{ "cells": [ { "cell_type": "code", "execution_count": 1, "metadata": { "collapsed": true }, "outputs": [], "source": [ "import numpy as np\n", "import matplotlib.pyplot as plt\n", "import pandas as pd\n", "import seaborn as sns\n", "plt.style.use('ggplot')\n", "import matplotlib.figure as figure\n", "%matplotlib inline" ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "collapsed": false }, "outputs": [], "source": [ "from fractions import Fraction\n", "normal_uniform = {2: Fraction(1, 36), 3: Fraction(2,36), 4: Fraction(3, 36),\n", " 5: Fraction(4, 36), 6: Fraction(5, 36), 7: Fraction(6, 36),\n", " 8: Fraction(5, 36), 9: Fraction(4, 36), 10: Fraction(3, 36),\n", " 11: Fraction(2, 36), 12: Fraction(1, 36)}\n", "# biased= {2: Fraction(0, 32), 3: Fraction(3,32), 4: Fraction(3, 32),\n", "# 5: Fraction(4, 32), 6: Fraction(4, 32), 7: Fraction(6, 32),\n", "# 8: Fraction(3, 32), 9: Fraction(2, 32), 10: Fraction(3, 32),\n", "# 11: Fraction(4, 32), 12: Fraction(0, 32)}\n", "biased= {2: Fraction(1, 26), 3: Fraction(2,26), 4: Fraction(3, 26),\n", " 5: Fraction(4, 26), 6: Fraction(5, 26), 7: Fraction(6, 26),\n", " 8: Fraction(1, 26), 9: Fraction(1, 26), 10: Fraction(1, 26),\n", " 11: Fraction(1, 26), 12: Fraction(1, 26)}\n", "def update(x, priors, distributions):\n", " weighted = []\n", " for d, p in zip(distributions, priors):\n", " weighted.append(d[x] * p)\n", " total = sum(weighted)\n", " return list(map(lambda e: e / total, weighted))" ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "[0.9992614896212075, 0.0007385103787924079]" ] }, "execution_count": 3, "metadata": {}, "output_type": "execute_result" } ], "source": [ "priors = [.5, .5]\n", "priors = update(3, priors, [normal_uniform, biased])\n", "priors = update(3, priors, [normal_uniform, biased])\n", "priors = update(4, priors, [normal_uniform, biased])\n", "priors = update(4, priors, [normal_uniform, biased])\n", "priors = update(4, priors, [normal_uniform, biased])\n", "priors = update(5, priors, [normal_uniform, biased])\n", "priors = update(5, priors, [normal_uniform, biased])\n", "priors = update(5, priors, [normal_uniform, biased])\n", "priors = update(5, priors, [normal_uniform, biased])\n", "priors = update(6, priors, [normal_uniform, biased])\n", "priors = update(6, priors, [normal_uniform, biased])\n", "priors = update(6, priors, [normal_uniform, biased])\n", "priors = update(6, priors, [normal_uniform, biased])\n", "priors = update(6, priors, [normal_uniform, biased])\n", "priors = update(7, priors, [normal_uniform, biased])\n", "priors = update(7, priors, [normal_uniform, biased])\n", "priors = update(7, priors, [normal_uniform, biased])\n", "priors = update(7, priors, [normal_uniform, biased])\n", "priors = update(7, priors, [normal_uniform, biased])\n", "priors = update(7, priors, [normal_uniform, biased])\n", "priors = update(8, priors, [normal_uniform, biased])\n", "priors = update(8, priors, [normal_uniform, biased])\n", "priors = update(8, priors, [normal_uniform, biased])\n", "priors = update(8, priors, [normal_uniform, biased])\n", "priors = update(8, priors, [normal_uniform, biased])\n", "priors = update(9, priors, [normal_uniform, biased])\n", "priors = update(9, priors, [normal_uniform, biased])\n", "priors = update(9, priors, [normal_uniform, biased])\n", "priors = update(9, priors, [normal_uniform, biased])\n", "priors = update(10, priors, [normal_uniform, biased])\n", "priors = update(10, priors, [normal_uniform, biased])\n", "priors = update(10, priors, [normal_uniform, biased])\n", "priors = update(11, priors, [normal_uniform, biased])\n", "priors = update(11, priors, [normal_uniform, biased])\n", "priors" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The idea here is that I manually loaded a normally uniform set of dice into this model, did updates every time, found that I began to get a posterior belief that this was a normal_uniform distribution. I did this 4 times, and I ended up with a 70+% probability that this was normal uniform.\n", "\n", "Now, I could get a different model that measured the switch point, assuming biased for a while. Or, I could build a model that was some sort of mix from bias to normal. I would need a record of a lot of games. Over 6494 games, the dice are very normally distributed. I mean, perfectly. So, if there is an introduction of bias, it's got to be because over that many games, the bias would have been normally distributed as well." ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "collapsed": true }, "outputs": [], "source": [ "import random\n", "def weighted_pick(d):\n", " r = random.uniform(0, sum(d.itervalues()))\n", " s = 0.0\n", " for k, w in d.iteritems():\n", " s += w\n", " if r < s: return k\n", " return k" ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "[0.9999987063264542, 1.2936735458075107e-06]" ] }, "execution_count": 5, "metadata": {}, "output_type": "execute_result" } ], "source": [ "priors = [.5, .5]\n", "for e in xrange(100):\n", " x = weighted_pick(normal_uniform)\n", " while x < 3 or x > 11:\n", " x = weighted_pick(normal_uniform)\n", " priors = update(x, priors, [normal_uniform, biased])\n", "priors" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Since I'm not seeing stable results, I'm going to have to think about this for a while. Updates on the data, every time I see a new die rolled seems to create a bias towards normal_uniform or biased, rather than learning what the real distribution is." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "I reset biased to be more different than random uniform, and got stable results both directions. I think what was happening was something that looks more like a random walk when the two distributions are hard to distinguish.\n", "\n", "What's next is a plot on these values." ] }, { "cell_type": "code", "execution_count": 6, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "
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NormalBiasedSample
00.4193550.5806450
10.3427990.6572011
20.6010940.3989062
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" ], "text/plain": [ " Normal Biased Sample\n", "0 0.419355 0.580645 0\n", "1 0.342799 0.657201 1\n", "2 0.601094 0.398906 2\n", "3 0.521139 0.478861 3\n", "4 0.440085 0.559915 4" ] }, "execution_count": 6, "metadata": {}, "output_type": "execute_result" } ], "source": [ "prior = [.5, .5]\n", "n = 100\n", "posteriors = []\n", "for e in xrange(n):\n", " x = weighted_pick(biased)\n", " posterior = update(x, prior, [normal_uniform, biased])\n", " posteriors.append(posterior)\n", " prior = posterior\n", "df = pd.DataFrame(posteriors, columns=['Normal', 'Biased'])\n", "df['Sample'] = list(xrange(n))\n", "df.head()" ] }, { "cell_type": "code", "execution_count": 7, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 7, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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oD2xsK5QnM1+7Xs27SmV0kRHnMkvSrBjSs5SfOQ37vz02lBuNsRetXgfbRkdf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\nTkSuQmCC\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "g = sns.lmplot(x='Sample', y='Biased', data=df)\n", "g.set(ylim=(0,1.05))\n", "g.set(xlim=(0,n))" ] } ], "metadata": { "kernelspec": { "display_name": "Python 2", "language": "python", "name": "python2" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 2 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython2", "version": "2.7.12" } }, "nbformat": 4, "nbformat_minor": 1 }