB+3BFp6vvjq8tZVlYZY0Qi8VOCylGLV22hprYOgFHDBjBisEYvj9usK6ZwQWljR5X/ePwlDhzWlBySu5SgctQrC8sSy5ep9pQVzIy7P3x1olff/kPH+L+PvkBNTV3MkYnEQwkqB+09cKTJ809XXTQxxmgkql9hTz7/0WsSD/CWbdrJI79+jWCQf5HcogSVg15dtD4x++PUkuEMGdgn1nikqemTRvHR2Y33o15asJY/vrIixohE4qEElWPq6+t54Y3VifVrLp4UYzTSnJvefR5XzihJrD/2u781aZYVyQVKUDlm0cotVO0/DEDvngXqvZelzIzP3HoVE4uHJLb94ImXeXPpxhb2EulclKByzLOvNjYVvfeyUrp1zeiUYHIWunXN53986n2JGXgdePiXf9agspIzlKByyLrNu1hVvh2ALmZcf8WUmCOS1vTuWcDX7r6R4eEoH3V19Xzr0fn85a01MUcmknlKUDlk7vONA5FeceEEBvXvHWM00lb9Cnvytbv/jqGDgs4sDvzoyVf59fwl6t0nnZoSVI5Yu3FnYmJCA265/sJ4A5LTMqh/b77xhb9n7MhBiW1znlvEt372AkePV8cYmUjmKEHlAHfnZ8+8kVi/7IIJGjmiA+pb2IMH7rkpMbAswILlm/jKt5/RCOjSKSlB5YCXFqxlQ0UVAPn5edx+48yYI5Iz1bNHN/710+/nxqvOS2zbUXWQL3/7Geb8aRG1tRp1QjoPJahObs/+Izz22zcT67PfPU0P5nZw+fl5fOLmy/inj12X6IVZX1/Pr59fwn//99+wcv22mCMUSQ8lqE6srq6eH/zqZY6F04gPGdiHm99zfsxRSbpcceEEvv3lWzhn7NDEtq079vG1H/yBbz06n227D8QYncjZU4LqxB7/wwJWrAs+TRtwz+3vpntB13iDkrQaPrgf//vem7jjA5cm5pMCeGv5Jj7/4Bz+/ecvsmX73hgjFDlzekqzk3rmxXeY9/KyxPp/u/5CSscPizEiyZQuXbpw07uncdn08Tz+hwW8tmQ9EHRHf3PpBt5cuoHpk0Zx3aWTuWjqGPIjiUwkm1kuPEcxY8YMX7x4cesFOwF351d/XMgzf34nse2iqcV85ZPXY2Yt7CmdxbrNu5j7/OLEYwVRfQt7cNWMiVw6fRwlYwbrd0JiYWZL3H1Gq+WUoDqP3fsO8+MnX2X5usaZWKeWDOdf7rqBgm5q2ss1G7ZW8cyLb7Ng+SZS/ZUP7NeLi6YWM23SKKZMGEavHgXtHqPkJiWoiM6eoLbtPsALr6/m+TdWNelmfP7kUXzpE+/Vfacct2vvIV56ay1/eWst+w+lnqHXgHGjipgwejDjRw9i3MgiRg3tr+ZAyYisSFBmNgv4HpAH/NTdv5n0egHwS+BCYC/wIXffHL52P3AnUAfc6+7z23LMVDpTgqqtrWPn3kNs332Q8i27WVZWSfnW3U3KGPCBa6fz4Rtn0qWL+sFIoK6unqVrK3hz2UYWrdjMkWMtj0CRl9eFIQMKGTKoD8OK+jJ4QB/6FfagT2EP+hX2oG9hD3p270bX/Dw1FcppiT1BmVkesA54D1AJLAJuc/fVkTKfBc5z90+b2a3A37v7h8ysFHgSmAkMB/4MNEz72uIxUznTBPW7vyxl/eZdOCTGPGu4XO5O9NI53mKZ6OsNZU4pjzfZt+F7Xb1z9Fg1R45Vc+x4dcrmmgbjRxXxjzdfzqRxQ1soJbmurq6e1Rt2sGxtBcvXbWNjRVWLv1ctMaCgoCvdu3Wle0E+3brmk5+fR14Xo0uXLuF3o4t1IS8v+G7GaSW15oqmOoZSZfu48erzmHyGHa/amqAy2YtvJlDu7hvDgOYAs4FoMpkNfD1cfhr4gQW/cbOBOe5eDWwys/LweLThmGmzbvOuDjG1QRczLpwyhusum8yFpaP1aVZalZfXhXMnjuDciSMAOHKsmnWbd7Gxcg+bKqrYULEnMW9Yaxw4UV3DieoaaNsu0glcOn18xs+RyQQ1Aoh2I6oELm6ujLvXmtlBYGC4/a2kfUeEy60dEwAzuwu4C2D06NFn9Aay9d/8wH69GDG4PyOH9qN0/HCmlgynsFf3uMOSDqx3zwIuKB3NBaWNfysnqmvYFTYn79p7iD37j3Dg8HEOHj7GoSMnOHD4GMera6irq48xcunMMpmgUv1/T25FaK5Mc9tT3VBJ2TLh7o8Aj0DQxNd8mM276ZppXH7hBCwMp6FiYmaJWkp0G2Hg0RpMUDZpW7R88mtmpxwjL8/o2aOAwp4F9OpRQF6e7itJ5nUv6MqY4QMZM3xgi+Vqa+uorqkNalEnazl5spa6unrq3Zv9nurOQnO3G5rf3vb34mfcgCnNKRk9OOPnyGSCqgRGRdZHAtubKVNpZvlAX2BfK/u2dsy0iQ4hIyKp5efnkZ+fp27qknaZ/Ci+CCgxs7Fm1g24FZiXVGYecEe4fAvwkgcfl+YBt5pZgZmNBUqAhW08poiIdAIZq0GF95TuAeYTdAn/mbuvMrMHgMXuPg94FPivsBPEPoKEQ1huLkHnh1rgbnevA0h1zEy9BxERiY8e1BURkXbV1m7mutsuIiJZSQlKRESykhKUiIhkJSUoERHJSjnRScLMqoAtZ3GIQcCeNIXTUeka6BqArgHoGsDZX4Mx7l7UWqGcSFBny8wWt6XHSWema6BrALoGoGsA7XcN1MQnIiJZSQlKRESykhJU2zwSdwBZQNdA1wB0DUDXANrpGugelIiIZCXVoEREJCspQYmISFZSgmqBmc0yszIzKzez++KOJ5PM7GdmttvMVka2DTCzF81sffi9f7jdzOz74XVZbmYXxBd5epjZKDN72czWmNkqM/t8uD2XrkF3M1toZsvCa/Bv4faxZrYgvAZPhVPdEE6H81R4DRaYWXGc8aeTmeWZ2Ttm9sdwPaeugZltNrMVZrbUzBaH29r9b0EJqhlmlgf8ELgBKAVuM7PSeKPKqMeAWUnb7gP+4u4lwF/CdQiuSUn4dRfw43aKMZNqgX9298nAJcDd4c87l65BNXCNu08DpgOzzOwS4CHg4fAa7AfuDMvfCex39wnAw2G5zuLzwJrIei5eg3e7+/TI807t/7fg7vpK8QVcCsyPrN8P3B93XBl+z8XAysh6GTAsXB4GlIXL/wnclqpcZ/kCfg+8J1evAdATeBu4mGDEgPxwe+LvgmBetkvD5fywnMUdexre+0iCf8DXAH8ELAevwWZgUNK2dv9bUA2qeSOAish6Zbgtlwxx9x0A4ffB4fZOfW3CZprzgQXk2DUIm7aWAruBF4ENwAF3rw2LRN9n4hqErx8EBrZvxBnxXeDLQH24PpDcuwYOvGBmS8zsrnBbu/8tZGxG3U7AUmxTn/xAp702ZtYb+A3wBXc/ZJbqrQZFU2zr8NfAg5mrp5tZP+C3wORUxcLvne4amNmNwG53X2JmVzdsTlG0016D0OXuvt3MBgMvmtnaFspm7BqoBtW8SmBUZH0ksD2mWOKyy8yGAYTfd4fbO+W1MbOuBMnpCXd/JtycU9eggbsfAF4huB/Xz8waPsxG32fiGoSv9wX2tW+kaXc5cJOZbQbmEDTzfZfcuga4+/bw+26CDyozieFvQQmqeYuAkrD3TjfgVmBezDG1t3nAHeHyHQT3ZRq2fyzsvXMJcLCh6t9RWVBVehRY4+7fibyUS9egKKw5YWY9gOsIOgq8DNwSFku+Bg3X5hbgJQ9vQnRU7n6/u49092KCv/mX3P12cugamFkvMytsWAbeC6wkjr+FuG/GZfMX8D5gHUE7/P+IO54Mv9cngR1ADcEnojsJ2tL/AqwPvw8IyxpBD8cNwApgRtzxp+H9X0HQLLEcWBp+vS/HrsF5wDvhNVgJfDXcPg5YCJQDvwYKwu3dw/Xy8PVxcb+HNF+Pq4E/5to1CN/rsvBrVcP/vjj+FjTUkYiIZCU18YmISFZSghIRkaykBCUiIllJCUpERLKSEpSIiGQlJSjpFMzMzezbkfUvmdnX03Tsx8zsltZLnvV5PhiOpv5yBo79cTMbHln/aUuDH4flf5CG8/Yws1fDwZdbKjfHzErO9nzSuShBSWdRDdxsZoPiDiSqtX/MSe4EPuvu785ADB8HEgnK3T/p7qvTeZ5m/CPwjAdDKLXkxwTj34kkKEFJZ1ELPAL8U/ILyTUgMzsSfr86/HQ/18zWmdk3zex2C+ZEWmFm4yOHuc7MXgvL3Rjun2dm3zKzReE8OJ+KHPdlM/sVwYOLyfHcFh5/pZk9FG77KsHDwj8xs28llb/azP5qZr