{ "metadata": { "name": "3.Throwing Marbles into Jars.ipynb" }, "nbformat": 3, "nbformat_minor": 0, "worksheets": [ { "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Poisson Distribution\n", "## *If I throw 4000 marbles into 100 jars, how many jars will have exactly 42 marbles?*\n", "---" ] }, { "cell_type": "code", "collapsed": false, "input": [ "import math\n", "import random\n", "\n", "num_marbles = 4000\n", "num_jars = 100\n", "\n", "jars = []\n", "\n", "## empty out all the jars\n", "\n", "for j in xrange(num_jars):\n", " jars.append(0)\n", " \n", "## fill the jars randomly\n", "for i in xrange(num_marbles):\n", " jar = random.randint(0,num_jars-1) ## make sure in the range [0..num_jars-1]\n", " jars[jar] += 1\n", " \n", "## count how many jars have 42 marbles\n", "target_val = 42\n", "target_count = 0.\n", "\n", "for j in xrange(num_jars):\n", " if (jars[j] == target_val):\n", " print \"Jar %d has %d marbles\" % (j, target_val)\n", " target_count += 1\n", "\n", "sample_mean = (sum(jars)+0.) / num_jars\n", "print \"There were %d jars with %d marbles for a probability of %.05f\" % (target_count, target_val, target_count / num_jars)\n", "print \"The mean number of marbles per jar was %.02f\" % (sample_mean)" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Jar 23 has 42 marbles\n", "Jar 37 has 42 marbles\n", "Jar 43 has 42 marbles\n", "Jar 48 has 42 marbles\n", "Jar 74 has 42 marbles\n", "Jar 80 has 42 marbles\n", "There were 6 jars with 42 marbles for a probability of 0.06000\n", "The mean number of marbles per jar was 40.00\n" ] } ], "prompt_number": 2 }, { "cell_type": "code", "collapsed": false, "input": [ "## Plot the number of marbles in each jar\n", "import matplotlib.pyplot as plt\n", "plt.figure(figsize=(15,4), dpi=100)\n", "plt.xlabel(\"Jar Index\")\n", "plt.ylabel(\"Marbles in Jar\")\n", "plt.bar(range(num_jars), jars)\n", "plt.show()\n" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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"text": [ "" ] } ], "prompt_number": 3 }, { "cell_type": "code", "collapsed": false, "input": [ "## Plot the distribution on the number of marbles in each jar\n", "plt.figure()\n", "plt.xlabel(\"Number of Marbles\")\n", "plt.ylabel(\"Number of Jars with that many marbles\")\n", "plt.hist(jars, bins=range(max(jars)+3))\n", "plt.show()\n" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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"text": [ "" ] } ], "prompt_number": 4 }, { "cell_type": "code", "collapsed": false, "input": [ "## Plot the density function, notice bars sum to exactly 1 but otherwise just scales display\n", "plt.figure()\n", "plt.xlabel(\"Number of Marbles\")\n", "plt.ylabel(\"Probability of Jars with that many marbles\")\n", "plt.hist(jars, bins=range(max(jars)+3), normed=True)\n", "plt.show()\n" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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YIzYiIjIDGnsUdnZ2+Pnnn/Hss8/id7/7HTw8PNCnTx9jxEZERGZA42B2WVkZXF1dAQBf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\nBISEhOB//ud/AAAfffQR0tP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"text": [ "" ] } ], "prompt_number": 5 }, { "cell_type": "code", "collapsed": false, "input": [ "## Compute mean & stdev of distribution\n", "mean = (sum(jars) + 0.) / num_jars\n", "sumdiff = 0.0\n", "for count in jars:\n", " diff = (count - mean) ** 2\n", " sumdiff += diff\n", "\n", "sumdiff /= num_jars\n", "stdev = math.sqrt(sumdiff)\n", "\n", "print \"The mean values was %0.2f +/- %0.2f\" % (mean, stdev)\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "The mean values was 40.00 +/- 5.61\n" ] } ], "prompt_number": 6 }, { "cell_type": "heading", "level": 4, "metadata": {}, "source": [ "What happens to the mean or standard deviation if we change the number of jars or marbles?" ] }, { "cell_type": "code", "collapsed": false, "input": [ "## Overlap the normal distribution with this mean and stdev\n", "gaus_prob_dist = []\n", "pi = 3.1415926\n", "\n", "for k in xrange(int(max(jars)*1.2)+3):\n", " var = float(stdev)**2\n", " num = math.exp(-(float(k)-float(mean))**2/(2*var))\n", " denom = (2*pi*var)**.5\n", " gaus_prob = num/denom\n", " gaus_prob_dist.append(gaus_prob)\n", "\n", "\n", "\n", "## overlay the analytic distributions over the data\n", "plt.figure()\n", "plt.xlabel(\"Number of Marbles\")\n", "plt.ylabel(\"Probability