03-Probability-and-Statistics-Refresher.ipynb

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   "source": [
    "# Probability and Statistics Refresher"
   ]
  },
  {
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   "execution_count": 1,
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     "slide_type": "skip"
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    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n"
     ]
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   "source": [
    "%matplotlib inline\n",
    "%config InlineBackend.figure_format='retina'\n",
    "# import libraries\n",
    "import numpy as np\n",
    "import matplotlib as mp\n",
    "import pandas as pd\n",
    "import matplotlib.pyplot as plt\n",
    "import pandas as pd\n",
    "import slideUtilities as sl\n",
    "from importlib import reload\n",
    "from datetime import datetime\n",
    "from IPython.display import Image\n",
    "from IPython.display import display_html\n",
    "from IPython.display import display\n",
    "from IPython.display import Math\n",
    "from IPython.display import Latex\n",
    "from IPython.display import HTML\n",
    "print('')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
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    "%%html\n",
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   "cell_type": "markdown",
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   "source": [
    "Today we'll review the essentials of probability and statistics.  I assume that you learned all of this once.  What I want to do today is bring the material back into your mind fresh."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
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     "slide_type": "slide"
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   "source": [
    "## Probability\n",
    "\n",
    "What is probability?  "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "Historically, the notion of probability has actually been very slippery and hard to pin down exactly.   There are probably at least three ways to view probability in practice:\n",
    "\n",
    "1. as a mathematical exercise involving positive functions that integrate to 1 (i.e., distributions).\n",
    "2. as an encoding of natural rules for reasoning under uncertainty. \n",
    "3. as an idealization of properties of data and processes."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "For our purposes, we use probability as an abstraction that hides details we don't want to deal with.  This is a time-honored use of probability."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    ">Any simple idea is approximate; as an illustration, consider an object ... what is an object? Philosophers are always \n",
    ">saying, “Well, just take a chair for example.” The moment they say that, you know that they do not know what they are \n",
    ">talking about any more. What is a chair? ... every object is a mixture of a lot of things, so we can deal with it \n",
    "> only as a series of approximations and idealizations.\n",
    "\n",
    ">The trick is the idealizations.\n",
    "\n",
    "Richard Feynman, _The Feynman Lectures on Physics, 12-2_"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "Here is an illustration of this principle applied to probability:"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "-"
    }
   },
   "source": [
    ">In a serious work ... an expression such as “this phenomenon is due to chance” constitutes simply, \n",
    ">an elliptic form of speech. ... It really means “everything occurs as if this phenomenon were due to chance,” \n",
    ">or, to be more precise: “To describe, or interpret or formalize this phenomenon, \n",
    ">only probabilistic models have so far given good results.”\n",
    "\n",
    "Georges Matheron, _Estimating and Choosing: An Essay on Probability in Practice_"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Probability and Conditioning"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "__Definition.__  Consider a set $\\Omega$, referred to as the\n",
    "_sample space._  A _probability\n",
    "  measure_ on $\\Omega$ is a function $P[\\cdot]$ defined on all the subsets of $\\Omega$ (the\n",
    "  _events_) such that:\n",
    "  \n",
    "1. $P[\\Omega] = 1$\n",
    "2. For any event $A \\subset \\Omega$, $P[A] \\geq 0.$\n",
    "3. For any events $A, B \\subset \\Omega$ where $A \\cap B =\n",
