{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
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sfXpb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\nphy+Op7fwL/jxx5Kfzf+uLH2p/xfT/HH/9k=\n",
      "text/plain": [
       "<IPython.core.display.Image object>"
      ]
     },
     "execution_count": 1,
     "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": 2,
   "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": "markdown",
   "metadata": {},
   "source": [
    "As we have seen, outside of some  toy problems, it can be very difficult  or\n",
    "impossible to determine  the probability density distribution of the estimator\n",
    "of some quantity. The idea behind the bootstrap is that we can use computation\n",
    "to approximate  these functions which would otherwise be impossible to solve\n",
    "for analytically. \n",
    "\n",
    "Let's start with a simple example. Suppose we have the following set of random\n",
    "variables, $\\lbrace X_1, X_2, \\ldots, X_n \\rbrace$ where each $X_k \\sim F$. In\n",
    "other words the samples are all drawn from the same unknown distribution $F$.\n",
    "Having run the experiment, we thereby obtain the following sample set:"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$\n",
    "\\lbrace x_1, x_2, \\ldots, x_n \\rbrace\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " The sample mean is computed from this set as,"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$\n",
    "\\bar{x} = \\frac{1}{n}\\sum_{i=1}^n x_i\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " The next question is how close is the sample mean to the true mean,\n",
    "$\\theta = \\mathbb{E}_F(X)$. Note that the second central moment of $X$ is as\n",
    "follows:"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$\n",
    "\\mu_2(F) := \\mathbb{E}_F (X^2)  - (\\mathbb{E}_F (X))^2\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " The standard deviation of the sample mean, $\\bar{x}$, given $n$\n",
    "samples from an underlying distribution $F$, is the following:"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$\n",
    "\\sigma(F) = (\\mu_2(F)/n)^{1/2}\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " Unfortunately, because we have only the set of samples $\\lbrace x_1,\n",
    "x_2, \\ldots, x_n \\rbrace$ and not $F$ itself, we cannot compute this and\n",
    "instead must use the estimated standard error,"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$\n",
    "\\bar{\\sigma} = (\\bar{\\mu}_2/n)^{1/2}\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " where $\\bar{\\mu}_2 = \\sum (x_i -\\bar{x})^2/(n-1) $, which is the\n",
    "unbiased estimate of $\\mu_2(F)$. However, that is not the only way to proceed.\n",
    "Instead, we could replace $F$ by some estimate, $\\hat{F}$ obtained as a\n",
    "piecewise function of $\\lbrace x_1, x_2, \\ldots, x_n \\rbrace$ by placing\n",
    "probability mass $1/n$ on each $x_i$. With that in place, we can compute the\n",
    "estimated standard error as the following:"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$\n",
    "\\hat{\\sigma}_B  = (\\mu_2(\\hat{F})/n)^{1/2}\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " which is called the *bootstrap estimate* of the standard error.\n",
    "Unfortunately, the story effectively ends here. In even a slightly more general\n",