81s9Vm9hMz6xK+9mMzW2yR+ZvC7ZvN7Ktm9jpwGzADeMKC+X16mNkrZjYjLDvLzN62YB6ov6SIt8jMfhO+z0Vmdnm4/arweEstmDupMMXP5XbCEQfC9/GKmT1tZmvN7IlwBA+A18JrrPFBJUG/DNKZ/BBYbmb/9zT2mUYwIOo+YCPwU3efacGEhZ8DvhCWKwauAsYDL5vZBOBjBMO6XGRmBcAbZvZCWH4mMNXdN0VPFjazPQRcSDCv0Atm9gF3f8DMrgG+5O6LU8Q5k2Besi3A88DNwNMET/nvC2tJfzGz89x9ebjPCXe/IjzvJ6PHbsgLZlYE/D/gSnffZGYDUpz7ewRzIb1uZqMJppiYDHwJuNvd37BgkN0TSe+1G8HICpsjm88HphCM1fYGwdh3r7t7vZmVhz+PJSlikBykGpR0Gu5+CPglcO9p7LbI3Xe4ezXBUC0NCWYFQVJqMNfd6919PUEim0QwRtnHLJieYgHBUDAN91EWJien0EXAK+5e5cH0DE8AV7YhzoXuvjFsKnuSoLYF8A9m9jbBEEVTCJJYg6facNxLgL82xOruqQY6vQ74Qfg+5wF9wtrSG8B3zOxeoJ83TkfRYBBwIMX7qHT3eoLhpIojr+0m0gwpohqUdDbfJZho7+eRbbWEH8bCJqVukdeqI8v1kfV6mv59JI8J5gRjkH3O3edHX7BgmoajzcTX7PwdrTjl/GY2lqAWc5G77zezxwjGhmvQXAzJ8bQ23lkXgkn5jidt/6aZPUswZuFbZnadu0enZTieFA80vd51NL3G3cN9RADVoKSTCWsAc2mckhuC2UEvDJdnA13P4NAfNLMu4X2pcQSzhs4HPmPBNB2Y2UQLRn9uyQLgKjMbFDbL3Qa82obzz7RgZP0uwIeA14E+BEnooJkNIZh6uzmHgVT3iN4M4xkbvodUTXwvAPc0rJjZ9PD7eHdf4e4PAYsJapUJ7r4fyDOz5CTVnIkEg5OKAEpQ0jl9m6B5qcH/I/gnvJBgCvO21CySlREkkj8Bn3b3E8BPgdXA22a2kmDq6xZbJTyYhuB+gukblgFvu/vvW9on9CbwTYJRxjcBv3X3ZQRNe6uAnxE0uTXnMYIOGEstmEqjIZ4q4C7gGTNbRupmwXuBGWFHkNXAp8PtXwg7eiwjqPn8KcW+L9DYHNmsMMEe9w4+ZYmkl0YzF8lyYZPhl9z9xrhjOV1mdj7wRXf/aCvl/gk45O6Ptk9k0hGoBiUiGePu7xD0emztebADwC/aISTpQFSDEhGRrKQalIiIZCUlKBERyUpKUCIikpWUoEREJCspQYmISFb6/wHgDinAjIIHfAAAAABJRU5ErkJggg==\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "pmf_n = suite.Marginal(1)\n", "thinkplot.Pdf(pmf_n)\n", "thinkplot.decorate(xlabel='Number of particles (n)',\n", " ylabel='PMF',\n", " title='Posterior marginal distribution')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Hierarchical version, as in the book" ] }, { "cell_type": "code", "execution_count": 30, "metadata": {}, "outputs": [], "source": [ "class Detector(Suite):\n", " \"\"\"Represents hypotheses about n.\"\"\"\n", "\n", " def __init__(self, r, f, high=500):\n", " \"\"\"Initializes the suite.\n", "\n", " r: known emission rate, r\n", " f: fraction of particles registered\n", " high: maximum number of particles, n\n", " \"\"\"\n", " pmf = MakePoissonPmf(r, high)\n", " super().