{
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   "source": [
    "# Lecture 11: Poisson Distribution and Approximation\n",
    "\n",
    "\n",
    "## Stat 110, Prof. Joe Blitzstein, Harvard University\n",
    "\n",
    "----"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Sympathetic Magic, or _[Confusing the map for the territory](http://nobeliefs.com/MapandTerritory.htm)_\n",
    "\n",
    "### Don't mistake a random variable for its distribution\n",
    "\n",
    "As a case in point, say we have two random variables $X$ and $Y$.\n",
    "\n",
    "\\begin{align}\n",
    "  P(X + Y) \\ne P(X=x) + P(Y=y)\n",
    "\\end{align}\n",
    "\n",
    "Claiming equality is clearly nonsense, since $X + Y$ is itself a random variable, and it should be recognized that $P(X=x) + P(Y=y)$ can exceed 1.\n",
    "\n",
    "### Think of them as houses & blueprints\n",
    "\n",
    "Metaphorically, the distribution is the _blueprint_, and the random variable is the _house_.\n",
    "\n",
    "----"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Poisson Distribution\n",
    "\n",
    "### Description\n",
    "\n",
    "The single most often used real-world discrete model. Applicable when there are a _large number of trials_ with a _small probability of success in each trial_.\n",
    "\n",
    "Note that the probability of success in each trial does _not_ have to be the same in each trial (unlike $\\operatorname{Bin}(n,p)$).\n",
    "\n",
    "The Poisson distribution expresses the probability of a given number of events occurring in a fixed interval of time and/or space, if these events occur with a known average _rate_ and independently of the time since the last event. The Poisson distribution can also be used for the number of events in other specified intervals such as distance, area or volume.\n",
    "\n",
    "Examples might be counting:\n",
    "\n",
    "- e-mails coming into your mailbox in an hour\n",
    "- buses following the same route arriving at a bus-stop in a day\n",
    "- natural phenomena, like earthquakes or meteor sightings, etc., in a month\n",
    "- chips in a chocolate-chip cookie (area/volume)\n",
    "\n",
    "\n",
    "### Notation\n",
    "\n",
    "$X \\sim \\operatorname{Pois}(\\lambda)$\n",
    "\n",
    "### Parameters\n",
    "\n",
    "$\\lambda$ - the average number of events per interval (rate), where $\\lambda \\gt 0$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
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xiD88XvDxCzevBNTW1sLr9TbrO/ILtl6vF3+cOp1OLPgSEhKQkpICvV4PjUYj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iloOmK5I9e3lSQZTXMvgq9yIiTZc/A1lIOvU9G8EDWTT3bgLyEiIipNTmROXkayVzAYBABEIhGX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\nY6wW+V97pNEtbNCKjQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1fa3fc36940>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "from matplotlib.ticker import (MultipleLocator, FormatStrFormatter,\n",
    "                               AutoMinorLocator)\n",
    "from scipy.stats import poisson\n",
    "\n",
    "%matplotlib inline\n",
    "\n",
    "plt.xkcd()\n",
    "_, ax = plt.subplots(figsize=(12,8))\n",
    "\n",
    "# seme Poisson parameters\n",
    "lambda_values = [1, 4, 8, 16]\n",
    "\n",
    "# colorblind-safe, divergent color scheme\n",
    "colors = ['#018571', '#80cdc1', '#dfc27d', '#a6611a']\n",
    "\n",
    "for i,l in enumerate(lambda_values):\n",