    "    \\emptyset$, $P[A \\cup B] = P[A] + P[B]$.\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "Often we want to ask how a probability measure changes if we restrict the sample space to be some subset of $\\Omega$.  \n",
    "\n",
    "This is called __conditioning.__"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "__Definition.__ The _conditional probability_ of an event $A$ given that\n",
    "event $B$ (having positive probability) is known to occur, is \n",
    "\n",
    "$$ P[A|B] = \\frac{P[A \\cap B]}{P[B]}  \\mbox{ where } P[B] > 0 $$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "The function $P[\\cdot|B]$ is a probability measure over the sample space\n",
    "$B$.  \n",
    "\n",
    "Note that in the expression $P[A|B]$, $A$ is random but $B$ is fixed. \n",
    "\n",
    "Now if $B$ is a proper subset of $\\Omega,$ then $P[B] < 1$.   So $P[\\cdot|B]$ is a rescaling of the quantity $P[A\\cap B]$ so that $P[B|B] = 1.$ "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "The sample space $\\Omega$ may be continuous or discrete, and bounded or unbounded."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "__Independent Events.__\n",
    "\n",
    "__Definition.__ Two events $A$ and $B$ are __independent__ if $P[A\\cap B] = P[A] \\cdot P[B].$\n",
    "\n",
    "This is exactly the same as saying that $P[A|B] = P[A].$  \n",
    "\n",
    "So we can see that the intuitive notion of independence is that \"if one event occurs, that does not change the probability of the other event.\""
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Random Variables"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "We are usually interested in numeric values associated with events.  \n",
    "\n",
    "When a random event has a numeric value we refer to it as a random variable.\n",
    "\n",
    "Notationally, we use CAPITAL LETTERS for random variables and lowercase for non-random quantities."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "To collect information about what values of the random variable are more probable than others, we have some more definitions."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "__Definition.__ The cumulative distribution function (CDF) F for a random\n",
    " variable $X$ is equal to the probability measure for the event that\n",
    " consists of all possible outcomes with a value of the random variable $X$\n",
    " less than or equal to $x$, that is, $F(x) = P[X \\leq x].$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "__Example.__  Consider the roll of a single die.  The random variable here is the number of points showing.  What is the CDF?"
   ]
  },
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   "cell_type": "code",
   "execution_count": 3,
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+nd4Klu9K8rIkr55mnT9LLwi5J8m/b63dfszndyT5H1W1fexwWQAAAOAYC+XM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\nAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x104695be0>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 375,
       "width": 545
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "sl.hide_code_in_slideshow()\n",
    "plt.figure()\n",
    "for i in range(7):\n",
    "    plt.plot(i,i/6.,'ob')\n",
    "    plt.plot([i,i+1],[i/6.,i/6.],'-b')\n",
    "plt.xlim([-0.5,7])\n",
    "plt.ylim([-0.05,1.1])\n",
    "plt.xlabel('Number of points showing',size=14)\n",
    "plt.ylabel(r'$P[X\\leq x]$',size=14)\n",
    "print('')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "Now, consider this CDF of some random variable:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {
    "slideshow": {
     "slide_type": "-"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div id=\"f31870ee35c6f830\"></div>\n",
       "    <script type=\"text/javascript\">\n",
       "        $(function(){\n",
       "            var p = $(\"#f31870ee35c6f830\");\n",
       "            if (p.length==0) return;\n",
       "\n",
       "            while (!p.hasClass(\"cell\")) {\n",
       "                p=p.parent();\n",
       "\n",
       "                if (p.prop(\"tagName\") ==\"body\") return;\n",
       "            }\n",
       "            var cell = p;\n",
       "            cell.find(\".input\").addClass(\"hide-in-slideshow\")\n",
       "        });\n",
       "    </script>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n"
     ]
    },
    {
     "data": {