__init__(pmf)\n", " self.r = r\n", " self.f = f\n", "\n", " def Likelihood(self, data, hypo):\n", " \"\"\"Likelihood of the data given the hypothesis.\n", "\n", " data: number of particles counted\n", " hypo: number of particles hitting the counter, n\n", " \"\"\"\n", " k = data\n", " n = hypo\n", "\n", " return EvalBinomialPmf(k, n, self.f)" ] }, { "cell_type": "code", "execution_count": 31, "metadata": {}, "outputs": [], "source": [ "r = 160\n", "k = 15\n", "f = 0.1\n", "\n", "suite = Detector(r, f);" ] }, { "cell_type": "code", "execution_count": 32, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "0.09921753162215896" ] }, "execution_count": 32, "metadata": {}, "output_type": "execute_result" } ], "source": [ "suite.Update(15)" ] }, { "cell_type": "code", "execution_count": 33, "metadata": {}, "outputs": [], "source": [ "class Emitter(Suite):\n", " \"\"\"Represents hypotheses about r.\"\"\"\n", "\n", " def Likelihood(self, data, hypo):\n", " \"\"\"Likelihood of the data given the hypothesis.\n", "\n", " data: number of counted per unit time\n", " hypo: Detector object\n", " \"\"\"\n", " return hypo.Update(data)" ] }, { "cell_type": "code", "execution_count": 34, "metadata": {}, "outputs": [], "source": [ "rs = np.linspace(0, 300, 51);" ] }, { "cell_type": "code", "execution_count": 35, "metadata": {}, "outputs": [], "source": [ "detectors = [Detector(r, f=0.1) for r in rs[1:]]\n", "suite = Emitter(detectors);" ] }, { "cell_type": "code", "execution_count": 36, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "0.03327817252458951" ] }, "execution_count": 36, "metadata": {}, "output_type": "execute_result" } ], "source": [ "suite.Update(15)" ] }, { "cell_type": "code", "execution_count": 37, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "pmf_r = Pmf()\n", "for detector, p in suite.Items():\n", " pmf_r[detector.r] = p\n", " \n", "thinkplot.Pdf(pmf_r)" ] }, { "cell_type": "code", "execution_count": 38, "metadata": {}, "outputs": [], "source": [ "mix = MakeMixture(suite);" ] }, { "cell_type": "code", "execution_count": 39, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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