    "    x = np.arange(poisson.ppf(0.01, l), poisson.ppf(0.99, l))\n",
    "    pmf = poisson.pmf(x, l)\n",
    "    ax.plot(x, pmf, 'o', color=colors[i], ms=8, label=r'$\\lambda={}$'.format(l))\n",
    "    ax.vlines(x, 0, pmf, lw=2, color=colors[i], alpha=0.3)\n",
    "\n",
    "# legend styling\n",
    "legend = ax.legend()\n",
    "for label in legend.get_texts():\n",
    "    label.set_fontsize('large')\n",
    "for label in legend.get_lines():\n",
    "    label.set_linewidth(1.5)\n",
    "\n",
    "# y-axis\n",
    "ax.set_ylim([0.0, 0.4])\n",
    "ax.set_ylabel(r'$P(X=k)$')\n",
    "\n",
    "# x-axis\n",
    "ax.set_xlim([0, 26])\n",
    "ax.set_xlabel(r'total # of occurrences $k$ under $\\lambda$')\n",
    "\n",
    "# x-axis tick formatting\n",
    "majorLocator = MultipleLocator(5)\n",
    "majorFormatter = FormatStrFormatter('%d')\n",
    "minorLocator = MultipleLocator(1)\n",
    "ax.xaxis.set_major_locator(majorLocator)\n",
    "ax.xaxis.set_major_formatter(majorFormatter)\n",
    "ax.xaxis.set_minor_locator(minorLocator)\n",
    "\n",
    "ax.grid(color='grey', linestyle='-', linewidth=0.3)\n",
    "\n",
    "plt.suptitle(r'Poisson PMF: $P(X = k) = e^{-\\lambda} \\frac{\\lambda^k}{k!}$')\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Probability mass function\n",
    "\n",
    "\\begin{align}\n",
    "  P(X = k) = e^{-\\lambda} \\frac{\\lambda^k}{k!} ~~ \\text{, where } k \\in \\{0,1,2,\\dots,\\}\n",
    "\\end{align}\n",
    "\n",
    "Checking the validity of this PMF it is easy to see that it is always non-negative.\n",
    "\n",
    "Furthermore,\n",
    "\n",
    "\\begin{align}\n",
    "  \\sum_{k=0}^{\\infty} P(X = k) &= \\sum_{k=0}^{\\infty} e^{-\\lambda} \\frac{\\lambda^k}{k!} \\\\\n",
    "  &= e^{-\\lambda} \\sum_{k=0}^{\\infty} \\frac{\\lambda^k}{k!} & &\\text{since } e^{-\\lambda} \\text{ is constant} \\\\ \n",
    "  &= e^{-\\lambda} e^{\\lambda} & &\\text{recall Taylor series for } e^{\\lambda} \\\\\n",
    "  &= 1 ~~~~ \\blacksquare\n",
    "\\end{align}\n",
    "\n",
    "### Expected value\n",
    "\n",
    "\\begin{align}\n",
    "  \\mathbb{E}(X) &= \\sum_{k=0}^{\\infty} k ~~ e^{-\\lambda} \\frac{\\lambda^k}{k!} \\\\\n",
    "  &= e^{-\\lambda} \\sum_{k=1}^{\\infty} k \\frac{\\lambda^k}{k!} \\\\\n",
    "  &= e^{-\\lambda} \\sum_{k=1}^{\\infty} \\frac{\\lambda^k}{(k-1)!} \\\\\n",
    "  &= \\lambda e^{-\\lambda} \\sum_{k=1}^{\\infty} \\frac{\\lambda^{k-1}}{(k-1)!} \\\\\n",
    "  &= \\lambda e^{-\\lambda} e^{\\lambda} \\\\\n",
    "  &= \\lambda ~~~~ \\blacksquare\n",
    "\\end{align} \n",
    "\n",
    "----"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Poisson Paradigm (Approximate)\n",
    "\n",
    "Suppose we have:\n",
    "\n",
    "1. a lot of events $A_1, A_2, \\dots, A_n$, with $P(A_j) = p$\n",
    "1. number of trials $n$ is very large\n",
    "1. $p$ is very small\n",
    "\n",
    "The events could be _independent_ (knowing that $A_1$ occurred has no bearing whatsoever on $A_2$.\n",
    "\n",
    "They could even be _weakly dependent_ ($A_1$ occurring has some level of affect on the likelihood of $A_2$).\n",
    "\n",
    "Either way, the expected number of events $A_j$ occurring is approximately $\\operatorname{Pois}(\\lambda)$, and by Linearity\n",
    "\n",
    "\\begin{align}\n",
    "  \\mathbb{E}(A) &= \\lambda = \\sum_{j=1}^n p_j\n",
    "\\end{align}\n",
    "\n",
    "### Relating the Binomial distribution to the Poisson\n",
    "\n",