      "image/png": 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DJEmSVCUvvQQzZ5YfP2AAvPOd+fqRJGkLwxBJkiRVxc9/XjwmU9bb3w4775yv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\nAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x118669e10>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 382,
       "width": 545
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "sl.hide_code_in_slideshow()\n",
    "from scipy.stats import norm\n",
    "plt.figure()\n",
    "x = np.linspace(norm.ppf(0.001), norm.ppf(0.999), 100)\n",
    "plt.plot(x, norm.cdf(x),'b-', lw=5, alpha=0.6)\n",
    "plt.xlabel('x',size=14)\n",
    "plt.ylabel(r'$P[X\\leq x]$',size=14)\n",
    "print('')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "What does it mean when the slope is steeper for some $x$ values?\n",
    "\n",
    "The slope tells us how likely values are in a particular range."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This is important enough that we define a function to capture it.  \n",
    "\n",
    "__Definition.__ The _probability density function_ (pdf) is the derivative of the CDF, when that is defined.\n",
    "\n",
    "$$ f(x) = \\frac{dF(x)}{dx}.$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Often we will go the other way as well:\n",
    "\n",
    "$$ F(x) = \\int_{-\\infty}^{x} f(t)\\; dt $$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "You should be able to see that:\n",
    "\n",
    "$$ \\int_{-\\infty}^{+\\infty} f(x)\\; dx = 1 $$\n",
    "\n",
    "and\n",
    "\n",
    "$$      f(x) \\geq 0 $$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "Now, for a discrete random variable, the CDF is not differentiable (because the CDF is a step function).  \n",
    "\n",
    "For the PDF of discrete RVs, we simply plot the probability function of\n",
    "each value.  That is, we plot $P[X = x]$ for the various values of $x$.\n",
    "\n",
    "Another way to think of the PDF is that it consists of impulses at the\n",
    "points of discontinuity of the CDF. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "For our example of the single die:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "slideshow": {
     "slide_type": "-"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div id=\"8f03b30d6764e14e\"></div>\n",
       "    <script type=\"text/javascript\">\n",
       "        $(function(){\n",
       "            var p = $(\"#8f03b30d6764e14e\");\n",
       "            if (p.length==0) return;\n",
       "\n",
       "            while (!p.hasClass(\"cell\")) {\n",
       "                p=p.parent();\n",
       "\n",
       "                if (p.prop(\"tagName\") ==\"body\") return;\n",
       "            }\n",
       "            var cell = p;\n",
       "            cell.find(\".input\").addClass(\"hide-in-slideshow\")\n",
       "        });\n",
       "    </script>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n"
     ]
    },
    {
     "data": {
      "image/png": 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t7suX06S73z23FQMAAABb1nrcdeWlVfXKTC5P+S9JduX/DDi+nOSVSb4nye2T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\nAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x114c5eda0>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 375,
       "width": 541
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "sl.hide_code_in_slideshow()\n",
    "plt.figure()\n",
    "x = np.arange(7)\n",
    "plt.plot(x, 7*[1/6.], 'bo', ms=8)\n",
    "plt.vlines(x, 0, 1/6., colors='b', lw=5, alpha=0.5)\n",
    "plt.xlim([-0.5,6.5])\n",
    "plt.ylim([0,1.1])\n",
    "plt.xlabel('Number of points showing',size=14)\n",
    "plt.ylabel(r'$P[X = x]$',size=14)\n",
    "print('')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Characterizing Random Variables"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "__Definition.__ The _expected value_ $E[X]$ of a random\n",
    "variable $X$ is the probability-weighted sum or integral of all possible values of\n",
    "the R.V.  \n",
    "\n",
    "For a discrete random variable, this is:\n",
    "\n",
    "$$ E[K] \\equiv \\sum_{-\\infty}^{+\\infty} k\\; P[K=k] $$\n",
    "\n",
    "and for a continuous random variable with pdf $p():$\n",
    "\n",
    "$$ E[K] \\equiv \\int_{-\\infty}^{+\\infty} k\\; p(k)\\; dk $$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "The expected value is also called the average or the mean, although we\n",
    "prefer to reserve those terms for empirical statistics (actual\n",