    "setting, there is no clean formula $\\sigma(F)$ within which $F$ can be swapped\n",
    "for $\\hat{F}$.\n",
    "\n",
    "This is where the computer saves the day. We actually do not need to know the\n",
    "formula $\\sigma(F)$ because we can compute it using a resampling method. The\n",
    "key idea is to sample with replacement from $\\lbrace x_1, x_2, \\ldots, x_n\n",
    "\\rbrace$. The new set of $n$ independent draws (with replacement) from this set\n",
    "is the *bootstrap sample*,"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$\n",
    "y^* = \\lbrace x_1^*, x_2^*, \\ldots, x_n^* \\rbrace\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The Monte Carlo algorithm proceeds by first by selecting a large number  of\n",
    "bootstrap samples, $\\lbrace y^*_k\\rbrace$, then computing the statistic on each\n",
    "of these samples, and then computing the sample standard deviation of the\n",
    "results in the usual way. Thus, the bootstrap estimate of the statistic\n",
    "$\\theta$ is the following,"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$\n",
    "\\hat{\\theta}^*_B = \\frac{1}{B} \\sum_k \\hat{\\theta}^*(k)\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " with the corresponding square of the sample standard deviation as"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$\n",
    "\\hat{\\sigma}_B^2 = \\frac{1}{B-1} \\sum_k (\\hat{\\theta}^*(k)-\\hat{\\theta}^*_B )^2\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " The process is much simpler than  the notation implies.\n",
    "Let's explore this with a simple example using Python. The next block\n",
    "of code sets up some samples from a $\\beta(3,2)$ distribution,"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "_=np.random.seed(123456)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "from scipy import stats\n",
    "rv = stats.beta(3,2)\n",
    "xsamples = rv.rvs(50)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " Because this is simulation data, we already know that the\n",
    "mean is $\\mu_1 = 3/5$ and the standard deviation of the sample mean\n",
    "for $n=50$ is $\\bar{\\sigma} =1/\\sqrt {1250}$, which we will verify\n",
    "this later."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
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iRmWrcePGdOvWzfp/ZefOnbRq1Yro6AxvBiiVLZ3oTyl1wy5fvszzzz+f7gkpEeGll14i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\nOXEAAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0xaf9a9b0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "%matplotlib inline\n",
    "\n",
    "from matplotlib.pylab import subplots\n",
    "fig,ax = subplots()\n",
    "fig.set_size_inches(8,4)\n",
    "_=ax.hist(xsamples,normed=True,color='gray')\n",
    "ax2 = ax.twinx()\n",
    "_=ax2.plot(np.linspace(0,1,100),rv.pdf(np.linspace(0,1,100)),lw=3,color='k')\n",
    "_=ax.set_xlabel('$x$',fontsize=28)\n",
    "_=ax2.set_ylabel('  $y$',fontsize=28,rotation='horizontal')\n",
    "fig.tight_layout()\n",
    "#fig.savefig('fig-statistics/Bootstrap_001.png')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<!-- dom:FIGURE: [fig-statistics/Bootstrap_001.png, width=500 frac=0.85] The $\\beta(3,2)$ distribution and the histogram that approximates it. <div id=\"fig:Bootstrap_001\"></div> -->\n",
    "<!-- begin figure -->\n",