    "This example will relate the Binomial distribution to the Poisson distribution.\n",
    "\n",
    "Suppose we have $X \\sim \\operatorname{Bin}(n,p)$, and let $n \\rightarrow \\infty$, $p \\rightarrow 0$. \n",
    "\n",
    "We will hold $\\lambda = np$ constant, which will let us see what happens to the Binomial distribution when the number of trails approaches $\\infty$ while the probabability of success $p$ gets very small.\n",
    "\n",
    "Specifically let's see what happens to the Binomial PMF under these conditions.\n",
    "\n",
    "\\begin{align}\n",
    "  P(X = k) &= \\binom{n}{k} p^k q^{n-k} ~~~~ \\text{where k is fixed} \\\\\n",
    "  &= \\underbrace{\\frac{n (n-1) \\dots (n-k+1)}{k!} \\left(\\frac{\\lambda}{n}\\right)^k}_{\\text{n terms cancel out}} ~~ \\underbrace{\\left(1 - \\frac{\\lambda}{n}\\right)^n}_{\\text{continuous compounding and e}} ~~ \\underbrace{\\left(1 - \\frac{\\lambda}{n}\\right)^{-k}}_{\\text{goes to 1}}   \\\\\n",
    "  \\\\\n",
    "  &\\rightarrow \\frac{\\lambda^k}{k!} e^{-\\lambda} ~~ \\text{which is the Poisson PMF at k}\n",
    "\\end{align}\n",
    "\n",
    "\n",
    "### Thought-experiment: counting raindrops\n",
    "\n",
    "Let's say we want to count the number of raindrops that fall on a certain area on the ground.\n",
    "\n",
    "We could divide this area with a grid, with each grid cell being very, very tiny. \n",
    "\n",
    "Therefore:\n",
    "\n",
    "- the number grid cells is very, very large\n",
    "- the probability of a rain drop landing in an arbitrary cell is very, very small\n",
    "\n",
    "_What distribution could we use to model this situation?_\n",
    "\n",
    "\n",
    "#### How about $X \\sim \\operatorname{Bin}(n,p)$?\n",
    "Considering the Binomial distribution, we would have to make certain assumptions:\n",
    "\n",
    "1. the event of a raindrop hitting a cell is independent of other events\n",
    "1. the probability $p$ of a raindrop hitting an arbitrary cell is identical. \n",
    "\n",
    "While it might be OK to make these assumptions, but one **big** stumbling block in using the Binomial is that we would end up calculating factorials of a very large $n$, which even for a computer would be problematic.\n",
    "\n",
    "#### How about $X \\sim \\operatorname{Pois}(\\lambda)$?\n",
    "\n",
    "The Poisson distribution is a better model approximation than the Binomial, since\n",
    "\n",
    "1. no factorials involved, so much simpler than the Binomial\n",
    "1. we can deal with the case where more than one raindrop lands in a cell\n",
    "1. we don't need to make any assumption on $p$ being identical\n",
    "\n",
    "#### Example: Graph comparing $X \\sim \\operatorname{Bin}(n,p)$ vs $X \\sim \\operatorname{Pois}(\\lambda = np)$ where $n = 1e^{6}$ and $p = 1e^{-5}$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
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JybR+/Xpemfvrr78IAM2YMaNUuZcvX86XeWkDHMHBwRQSElKuMiEiOnr0KAEQLB0dOHAg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dIdAeWJ8lCeKA/libJQfigP9blaR0vECNG/xEgrYVfiIy2L5/l2dVJjR8DzPESabVUU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\nSe9DlmXMnz8fO3bsSGr7F154AUuXLo2avrZ//3488sgjmDBhAt57772Uz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+AAACAASURB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\nEUIIIYQQQkgv/T/VeMnVCu2YUAAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1fa40e30160>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from scipy.stats import binom\n",