    "measurements, not idealizations like these formulas).\n",
    "\n",
    "The expected value is in some sense the \"center of mass\" of the random\n",
    "variable.   It is often denoted $\\mu$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "The mean is usually a quite useful characterization of the random variable.\n",
    "\n",
    "However, be careful: in some cases, the mean may not be very informative, or important.  \n",
    "\n",
    "In some cases a\n",
    "random variable may not ever take on the mean as a possible value.  (Consider again the single die, whose mean is 3.5)\n",
    "\n",
    "In other cases the notion of average isn't useful, as for the person\n",
    "with their head in the oven and feet in the freezer who claims \"on\n",
    "average I feel fine.\" \n",
    "\n",
    "In other words, the mean may not be very informative when\n",
    "observations are highly variable.   "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "In fact, the variability of random quantities is crucially important to characterize.\n",
    "\n",
    "For this we use __variance,__ the mean squared difference of the random variable from its mean.\n",
    "\n",
    "__Definition.__ The variance of a random variable $X$ is\n",
    "\n",
    "$$ Var(X) \\equiv E[(X - E[X])^2]$$.\n",
    "\n",
    "For a discrete R.V. with $E[X] = \\mu$ this would be:\n",
    "$$ Var(X) = \\sum_{x=-\\infty}^{+\\infty} (x-\\mu)^2\\; P[X=x]. $$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "The units of variance are the square of the units of the mean. \n",
    "\n",
    "To compare variance and mean, we take the square root of the variance.\n",
    "\n",
    "This is called the __standard deviation__ and is denoted $\\sigma$.\n",
    "So variance is denoted $\\sigma^2$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "Next, let's recall the case of the Tesla and Yelp returns from the last lecture:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div id=\"d927b256cb290fea\"></div>\n",
       "    <script type=\"text/javascript\">\n",
       "        $(function(){\n",
       "            var p = $(\"#d927b256cb290fea\");\n",
       "            if (p.length==0) return;\n",
       "\n",
       "            while (!p.hasClass(\"cell\")) {\n",
       "                p=p.parent();\n",
       "\n",
       "                if (p.prop(\"tagName\") ==\"body\") return;\n",
       "            }\n",
       "            var cell = p;\n",
       "            cell.find(\".input\").addClass(\"hide-in-slideshow\")\n",
       "        });\n",
       "    </script>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x106a41a58>"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
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BWTa7TZnB4BpgiImIwfDOw/HR7o/cXstvJRJEREREFBL1fRfqb9rN9GGYNWsWnnnmGZSU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\nAOj2X2VOH5Vl/ap+AAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11822e860>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 379,
       "width": 524
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "sl.hide_code_in_slideshow()\n",
    "import pandas as pd\n",
    "import pandas_datareader.data as web\n",
    "\n",
    "stocks = ['TSLA', 'YELP']\n",
    "attr = 'Close'\n",
    "data_source = 'yahoo'\n",
    "df = web.DataReader(stocks, \n",
    "                    data_source,                               \n",
    "                    start=datetime(2014, 1, 1), \n",
    "                    end=datetime(2014, 12, 31))[attr]\n",
    "rets = df.pct_change(30)\n",
    "rets.TSLA.plot(label = 'tesla',lw=2)\n",
    "rets.YELP.plot(label = 'yelp',lw=2)\n",
    "plt.legend(loc='best')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "Treating these two timeseries as random variables, we are interested in how the vary __together__.\n",
    "\n",
    "This is captured by the concept of __covariance.__\n",
    "\n",
    "__Definition.__ For two random variables $X$ and $Y$, their _covariance_ is defined as:\n",
    "\n",
    "$$\\text{Cov}(X,Y) = E\\left[(X-\\mu_X)(Y-\\mu_Y)\\right]$$\n",
    "\n",
    "Basically, covariance is large when $X$ and $Y$ tend to be both above their means together, and both below their means together."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Low and High Variability"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "Historically, most sources of random variation that have concerned\n",