    "<div id=\"fig:Bootstrap_001\"></div>\n",
    "\n",
    "<p>The $\\beta(3,2)$ distribution and the histogram that approximates it.</p>\n",
    "<img src=\"fig-statistics/Bootstrap_001.png\" width=500>\n",
    "\n",
    "<!-- end figure -->\n",
    "\n",
    "\n",
    "[Figure](#fig:Bootstrap_001) shows the $\\beta(3,2)$ distribution and\n",
    "the corresponding histogram of the samples. The histogram represents\n",
    "$\\hat{F}$ and is the distribution we sample from to obtain the\n",
    "bootstrap samples. As shown, the $\\hat{F}$ is a pretty crude estimate\n",
    "for the $F$ density (smooth solid line), but that's not a serious\n",
    "problem insofar as the following bootstrap estimates are concerned.\n",
    "In fact, the approximation $\\hat{F}$ has a naturally tendency to\n",
    "pull towards where most of the probability mass is. This is a\n",
    "feature, not a bug; and is the underlying mechanism for why\n",
    "bootstrapping works, but the formal proofs that exploit this basic\n",
    "idea are far out of our scope here.  The next block generates the\n",
    "bootstrap samples"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "yboot = np.random.choice(xsamples,(100,50))\n",
    "yboot_mn = yboot.mean()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " and the bootstrap estimate is therefore,"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.025598763883825818"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.std(yboot.mean(axis=1)) # approx sqrt(1/1250)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " [Figure](#fig:Bootstrap_002) shows the distribution of computed\n",
    "sample means from the bootstrap samples.  As promised, the next block\n",
    "shows how to use `sympy.stats` to compute the $\\beta(3,2)$ parameters we quoted\n",
    "earlier."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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kqToGHEmSVB0DjiRJqo4BR5IkVceAI0mSqmPAkSRJ1Zk14ETEpyJibURc2hr2NxFxZURc\nHBFnR8SO81tMSZKk3vXSgrMCeG7HsHOB/TLzAOBnwDuGXTBJkqR+zRpwMvO7wG0dw76VmRtL778B\ny+ahbJIkSX0Zxj04rwK+PoTlSJIkDcVAASci3gXcnZlnDKk8kiRJA1vc74wR8UrgMOCZs007Pj6+\n6fPY2BhjY2P9fq0kSarI5OQkk5OTQ19urwEnStf0RBwKvBX4w8z8z9lmbgccSZKkKZ0NHxMTE0NZ\n7qwBJyLOAMaA3SJiFXAC8E5gCfDNiAD4t8x83VBKJKknixYtovz9VWHp0qWsXr161MWQVIlZA05m\nHtll8Ip5KIukOdiwYUNVraM1rYuk0fNNxpIkqToGHEmSVB0DjiRJqo4BR5IkVceAI0mSqmPAkSRJ\n1THgSJKk6hhwJElSdQw4kiSpOgYcSZJUHQOOJEmqjgFHkiRVx4AjSZKqM+v/Ji5J94dFixYREaMu\nhqRKGHAkLQgbNmxgfHx81MUYilrWQ9qSeYlKkiRVx4AjSZKqY8CRJEnVMeBIkqTqGHAkSVJ1DDiS\nJKk6BhxJklQdA44kSaqOAUeSJFXHgCNJkqpjwJEkSdWZNeBExKciYm1EXNoatktEnBsRV0fENyJi\np/ktpiRJUu96acFZATy3Y9jbgW9l5mOB84B3DLtgkiRJ/Zo14GTmd4HbOgYfDpxaPp8K/PGQyyVJ\nktS3fu/BeVhmrgXIzJuAhw2vSJIkSYNZPKTl5Ewjx8fHN30eGxtjbGxsSF8rSZK2ZJOTk0xOTg59\nuf0GnLUR8fDMXBsRuwM3zzRxO+BIkiRN6Wz4mJiYGMpye71EFaWb8hXgleXzK4AvD6U0kiRJQ9DL\nY+JnAN8H9omIVRFxDPAB4DkRcTXwrNIvSZK0IMx6iSozj5xm1LOHXBZJkqSh8E3GkiSpOgYcSZJU\nHQOOJEmqjgFHkiRVx4AjSZKqY8CRJEnVMeBIkqTqGHAkSVJ1DDiSJKk6BhxJklQdA44kSaqOAUeS\nJFXHgCNJkqpjwJEkSdUx4EiSpOoYcCRJUnUMOJIkqToGHEmSVB0DjiRJqo4BR5IkVceAI0mSqrN4\n1AWoybJly1izZs2oiyFJ0lbPgDNEa9asYXx8fNTFGJqa1kWStHXxEpUkSaqOAUeSJFVnoIATEW+K\niJ9ExKURcXpELBlWwSRJkvrVd8CJiD2ANwAHZub+NPfzHDGsgkmSJPVr0JuMFwEPjoiNwHbAjYMX\nSZIkaTB9t+Bk5o3Ah4BVwBrg9sz81rAKJkmS1K++W3AiYmfgcGA58GvgrIg4MjPP6Jy2/bjx2NgY\nY2Nj/X6tJEmqyOTkJJOTk0Nf7iCXqJ4NXJuZtwJExBeBg4EZA44kSdKUzoaPiYmJoSx3kKeoVgFP\njogHRkQAzwKuHEqpJEmSBjDIPTg/As4CLgIuAQI4eUjlkiRJ6ttAT1Fl5gQwnLYkSZKkIfFNxpIk\nqToGHEmSVB0DjiRJqo4BR5IkVceAI0mSqmPAkSRJ1THgSJKk6hhwJElSdQw4kiSpOgYcSZJUHQOO\nJEmqjgFHkiRVx4AjSZKqY8CRJEnVMeBIkqTqGHAkSVJ1DDiSJKk6BhxJklQdA44kSaqOAUeSJFXH\ngCNJkqpjwJEkSdUx4EiSpOoYcCRJUnUMOJIkqToDBZyI2CkivhARV0bE5RHxpGEVTJIkqV+LB5z/\no8DXMvNPI2IxsN0QyiRJkjSQvgNOROwIPD0zXwmQmfcA64dULkmSpL4NconqUcC6iFgRERdGxMkR\n8aBhFUySJKlfg1yiWgwcCPxFZv44Ij4CvB04oXPC8fHxTZ/HxsYYGxsb4GslSVItJicnmZycHPpy\nBwk4q4EbMvPHpf8s4G3dJmwHHEmSpCmdDR8TExNDWW7fl6gycy1wQ0TsUwY9C7hiKKWSJEkawKBP\nUR0HnB4R2wLXAscMXiRJkqTBDBRwMvMS4A+GVBZJkqSh8E3GkiSpOgYcSZJUHQOOJEmqjgFHkiRV\nx4AjSZKqY8CRJEnVMeBIkqTqGHAkSVJ1DDiSJKk6BhxJklQdA44kSaqOAUeSJFXHgCNJkqpjwJEk\nSdUx4EiSpOoYcCRJUnUMOJIkqToGHEmSVB0DjiRJqo4BR5IkVceAI0mSqmPAkSRJ1THgSJKk6hhw\nJElSdQw4kiSpOgMHnIjYJiIujIivDKNAkiRJg1o8hGW8EbgC2HEIy5IkLTCLFi0iIkZdjKFZunQp\nq1evHnUxNM8GCjgRsQw4DDgROH4oJZIkLSgbNmxgfHx81MUYmprWRdMb9BLVh4G3AjmEskiSJA1F\n3y04EfF8YG1mXhwRY8C07ZfttDw2NsbY2Fi/XytJkioyOTnJ5OTk0Jc7yCWqpwIviojDgAcBO0TE\naZl5dOeENgdKkqRuOhs+JiYmhrLcvi9RZeY7M3PPzNwLOAI4r1u4kSRJur/5HhxJklSdYTwmTmae\nD5w/jGVJkiQNyhYcSZJUHQOOJEmqjgFHkiRVx4AjSZKqY8CRJEnVGcpTVP24+eabOemkk8j0f3mQ\nJEnDNbKA86UvfYlTTjmFxzzmMaMqwlBdf/31oy6CJKkH/u/oW4eRBRyAZcuWVfP/Uq1cudKQI0lb\nAP939K2D9+BIkqTqGHAkSVJ1DDiSJKk6BhxJklQdA44kSaqOAUeSJFXHgCNJkqpjwJEkSdUx4EiS\npOoYcCRJUnUMOJIkqToGHEmSVB0DjiRJqo4BR5IkVceAI0mSqmPAkSRJ1THgSJKk6vQdcCJiWUSc\nFxGXR8RlEXHcMAsmSZLUr8UDzHsPcHxmXhwR2wMXRMS5mXnVkMomSZLUl75bcDLzpsy8uHy+E7gS\nWDqsgkmSJPVrKPfgRMQjgQOAHw5jeZIkSYMYOOCUy1NnAW8sLTmSJEkjNcg9OETEYppw85nM/PJ0\n042Pj2/6PDY2xtjY2CBfK0mSKjE5Ocnk5OTQlztQwAFOAa7IzI/ONFE74EiSJE3pbPiYmJgYynIH\neUz8qcDLgGdGxEURcWFEHDqUUkmSJA2g7xaczPwesGiIZZEkSRoK32QsSZKqM+g9OJIkaYQWLVpE\nRIy6GAuOAUeSpC3Yhg0bqnqYZ1jr4iUqSZJUHQOOJEmqjgFHkiRVx4AjSZKqY8CRJEnVMeBIkqTq\nGHAkSVJ1DDiSJKk6BhxJklQdA44kSaqOAUeSJFXHgCNJkqpjwJEkSdUx4EiSpOoYcCRJUnUMOJIk\nqToGHEmSVB0DjiRJqo4BR5IkVceAI0mSqmPAkSRJ1THgSJKk6hhwJElSdQYKOBFxaERcFRE/jYi3\nDatQ6t1111036iJUy7qdX9bv/LJ+55f1u/D1HXAiYhvgJOC5wH7ASyPiccMqmHpz/fXXj7oI1bJu\n55f1O7+s3/ll/S58g7TgHAT8LDN/kZl3A58DDh9OsSRJkvq3eIB5lwI3tPpX04Senmy77bZcc801\nnH322QMUYeFYu3btqIsgSZKKyMz+Zoz478BzM/PY0v9y4KDMPK5juv6+QJIkbZUyMwZdxiAtOGuA\nPVv9y8qwzQyjkJIkSXMxyD04/w48OiKWR8QS4AjgK8MpliRJUv/6bsHJzA0R8XrgXJqg9KnMvHJo\nJZMkSepT3/fgSJIkLVSDvAdnxpf8RcQhEXF7RFxYund3jN+mDPeyVheD1G9E7BQRX4iIKyPi8oh4\n0v1b+oVvwPp9U0T8JCIujYjTyyVatfTyEtCIGIuIi0pdrpzLvFuzfus2IpZFxHnlN+GyiDiu27xb\nu0H23TLOY9sMBvxtmNuxLTPn3NEEo2uA5cC2wMXA4zqmOQT4ygzLeBPw2Zmm2Vq7QesX+DRwTPm8\nGNhx1Ou0kLpB6hfYA7gWWFL6Pw8cPep1Wkhdj/W7E3A5sLT0P6TXebfmbsC63R04oHzeHrjauh1e\n/bbGe2ybp/qd67Gt3xacXl/y1/UJqohYBhwGfLLP769d3/UbETsCT8/MFQCZeU9mrp/X0m55Btp/\ngUXAgyNiMbAdcOP8FHOL1Uv9HgmcnZlrADJz3Rzm3Zr1XbeZeVNmXlw+3wlcSfM+M91rkH3XY9vs\n+q7ffo5t/Qacbi/56/aH8pSIuDgivhoR+7aGfxh4K+ANQN0NUr+PAtZFxIrSTHpyRDxovgu8hem7\nfjPzRuBDwCqa1yLcnpnfmu8Cb2F6qd99gF0jYmVE/HtEHDWHebdmg9TtJhHxSOAA4IfzVM4t1aD1\n67FtZoPU75yPbfP5v4lfAOyZmQfQ/J9VXwKIiBcAa8uZRDD9WbJm1rV+aZrtDgQ+lpkHAncBbx9N\nEbdo0+2/O9OccSynuVy1fUQcObJSbrmm9tPnAYcC74mIR4+2SNWYsW4jYnvgLOCNpSVHc9O1fiPi\n+XhsG4bp9t85H9v6DTizvuQvM+/MzLvK568DiyNiV+Bg4EURcS1wJvCMiDitz3LUqp/63bbU72rg\nhsz8cZn0LJqdQvcapH6fDVybmbdm5gbgizT7tO7Vy0tAVwPfyMzfZuYtwHeAJ/Q479ZskLqlXFY9\nC/hMZn75fijvlmaQ+n0qHttmM0j9zv3Y1ueNQou490ahJTQ3Cj2+Y5qHtz4fBFzfZTkz3oi8tXaD\n1i9wPrBP+XwC8MFRr9NC6gap3/L5MuCBNGdonwb+YtTrtJC6Huv3ccA3y7TblTrdt5d5t+ZukLot\n404D/m7U67FQu0HrtzWNx7Z5qN+5Htv6etFfTvOSv4h4dTM6TwZeHBGvBe4G/gN4ST/ftTUaQv0e\nB5weEdvSPPFzzP27BgvbIPWbmT+KiLOAi8q4i4CTR7EeC1Uv9ZuZV0XEN4BLgQ3AyZl5BUC3eUez\nJgvPIHUbEU8FXgZcFhEX0dwn8s7M/NcRrc6CM+i+q5kNoX7ndGzzRX+SJKk683mTsSRJ0kgYcCRJ\nUnUMOJIkqToGHEmSVB0DjiRJqo4BR5IkVceAI0mSqvP/Afyia1+yRx53AAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0xaf9aba8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig,ax = subplots()\n",