    "\n",
    "plt.xkcd()\n",
    "\n",
    "fig = plt.figure(figsize=(12,8))\n",
    "\n",
    "# Binomial parameters\n",
    "n = 1e6\n",
    "p = 1e-5\n",
    "\n",
    "x = np.arange(binom.ppf(0.01, n, p), binom.ppf(0.99, n, p))\n",
    "\n",
    "# plot Bin(n,np)\n",
    "binom_pmf = binom.pmf(x, n, p)\n",
    "ax1 = fig.add_subplot(211)\n",
    "ax1.plot(x, binom_pmf, 'o', ms=8, color='#f46d43', label=r'$X \\sim Bin(n,p)$')\n",
    "ax1.vlines(x, 0, binom_pmf, lw=2, color='#f46d43', alpha=0.3)\n",
    "ax1.set_title(r'$P(x=k) = \\binom{n}{k} p^k (1-p)^{n-k}$')\n",
    "ax1.legend(loc='upper right')\n",
    "\n",
    "ax1.grid(color='grey', linestyle='-', linewidth=0.3)\n",
    "\n",
    "# y-axis\n",
    "ax1.set_ylim([0.0, 0.15])\n",
    "\n",
    "# plot Pois(np)\n",
    "pois_pmf = poisson.pmf(x, n*p)\n",
    "ax2 = fig.add_subplot(212)\n",
    "ax2.plot(x, pois_pmf, 'o', ms=8, color='#4575b4', label=r'$X \\sim Pois(\\lambda = np)$')\n",
    "ax2.vlines(x, 0, pois_pmf, lw=2, color='#4575b4', alpha=0.3)\n",
    "ax2.set_title(r'$P(X = k) = e^{-\\lambda} \\frac{\\lambda^k}{k!}$')\n",
    "ax2.legend(loc='upper right')\n",
    "\n",
    "ax2.grid(color='grey', linestyle='-', linewidth=0.3)\n",
    "\n",
    "# y-axis\n",
    "ax2.set_ylim([0.0, 0.15])\n",
    "\n",
    "fig.tight_layout()\n",
    "\n",
    "st = fig.suptitle(r'Approximating $X \\sim Bin(n,p)$ with $X \\sim Pois(\\lambda)$, where $n=1e^{6}, p=1e^{-5}$', fontsize=18)\n",
    "st.set_y(1.035)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "----"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Birthdays, revisited: triple matches\n",
    "\n",
    "Suppose we have $n$ people, and we want to know the _approximate probability_ that there are 3 people among the $n$ who share the same birthday.\n",
    "\n",
    "Doing this the way we did in Lecture 3 is possible, but it would get very messy.\n",
    "\n",
    "Let's set up the problem first.\n",
    "\n",
    "- there are $\\binom{n}{3}$ triplets\n",
    "- we used indicator r.v. $I_{ijk} \\text{, where } i < j < k$\n",
    "- $\\Rightarrow \\mathbb{E}(\\# \\text{ triple matches}) = \\binom{n}{3} \\frac{1}{365^2}$ \n",
    "\n",
    "But we are interested in the _approximate probability_ of triple matches, so now let's use the Poisson. \n",
    "\n",
    "_Why?_\n",
    "\n",
    "1. we expect the total number of trials $\\binom{n}{3}$ to be very large\n",
    "1. the probability $P(I_{ijk})$ is very small\n",
    "1. events are _weakly dependent_, since if persons $1$ and $2$ are already known to share a birthday, then  $I_{123} \\text{, } I_{124}$ are not completely independent\n",
    "\n",
    "We claim that these circumstances are _approximately_ $\\operatorname{Pois}(\\lambda)$ with $\\lambda = \\mathbb{E}(\\# \\text{ triple matches})$.\n",
    "\n",
    "Let $X = \\text{# triple matches}$\n",
    "\n",
    "\\begin{align}  \n",
    "  P(X \\ge 1) &= 1 - P(X=0) \\\\\n",
    "  &\\approx 1 - e^{-\\lambda} \\frac{\\lambda^0}{0!} \\\\\n",
    "  &= 1 - e^{-\\lambda} ~~~~ \\text{where you just plug in } \\lambda = \\binom{n}{3} \\frac{1}{365^2} ~~~~ \\blacksquare\n",
    "\\end{align}\n",
    "\n",
    "----"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "View [Lecture 11: The Poisson distribution | Statistics 110](http://bit.ly/2Pn99BO) on YouTube."
   ]
  }
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