    "statisticians are instances of low variability.  \n",
    "\n",
    "The original roots of\n",
    "probability in the study of games of chance, and later in the study of\n",
    "biology and medicine, have mainly studied objects with low variability.\n",
    "\n",
    "(Note that by \"low variability\" I don't mean that such variability is unimportant.)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "Some examples of random variation in this category are: \n",
    "\n",
    "* the heights of adult humans\n",
    "* the number of trees per unit area in a mature forest\n",
    "* the sum of 10 rolls of a die\n",
    "* the time between emission of subatomic particles from a radioactive material.\n",
    "\n",
    "In each of these cases, there are a range of values that are\n",
    " \"typical,\" and there is a clear threshold above what is typical, that essentially never occurs.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "On the other hand, there are some situations in which variability is\n",
    "quite different.  \n",
    "\n",
    "In these cases, there is no real \"typical\" range of\n",
    "values, and arbitrarily large values can occur with non-negligible\n",
    "frequency.   \n",
    "\n",
    "Some examples in this category are\n",
    "\n",
    "* the distribution of wealth among individuals in society\n",
    "* the sizes of human settlements\n",
    "* the areas burnt in forest fires\n",
    "* the runs of gains and losses in various financial markets over time\n",
    "* and the number of collaborators a scholar has over her lifetime.   "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "> The banking system (betting against rare events) just lost [more than] 1\n",
    "> Trillion dollars (so far) on a single error, more than was ever earned\n",
    "> in the history of banking.\n",
    "\n",
    "Nassim Nicholas Taleb, September 2008 \n",
    "\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "![](figs/derivatives-portfolio-variation.png)\n",
    "\n",
    "An example of a run of observations showing high variability.   This figure shows the daily\n",
    "variations in a derivatives portfolio over the timeframe 1988-2008.\n",
    "About 99% of the variation over the 20 years occurs in a single day\n",
    "(the day the European Monetary System collapsed).\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Important Random Variables"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "### Independent Trials"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "Here is our canonical experiment: flipping a weighted coin.  \n",
    "\n",
    "The coin\n",
    "comes up \"heads\" (aka \"success\") with probability $p$.  \n",
    "\n",
    "We use the standard notation that the corresponding probability (\"tails\", \"failure\") is denoted $q$\n",
    "(i.e., $q = 1-p$).  \n",
    "\n",
    "These are called _Bernoulli trials_; one can think of each trial as a timestep so these are about _discrete\n",
    "  time_.\n",
    "  \n",
    "Notice that by definition, Bernoulli trials are __independent events.__"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "Now we will extend this notion to continuous time.\n",
    "\n",
    "Imagine that you \"speed up\" the coin flipping so that instead of flipping a coin once per second,\n",
    "you flip it $m$ times per second, and you simultaneously decrease the\n",
    "probability of success to $p/m$.   \n",
    "\n",
    "Then you expect the same number of\n",
    "events (successes, heads) per second (i.e., $p$), but events can happen at finer time\n",
    "intervals.   "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "Now imagine the limit as $m \\rightarrow \\infty$.  \n",
    "\n",
    "This is a\n",
    "mathematical abstraction in which \n",
    "* an event can happen at _any_ time instant\n",
    "* an event at any time instant is equally likely\n",
    "* and an event at any time instant is independent of any other time instant (it's still a coin with no memory).   "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "Now we can think of events happening at some _rate_ $\\lambda$ that is\n",
    "equal to $p$ per second.  \n",
    "\n",
    "Note that $\\lambda$ has units of inverse time, e.g., sec$^{-1}$. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "For each of these two cases (discrete and continuous time) there are two questions we can ask:\n",
    "\n",
