{ "cells": [ { "cell_type": "code", "execution_count": 2, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/jpeg": "/9j/4AAQSkZJRgABAQEBLAEsAAD/7S4GUGhvdG9zaG9wIDMuMAA4QklNBCUAAAAAABAAAAAAAAAA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\nphy+Op7fwL/jxx5Kfzf+uLH2p/xfT/HH/9k=\n", "text/plain": [ "<IPython.core.display.Image object>" ] }, "execution_count": 2, "metadata": {}, "output_type": "execute_result" } ], "source": [ "from IPython.display import Image \n", "Image('../../../python_for_probability_statistics_and_machine_learning.jpg')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "[Python for Probability, Statistics, and Machine Learning](https://www.springer.com/fr/book/9783319307152)" ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Populating the interactive namespace from numpy and matplotlib\n" ] } ], "source": [ "from __future__ import division\n", "%pylab inline" ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "collapsed": true }, "outputs": [], "source": [ "from scipy import stats\n", "import sympy as S" ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "collapsed": false }, "outputs": [], "source": [ "d=stats.bernoulli(.1).rvs((10,5000)).mean(0)\n", "d=d[np.logical_not(np.isclose(d,1))]\n", "# print mean(d),var(d)" ] }, { "cell_type": "code", "execution_count": 6, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "0.124488095238 0.0186228105159\n" ] } ], "source": [ "print mean(d/(1-d)),var(d/(1-d))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "$$ \\frac{p}{n(1-p)^3} $$" ] }, { "cell_type": "code", "execution_count": 7, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "0.4" ] }, "execution_count": 7, "metadata": {}, "output_type": "execute_result" } ], "source": [ "ev = lambda p:p/10/(1-p)**3\n", "ev(.5)" ] }, { "cell_type": "code", "execution_count": 8, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "0.00729000000000000" ] }, "execution_count": 8, "metadata": {}, "output_type": "execute_result" } ], "source": [ "S.var('n,p',positive=True)\n", "(p/n*(1-p)**3).subs([(p,0.1),(n,10)])" ] }, { "cell_type": "code", "execution_count": 9, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAAYIAAAEACAYAAAC+gnFaAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nA7Qpx9K+RdOrAAAAAElFTkSuQmCC\n", "text/plain": [ "<matplotlib.figure.Figure at 0x1d7bfdd8>" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "hist(d/(1-d),30,align='mid');" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## sympy derivation" ] }, { "cell_type": "code", "execution_count": 10, "metadata": { "collapsed": true }, "outputs": [], "source": [ "S.init_printing(use_latex=True)" ] }, { "cell_type": "code", "execution_count": 11, "metadata": { "collapsed": false }, "outputs": [], "source": [ "x,p=S.symbols('x,p',real=True)\n", "g = x/(1-x)" ] }, { "cell_type": "code", "execution_count": 12, "metadata": { "collapsed": false }, "outputs": [], "source": [ "g.series(x=x,x0=p,n=3)\n", "gs=g.series(x=x,x0=p,n=3).removeO().subs(x,x-p).subs(x,x/10)" ] }, { "cell_type": "code", "execution_count": 13, "metadata": { "collapsed": false }, "outputs": [], "source": [ "from sympy.stats import E, Binomial\n", "X = Binomial('X',10,p)" ] }, { "cell_type": "code", "execution_count": 14, "metadata": { "collapsed": false, "scrolled": true }, "outputs": [ { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAAJwAAAArCAYAAACNd+GAAAAABHNCSVQICAgIfAhkiAAABRBJREFU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\ngg==\n", "text/latex": [ "$$- \\frac{p \\left(10 p^{2} - p + 1\\right)}{10 p^{3} - 30 p^{2} + 30 p - 10}$$" ], "text/plain": [ " ⎛ 2 ⎞ \n", " -p⋅⎝10⋅p - p + 1⎠ \n", "─────────────────────────\n", " 3 2 \n", "10⋅p - 30⋅p + 30⋅p - 10" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAAVUAAAArCAYAAADIUxsrAAAABHNCSVQICAgIfAhkiAAACDtJREFU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\nGj4AAAAASUVORK5CYII=\n", "text/latex": [ "$$- \\frac{p \\left(1006 p^{2} - 686 p + 121\\right)}{1000 p^{5} - 5000 p^{4} + 10000 p^{3} - 10000 p^{2} + 5000 p - 1000}$$" ], "text/plain": [ " ⎛ 2 ⎞ \n", " -p⋅⎝1006⋅p - 686⋅p + 121⎠ \n", "───────────────────────────────────────────────────────\n", " 5 4 3 2 \n", "1000⋅p - 5000⋅p + 10000⋅p - 10000⋅p + 5000⋅p - 1000" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "m =S.simplify(E(gs.subs(x,X)))\n", "display(m)\n", "v=S.simplify(E(gs.subs(x,X)**2)-m**2)\n", "display(v)" ] }, { "cell_type": "code", "execution_count": 15, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "0.0137174211248285 0.0105776558451456\n" ] } ], "source": [ "print m.subs(p,.1),v.subs(p,.1)" ] }, { "cell_type": "code", "execution_count": 16, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "0.124488095238 0.0186228105159\n" ] } ], "source": [ "print mean(d/(1-d)),var(d/(1-d))" ] }, { "cell_type": "code", "execution_count": 17, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "0.4*x + 8.0*(x/10 - 1.0)**2 - 3.0\n" ] } ], "source": [ "print (gs.subs(p,0.5))" ] }, { "cell_type": "code", "execution_count": 18, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAAXwAAAETCAYAAAA1Rb1FAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n", "text/plain": [ "<matplotlib.figure.Figure at 0x1d6959b0>" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "p1=S.plot(gs.subs(p,.5),(x,0,10),show=False,ylim=(0,5),line_color='k')\n", "p2,=S.plot(g.subs(x,x/10),(x,0,10),ylim=(0,5),show=False)\n", "p1.append(p2)\n", "p1.show()" ] }, { "cell_type": "code", "execution_count": 19, "metadata": { "collapsed": false }, "outputs": [], "source": [ "def gen_sample(p=0.1,nsamp=5000):\n", " d=stats.bernoulli(p).rvs((10,nsamp)).mean(axis=0)\n", " d=d[np.logical_not(np.isclose(d,1))]\n", " return mean(d),var(d)" ] }, { "cell_type": "code", "execution_count": 20, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAAMcAAAAWCAYAAAB0Z4hMAAAABHNCSVQICAgIfAhkiAAABfBJREFU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\n", "text/latex": [ "$$\\left ( 0.1004, \\quad 0.00904384\\right )$$" ], "text/plain": [ "(0.1004, 0.00904384)" ] }, "execution_count": 20, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# S.init_printing(use_latex=False)\n", "gen_sample(.1)" ] }, { "cell_type": "code", "execution_count": 21, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "1.20000000000000 0.472000000000000\n" ] } ], "source": [ "# S.init_printing(use_latex=True)\n", "print m.subs(p,0.5),v.subs(p,0.5)" ] }, { "cell_type": "code", "execution_count": 22, "metadata": { "collapsed": true }, "outputs": [], "source": [ "def model(n=3):\n", " gs=g.series(x=x,x0=p,n=n).removeO().subs(x,x-p).subs(x,x/10)\n", " m =S.simplify(E(gs.subs(x,X)))\n", " v=S.simplify(E(gs.subs(x,X)**2)-m**2)\n", " return m,v" ] }, { "cell_type": "code", "execution_count": 23, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "0.0137174211248285 0.0105776558451456\n" ] } ], "source": [ "m,v = model(3)\n", "print m.subs(p,0.1),v.subs(p,0.1)" ] }, { "cell_type": "code", "execution_count": 24, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/latex": [ "$$\\left(- p + x\\right) \\left(\\frac{p}{p^{2} - 2 p + 1} + \\frac{1}{- p + 1}\\right) + \\left(- p + x\\right)^{2} \\left(\\frac{p}{- p^{3} + 3 p^{2} - 3 p + 1} + \\frac{1}{p^{2} - 2 p + 1}\\right) + \\frac{p}{- p + 1} + \\mathcal{O}\\left(\\left(- p + x\\right)^{3}; x\\rightarrowp\\right)$$" ], "text/plain": [ " ⎛ p 1 ⎞ 2 ⎛ p 1 \n", "(-p + x)⋅⎜──────────── + ──────⎟ + (-p + x) ⋅⎜───────────────────── + ────────\n", " ⎜ 2 -p + 1⎟ ⎜ 3 2 2 \n", " ⎝p - 2⋅p + 1 ⎠ ⎝- p + 3⋅p - 3⋅p + 1 p - 2⋅p\n", "\n", " ⎞ p ⎛ 3 ⎞\n", "────⎟ + ────── + O⎝(-p + x) ; x → p⎠\n", " ⎟ -p + 1 \n", " + 1⎠ " ] }, "execution_count": 24, "metadata": {}, "output_type": "execute_result" } ], "source": [ "g.series(x,x0=p,n=3)" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [] } ], "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": "2.7.11" } }, "nbformat": 4, "nbformat_minor": 0 }