of Jars with that many marbles\")\n", "plt.hist(jars, bins=range(int(max(jars)*1.2+3)), normed=True, label=\"Observed\")\n", "plt.plot(gaus_prob_dist, color='green', linewidth=4, linestyle='dashed', label=\"Normal Fit\")\n", "plt.legend(loc=\"upper left\")\n", "plt.show()\n" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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q2WefVR999JFSSqnNmzcrf39/tWfPHpWZmamuX7+ufvnlF6WUUhcuXFAajUZlZWXpxHLn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\n/ux/ZT9hL4bh6eRpjPBFKXIi7gQJdxL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d16VhGJ73ia91QRBoHEfVda3jOOR5ntZ11b7v\n6rrueR+ZpunXufG/8M04AMCJqycAgBOhAAA4EQoAgBOhAAA4EQoAgBOhAAA4EQoAgBOhAAA4vQHj\neCV32As0bwAAAABJRU5ErkJggg==\n", "text": [ "" ] } ], "prompt_number": 7 }, { "cell_type": "code", "collapsed": false, "input": [ "## Mean value is intuitively num_marbles / num_jars\n", "## but what is the expected stdev?\n", "\n", "expected_mean = num_marbles / num_jars\n", "print \"The range in values was %0.2f +/- %0.2f\" % (mean, stdev)\n", "print \"The expected frequency is %.02f +/- ???\" % (expected_mean)" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "The range in values was 40.00 +/- 5.61\n", "The expected frequency is 40.00 +/- ???\n" ] } ], "prompt_number": 8 }, { "cell_type": "heading", "level": 4, "metadata": {}, "source": [ "Any guesses for stdev???" ] }, { "cell_type": "code", "collapsed": false, "input": [ "## Lets simulate many experiments with different mean values to see what happens to the stdev\n", "import sys\n", "num_trials = 100\n", "max_sim_mean = 1000\n", "\n", "sim_target_means = []\n", "sim_means = []\n", "sim_stdevs = []\n", "\n", "for t in xrange(num_trials):\n", " target_mean = random.randint(0,max_sim_mean)\n", " num_marbles = num_jars * target_mean\n", " \n", " sim_jars = []\n", "\n", " ## empty out all the jars\n", "\n", " for j in xrange(num_jars):\n", " sim_jars.append(0)\n", " \n", " ## fill the jars randomly\n", " for i in xrange(num_marbles):\n", " jar = random.randint(1,num_jars) - 1 ## make sure in the range 0..num_jars-1\n", " sim_jars[jar] += 1\n", " \n", " ## Compute mean & stdev of distribution\n", " sim_mean = (sum(sim_jars) + 0.) / num_jars\n", " sumdiff = 0.0\n", " for count in sim_jars:\n", " diff = (count - sim_mean) ** 2\n", " sumdiff += diff\n", "\n", " sumdiff /= num_jars\n", " sim_stdev = math.sqrt(sumdiff)\n", "\n", " sim_target_means.append(target_mean)\n", " sim_means.append(sim_mean)\n", " sim_stdevs.append(sim_stdev)\n", " \n", " if (t % 10 == 0):\n", " print \"Completed %d trials\" % (t)\n", " \n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Completed 0 trials\n", "Completed 10 trials" ] }, { "output_type": "stream", "stream": "stdout", "text": [ "\n", "Completed 20 trials" ] }, { "output_type": "stream", "stream": "stdout", "text": [ "\n", "Completed 30 trials" ] }, { "output_type": "stream", "stream": "stdout", "text": [ "\n", "Completed 40 trials" ] }, { "output_type": "stream", "stream": "stdout", "text": [ "\n", "Completed 50 trials" ] }, { "output_type": "stream", "stream": "stdout", "text": [ "\n", "Completed 60 trials" ] }, { "output_type": "stream", "stream": "stdout", "text": [ "\n", "Completed 70 trials" ] }, { "output_type": "stream", "stream": "stdout", "text": [ "\n", "Completed 80 trials" ] }, { "output_type": "stream", "stream": "stdout", "text": [ "\n", "Completed 90 trials" ] }, { "output_type": "stream", "stream": "stdout", "text": [ "\n" ] } ], "prompt_number": 9 }, { "cell_type": "code", "collapsed": false, "input": [ "## first make sure the target and simulated means agree\n", "plt.figure()\n", "plt.xlabel(\"Target means for simulations\")\n", "plt.ylabel(\"Simulated means\")\n", "plt.scatter(sim_target_means, sim_means)\n", "plt.show()\n" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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v9ebSpT9o2rSpxomFueVbVMLCwihRogRJSUm89dZbWFlZMXjw4MLIJoSwMJMnv8fFix1I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\n6Nq1K/v378fb25uTJ0+yZ88eunfvjp+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"text": [ "" ] } ], "prompt_number": 10 }, { "cell_type": "code", "collapsed": false, "input": [ "## Now plot the relationship between the mean and stdev of the different simulations\n", "plt.figure()\n", "plt.xlabel(\"Simulated means\")\n", "plt.ylabel(\"Simulated