    "1. Given that an event has just occured, how long until the next\n",
    "  success?\n",
    "2. In a fixed number of trials or amount of time, how many events\n",
    "  occur?\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "These four cases define four commonly-used random variables.\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "| | # Trials or Time Until Event | Number of Events in Fixed Time  |\n",
    "|-|:--:|:--:|\n",
    "|__Discrete Trials__| Geometric| Binomial |\n",
    "|__Continuous Rate__| Exponential | Poisson|\n",
    "\n",
    "Each one has an associated distribution."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "#### The Geometric Distribution"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "The geometric distribution answers the question: \"what is the probability there are exactly $k$ trials before the first success?\"\n",
    "\n",
    "Its PDF is given by:\n",
    "\n",
    "$$ P[X = k] = p(1-p)^k. $$ \n",
    "\n",
    "Its mean is $\\mu = \\frac{1-p}{p}$ and its variance is $\\sigma^2 = \\frac{1-p}{p^2}$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "Its pdf looks like:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "slideshow": {
     "slide_type": "-"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
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       "    <script type=\"text/javascript\">\n",
       "        $(function(){\n",
       "            var p = $(\"#4c480cb730787bf3\");\n",
       "            if (p.length==0) return;\n",
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     "output_type": "display_data"
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    {
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     "output_type": "stream",
     "text": [
      "\n"
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LykpSmzCS6FoJvKh6X46Hv7Tcbv186KSfE/f1WQJXZ+aotaoy807KilTNidHdBxZI5vMz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      "text/plain": [
       "<matplotlib.figure.Figure at 0x1187a9e80>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 397,
       "width": 556
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "sl.hide_code_in_slideshow()\n",
    "from scipy.stats import geom\n",
    "p = 0.3\n",
    "x = np.arange(geom.ppf(0.01, p), geom.ppf(0.995, p))\n",
    "plt.ylim([0,0.4])\n",
    "plt.xlim([-0.5,max(x)])\n",
    "plt.plot(x-1, geom.pmf(x, p), 'bo', ms=8, label='geom pmf')\n",
    "plt.vlines(x-1, 0, geom.pmf(x, p), colors='b', lw=5, alpha=0.6)\n",
    "plt.title('Geometric PDF.  p = 0.3',size=14)\n",
    "plt.xlabel(r'k',size=14)\n",
    "plt.ylabel(r'P[X = k]',size=14)\n",
    "print('')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "#### The Binomial Distribution"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "In this experiment there are precisely $N$ coin flips, and $p$ is still\n",
    "the probability of a success.  Now we ask: what is the probability there\n",
    "will be $k$ successes?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "For any given sequence of $k$ successes and $N-k$ failures, the probability is $p^k (1-p)^{N-k}$.\n",
    "\n",
    "But there are many different such sequences: $C^N_k$ of them in fact.\n",
    "\n",
    "So this distribution is $P[X=k] = C^N_k p^k (1-p)^{N-k}.$\n",
    "\n",
    "Its mean is $pN$, and its variance is $pqN$.  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div id=\"b5a0b0e7e4a6c158\"></div>\n",
       "    <script type=\"text/javascript\">\n",
       "        $(function(){\n",
       "            var p = $(\"#b5a0b0e7e4a6c158\");\n",
       "            if (p.length==0) return;\n",
       "\n",
       "            while (!p.hasClass(\"cell\")) {\n",
       "                p=p.parent();\n",
       "\n",
       "                if (p.prop(\"tagName\") ==\"body\") return;\n",
       "            }\n",
       "            var cell = p;\n",
       "            cell.find(\".input\").addClass(\"hide-in-slideshow\")\n",
       "        });\n",
       "    </script>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n"
     ]
    },
    {
     "data": {
      "image/png": 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EByNJ04E9RnoQEXsB+1H+GZ07zGRFZ1HmAQnglIjotCxotz5ImSjpvzLz/C5j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\nkiRJklRbBiOSJEmSJKm2/h9BPvlN2KdEegAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1187b2f98>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 397,