    "fig.set_size_inches(8,4)\n",
    "_=ax.hist(yboot.mean(axis=1),normed=True,color='gray')\n",
    "_=ax.set_title('Bootstrap std of sample mean %3.3f vs actual %3.3f'%\n",
    "             (np.std(yboot.mean(axis=1)),np.sqrt(1/1250.)))\n",
    "fig.tight_layout()\n",
    "#fig.savefig('fig-statistics/Bootstrap_002.png')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<!-- dom:FIGURE: [fig-statistics/Bootstrap_002.png, width=500 frac=0.85] For each bootstrap draw, we compute the sample mean. This is the histogram of those sample means that will be used to compute the bootstrap estimate of the standard deviation. <div id=\"fig:Bootstrap_002\"></div> -->\n",
    "<!-- begin figure -->\n",
    "<div id=\"fig:Bootstrap_002\"></div>\n",
    "\n",
    "<p>For each bootstrap draw, we compute the sample mean. This is the histogram of those sample means that will be used to compute the bootstrap estimate of the standard deviation.</p>\n",
    "<img src=\"fig-statistics/Bootstrap_002.png\" width=500>\n",
    "\n",
    "<!-- end figure -->"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "sqrt(-1/(20000*beta(3, 2)**2) + 1/(1500*beta(3, 2)))\n"
     ]
    }
   ],
   "source": [
    "import sympy as S\n",
    "import sympy.stats\n",
    "for i in range(50): # 50 samples\n",
    "    # load sympy.stats Beta random variables\n",
    "    # into global namespace using exec\n",
    "    execstring = \"x%d = S.stats.Beta('x'+str(%d),3,2)\"%(i,i)\n",
    "    exec(execstring) \n",
    "\n",
    "# populate xlist with the sympy.stats random variables\n",
    "# from above\n",
    "xlist = [eval('x%d'%(i)) for i in range(50) ]\n",
    "# compute sample mean\n",
    "sample_mean = sum(xlist)/len(xlist)\n",
    "# compute expectation of sample mean\n",
    "sample_mean_1 = S.stats.E(sample_mean)\n",
    "# compute 2nd moment of sample mean\n",
    "sample_mean_2 = S.stats.E(S.expand(sample_mean**2))\n",
    "# standard deviation of sample mean\n",
    "# use sympy sqrt function\n",
    "sigma_smn = S.sqrt(sample_mean_2-sample_mean_1**2) # 1/sqrt(1250)\n",
    "print sigma_smn"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Programming Tip.**\n",
    "\n",
    "Using the `exec` function enables the creation of a sequence of Sympy\n",
    "random variables. Sympy has the `var` function which can automatically\n",
    "create a sequence of Sympy symbols, but there is no corresponding\n",
    "function in the statistics module to do this for random variables.\n",
    "\n",
    "\n",
    "\n",
    "<!-- @@@CODE src-statistics/Bootstrap.py from-to:^import sympy as S@^print sigma_smn -->\n",
    "\n",
    "<!-- p.505 casella -->\n",
    "\n",
    "**Example.** Recall the delta method from the section ref{sec:delta_method}.  Suppose we have a set of Bernoulli coin-flips\n",
    "($X_i$) with probability of head $p$. Our maximum likelihood estimator\n",