standard deviations\")\n", "plt.scatter(sim_means, sim_stdevs)\n", "plt.show()\n" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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nTiPi4/tjMpVCrZ7OkiVfU6lSRfr2HUp0dBS1a9fj55+XPlcroT4PbLajXEGS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\nQ4YMYcuWLXh5eWUuz6HT6ejfvz9hYWH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"text": [ "" ] } ], "prompt_number": 11 }, { "cell_type": "code", "collapsed": false, "input": [ "## Now plot the relationship between the mean and stdev of the different simulations\n", "plt.figure()\n", "plt.xlabel(\"Simulated means\")\n", "plt.ylabel(\"Simulated standard deviations\")\n", "plt.scatter(sim_means, sim_stdevs, label=\"observed\")\n", "sx = []\n", "sy = []\n", "for i in xrange(max_sim_mean):\n", " sx.append(i)\n", " sy.append(math.sqrt(i))\n", "plt.plot(sx, sy, color='red', linewidth=4, label=\"sqrt\")\n", "plt.legend(loc=\"upper left\")\n", "plt.show()\n" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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z6FEDEhMLMG2aDzt2bKZx48bY2dlhMsUDiYA9YEIkFltbWzQaDX5+k5gy5U0M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\nx48fx927dyGVSqGjowNTU1MA9YeEBw4cwJMnT3Do0CH4+/v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"text": [ "" ] } ], "prompt_number": 12 }, { "cell_type": "markdown", "metadata": {}, "source": [ "**Eureka! The data look normal and the stdev is consistently the sqrt of the mean!**\n", "\n", "This is the hallmark of the Poisson distribution\n", "\n", "$$\n", "prob(\\text{jar has k marbles given the mean amount}) = \\frac{(mean^{k})}{k!} e^{-mean}\n", "$$" ] }, { "cell_type": "code", "collapsed": false, "input": [ "prob_42 = math.exp(-sample_mean) * (sample_mean ** 42) / math.factorial(42) \n", "print \"The probability of having 42 marbles when the mean is %.02f is %.05f\" % (sample_mean, prob_42)\n", "print \"There were %d jars with %d marbles for a probability of %.05f\" % (target_count, target_val, target_count / num_jars)\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "The probability of having 42 marbles when the mean is 40.00 is 0.05849\n", "There were 6 jars with 42 marbles for a probability of 0.06000\n" ] } ], "prompt_number": 13 }, { "cell_type": "code", "collapsed": false, "input": [ "## Compute the distribution analytically\n", "pois_prob_dist = []\n", "\n", "## This will crash for large sample means!\n", "for k in xrange(int(max(jars)*1.2)+3):\n", " prob_pois = math.exp(-sample_mean) * (sample_mean ** k) / math.factorial(k) \n", " pois_prob_dist.append(prob_pois)\n", " \n", "## Plot the poisson dist.\n", "plt.figure()\n", "plt.xlabel(\"Number of Marbles\")\n", "plt.ylabel(\"Probability of Jars with that many marbles\")\n", "plt.plot(pois_prob_dist, color='purple', linewidth=4, linestyle='solid')\n", "plt.show()\n" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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2Rc+ePQE0jFHcunVLPhESogCaLbTrQuMTjZoligvZYMQMZ+os6ZwkJorG1dgt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\n0XoJ8lrSf0vHifdOoLai+SFHZsPNMGn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"text": [ "" ] } ], "prompt_number": 14 }, { "cell_type": "code", "collapsed": false, "input": [ "## overlay the analytic distributions over the data\n", "plt.figure()\n", "plt.xlabel(\"Number of Marbles\")\n", "plt.ylabel(\"Probability of Jars with that many marbles\")\n", "plt.hist(jars, bins=range(int(max(jars)*1.2)+3), normed=True, label=\"observed\")\n", "plt.plot(pois_prob_dist, color='purple', linewidth=4, linestyle='solid', label=\"Poisson Fit\")\n", "plt.plot(gaus_prob_dist, color='green', linewidth=4, linestyle='dashed', label=\"Normal Fit\")\n", "plt.legend(loc=\"upper left\")\n", "plt.show()\n" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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6nKJi0Fmi8PX1/feXp2B79uwpfnQ6JolC6Fu5ShSoCL4UzI6oHXzW4zNMjLRe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\nc3NbNK2kLLd1t/npyE8cevsQm4I28V7P99j2v9v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"text": [ "" ] } ], "prompt_number": 15 }, { "cell_type": "markdown", "metadata": {}, "source": [ "## *What happens for very small sample means?*\n" ] }, { "cell_type": "code", "collapsed": false, "input": [], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 15 } ], "metadata": {} } ] }