       "width": 547
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "sl.hide_code_in_slideshow()\n",
    "from scipy.stats import binom\n",
    "p = 0.3\n",
    "x = np.arange(binom.ppf(0.01, 10, p), binom.ppf(0.9995, 10, p))\n",
    "plt.ylim([0,0.4])\n",
    "plt.xlim([-0.5,max(x)+0.5])\n",
    "plt.plot(x, binom.pmf(x, 10, p), 'bo', ms=8, label='binom pmf')\n",
    "plt.vlines(x, 0, binom.pmf(x, 10, p), colors='b', lw=5, alpha=0.6)\n",
    "plt.title('Binomial PDF.  p = 0.3, N = 10',size=14)\n",
    "plt.xlabel(r'k',size=14)\n",
    "plt.ylabel(r'P[X = k]',size=14)\n",
    "print('')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "#### The Exponential Distribution"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "This random variable is the analog of the geometric in the continuous case,\n",
    "_i.e.,_ the situation in which a success happens at some rate\n",
    "$\\lambda$.  This RV measures the time until a success occurs. \n",
    "\n",
    "Its pdf is:\n",
    "\n",
    "$$ p(x) = \\lambda e^{- \\lambda x}$$\n",
    "\n",
    "The mean is $1/\\lambda$, and the variance is $1/\\lambda^2$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
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       "    <script type=\"text/javascript\">\n",
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       "            if (p.length==0) return;\n",
       "\n",
       "            while (!p.hasClass(\"cell\")) {\n",
       "                p=p.parent();\n",
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       "                if (p.prop(\"tagName\") ==\"body\") return;\n",
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       "            var cell = p;\n",
       "            cell.find(\".input\").addClass(\"hide-in-slideshow\")\n",
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     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n"
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     "data": {
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2dpPxY8DSpcxcERF3U5KyOZ3aRsRWlNAiKQvIdiUiZgGvqo67JCJe1q5Z0/3t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dpjZs89W//6nTsHDl7q282vDdScyUKTkQFLa06pPW6hDNEZzBWV7ZNpIWABTgRmU4KRKwY7KDN3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\nhxLAB2vbS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      "text/plain": [
       "<matplotlib.figure.Figure at 0x117f476d8>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 398,
       "width": 556
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "sl.hide_code_in_slideshow()\n",
    "from scipy.stats import expon\n",
    "p = 0.3\n",
    "x = np.linspace(expon.ppf(0.01,scale=1/0.3), expon.ppf(0.995,scale=1/0.3), 100)\n",
    "plt.plot(x, expon.pdf(x,scale=1/0.3),'b-', lw=5, alpha=0.6, label='expon pdf')\n",
    "plt.title(r'Exponential PDF.  $\\lambda$ = 0.3',size=14)\n",
    "plt.xlabel(r'x',size=14)\n",
    "plt.ylabel(r'p(x)',size=14)\n",
    "plt.ylim([0,0.4])\n",
    "plt.xlim(xmax=14)\n",
    "print('')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "#### The Poisson Distribution"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "The Poisson Distribution is the limiting form of binomial, when the\n",
    "number of trials goes to infinity, happening at some rate $\\lambda$.\n",
    "\n",
    "$$ P[k \\mbox{ successes in time } T] = (\\lambda T)^k \\frac{e^{- \\lambda T}}{k!}$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "It answers the question: when events happen indepdently at some fixed rate, how many will occur in a given fixed interval?\n",
    "\n",
    "Its mean is $\\lambda T$ and its variance is $\\lambda T$ as well."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div id=\"87cdf9f5ad6ec116\"></div>\n",
       "    <script type=\"text/javascript\">\n",
       "        $(function(){\n",
       "            var p = $(\"#87cdf9f5ad6ec116\");\n",
       "            if (p.length==0) return;\n",
       "\n",
       "            while (!p.hasClass(\"cell\")) {\n",
       "                p=p.parent();\n",
       "\n",
       "                if (p.prop(\"tagName\") ==\"body\") return;\n",
       "            }\n",
       "            var cell = p;\n",
       "            cell.find(\".input\").addClass(\"hide-in-slideshow\")\n",
       "        });\n",
       "    </script>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n"
     ]
    },
    {
     "data": {