    "of $p$ is $\\hat{p}=\\sum X_i/n$ for $n$ flips.  We know this estimator\n",
    "is unbiased with $\\mathbb{E}(\\hat{p})=p$ and $\\mathbb{V}(\\hat{p}) =\n",
    "p(1-p)/n$. Suppose we want to use the data to estimate the variance of\n",
    "the Bernoulli trials ($\\mathbb{V}(X)=p(1-p)$). By the notation the\n",
    "delta method, $g(x) = x(1-x)$. By the plug-in principle, our maximum\n",
    "likelihood estimator of this variance is then $\\hat{p}(1-\\hat{p})$. We\n",
    "want the variance of this quantity.  Using the results of the delta\n",
    "method, we have"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$\n",
    "\\begin{align*}\n",
    "\\mathbb{V}(g(\\hat{p})) &=(1-2\\hat{p})^2\\mathbb{V}(\\hat{p})  \\\\\\\n",
    "\\mathbb{V}(g(\\hat{p})) &=(1-2\\hat{p})^2\\frac{\\hat{p}(1-\\hat{p})}{n} \\\\\\\n",
    "\\end{align*}\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " Let's see how useful this is with a short simulation."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "np.random.seed(123)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0 0 0 0 0 0 1 0 0 0]\n"
     ]
    }
   ],
   "source": [
    "from scipy import stats\n",
    "import numpy as np\n",
    "p= 0.25 # true head-up probability\n",
    "x = stats.bernoulli(p).rvs(10)\n",
    "print x"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " The maximum likelihood estimator of $p$ is $\\hat{p}=\\sum X_i/n$,"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.1\n"
     ]
    }
   ],
   "source": [
    "phat = x.mean()\n",
    "print phat"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " Then, plugging this into the delta method approximant above,"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.00064\n"
     ]
    }
   ],
   "source": [
    "print (1-2*phat)**2*(phat)**2/10."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " Now, let's try this using the bootstrap estimate of the variance"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.005049\n"
     ]
    }
   ],
   "source": [
    "phat_b=np.random.choice(x,(50,10)).mean(1)\n",
    "print np.var(phat_b*(1-phat_b))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " This shows that the delta method's estimated variance\n",
    "is different from the bootstrap method, but which one is better?\n",
    "For this situation we can solve for this directly using Sympy"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "import sympy as S\n",
    "from sympy.stats import E, Bernoulli\n",
    "xdata =[Bernoulli(i,p) for i in S.symbols('x:10')]\n",
    "ph = sum(xdata)/float(len(xdata))\n",
    "g = ph*(1-ph)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Programming Tip.**\n",
    "\n",
    "The argument in the `S.symbols('x:10')` function returns a sequence of Sympy\n",
    "symbols named `x1,x2` and so on. This is shorthand for creating and naming each\n",
    "symbol sequentially.\n",
    "\n",
    "\n",
    "\n",
    " Note that `g` is the $g(\\hat{p})=\\hat{p}(1- \\hat{p})$ \n",
    "whose variance we are trying to estimate. Then,\n",
    "we can plug in for the estimated $\\hat{p}$ and get the correct\n",
    "value for the variance,"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.00442968750000000\n"
     ]
    }
   ],
   "source": [
    "print E(g**2) - E(g)**2"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " This case is generally representative --- the delta method tends\n",
    "to underestimate the variance and the bootstrap estimate is better here.\n",
    "\n",
    "\n",
    "## Parametric Bootstrap\n",
    "\n",
    "In the previous example, we used the $\\lbrace x_1, x_2, \\ldots, x_n \\rbrace $\n",
    "samples themselves as the basis for $\\hat{F}$ by weighting each with $1/n$. An\n",
    "alternative is to *assume* that the samples come from a particular\n",
    "distribution, estimate the parameters of that distribution from the sample set,\n",
    "and then use the bootstrap mechanism to draw samples from the assumed\n",
    "distribution, using the so-derived parameters. For example, the next code block\n",
    "does this for a normal distribution."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "rv = stats.norm(0,2)\n",
    "xsamples = rv.rvs(45)\n",
    "# estimate mean and var from xsamples\n",
    "mn_ = np.mean(xsamples)\n",
    "std_ = np.std(xsamples)\n",
    "# bootstrap from assumed normal distribution with\n",
    "# mn_,std_ as parameters\n",
    "rvb = stats.norm(mn_,std_) #plug-in distribution\n",
    "yboot = rvb.rvs(1000)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<!-- @@@CODE src-statistics/Bootstrap.py from-to:^# In\\[7\\]:@^yboot -->\n",
    "\n",
    " Recall the sample variance estimator is the following:"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$\n",
    "S^2 = \\frac{1}{n-1} \\sum (X_i-\\bar{X})^2\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " Assuming that the samples are normally distributed, this\n",
    "means that $(n-1)S^2/\\sigma^2$ has a chi-squared distribution with\n",
    "$n-1$ degrees of freedom. Thus, the variance, $\\mathbb{V}(S^2) = 2\n",
    "\\sigma^4/(n-1) $. Likewise, the MLE plug-in estimate for this is\n",
    "$\\mathbb{V}(S^2) = 2 \\hat{\\sigma}^4/(n-1)$ The following code computes\n",
    "the variance of the sample variance, $S^2$ using the MLE and bootstrap\n",
    "methods."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "2.22670148618\n",
      "3.29467885682\n",
      "3.55555555556\n"
     ]
    }
   ],
   "source": [
    "# MLE-Plugin Variance of the sample mean \n",
    "print 2*(std_**2)**2/9. # MLE plugin\n",
    "# Bootstrap variance of the sample mean \n",
    "print yboot.var()\n",
    "# True variance of sample mean \n",
    "print 2*(2**2)**2/9."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<!-- @@@CODE src-statistics/Bootstrap.py from-to:^# In\\[8\\]:@^# end8 -->\n",
    "\n",
    " This shows that the bootstrap estimate is better here than the MLE\n",
    "plugin estimate.\n",
    "\n",
    "Note that this technique becomes even more powerful with multivariate\n",
    "distributions with many parameters because all the mechanics are the same.\n",
    "Thus, the bootstrap is a great all-purpose method for computing standard\n",
    "errors, but, in the limit,  is it converging to the correct value? This is the\n",
    "question of *consistency*. Unfortunately, to answer this question requires more\n",
    "and deeper mathematics than we can get into here.  The short answer is that for\n",
    "estimating standard errors, the bootstrap is a consistent estimator in a wide\n",
    "range of cases and so it definitely belongs in your toolkit."
   ]
  }
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