      "image/png": 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z9g//V0/UsIHXTNBXz5XLv/4dT51k9AU97m8gz1VFnENxkV+zAoORhso7QK4DngWcn5kf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\nyWz7OXluvlqezw47vmi0ARERwAXZxz7gX8uZIKX0LPAApQ1R3xwRY/1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5ZoSuVwK/rdrt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      "text/plain": [
       "<matplotlib.figure.Figure at 0x114ccd240>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 397,
       "width": 547
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "sl.hide_code_in_slideshow()\n",
    "from scipy.stats import poisson\n",
    "mu = 3\n",
    "x = np.arange(poisson.ppf(0.01, mu), poisson.ppf(0.9995, mu))\n",
    "# plt.ylim([0,1])\n",
    "plt.xlim([-0.5,max(x)+0.5])\n",
    "plt.ylim(ymax=0.4)\n",
    "plt.plot(x, poisson.pmf(x, mu), 'bo', ms=8, label='poisson pmf')\n",
    "plt.vlines(x, 0, poisson.pmf(x, mu), colors='b', lw=5, alpha=0.6)\n",
    "plt.title('Poisson PDF.  $\\lambda T$ = {}'.format(mu),size=14)\n",
    "plt.xlabel(r'k',size=14)\n",
    "plt.ylabel(r'P[X = k]',size=14)\n",
    "print('')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "The Poisson distribution has an interesting role in our perception of randomness (which you can read more about [here](http://www.empiricalzeal.com/2012/12/21/what-does-randomness-look-like/#more-2450)).    \n",
    "\n",
    "The classic example comes from history.  From the above site:\n",
    "\n",
    ">In 1898 Ladislaus Bortkiewicz, a Russian statistician of Polish descent, was trying to understand why, in some years, \n",
    ">an unusually large number of soldiers in the Prussian army were dying due to horse-kicks. In a single army corp, \n",
    ">there were sometimes 4 such deaths in a single year. Was this just coincidence?\n",
    "\n",
    "To assess whether horse-kicks were random (not following any pattern) Bortkiewicz simply compared the number per year to what would be predicted by the Poisson distribution."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div id=\"0234f7956a17d053\"></div>\n",
       "    <script type=\"text/javascript\">\n",
       "        $(function(){\n",
       "            var p = $(\"#0234f7956a17d053\");\n",
       "            if (p.length==0) return;\n",
       "\n",
       "            while (!p.hasClass(\"cell\")) {\n",
       "                p=p.parent();\n",
       "\n",
       "                if (p.prop(\"tagName\") ==\"body\") return;\n",
       "            }\n",
       "            var cell = p;\n",
       "            cell.find(\".input\").addClass(\"hide-in-slideshow\")\n",
       "        });\n",
       "    </script>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Number of Deaths Per Year</th>\n",
       "      <th>Predicted Instances (Poisson)</th>\n",
       "      <th>Observed Instances</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0.0</td>\n",
       "      <td>108.67</td>\n",
       "      <td>109.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1.0</td>\n",
       "      <td>66.29</td>\n",
       "      <td>65.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>2.0</td>\n",
       "      <td>20.22</td>\n",
       "      <td>22.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>3.0</td>\n",
       "      <td>4.11</td>\n",
       "      <td>3.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>4.0</td>\n",
       "      <td>0.63</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>5.0</td>\n",
       "      <td>0.08</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>6.0</td>\n",
       "      <td>0.01</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   Number of Deaths Per Year  Predicted Instances (Poisson)  \\\n",
       "0                        0.0                         108.67   \n",
       "1                        1.0                          66.29   \n",
       "2                        2.0                          20.22   \n",
       "3                        3.0                           4.11   \n",
       "4                        4.0                           0.63   \n",
       "5                        5.0                           0.08   \n",
       "6                        6.0                           0.01   \n",
       "\n",
       "   Observed Instances  \n",
       "0               109.0  \n",
       "1                65.0  \n",
       "2                22.0  \n",
       "3                 3.0  \n",
       "4                 1.0  \n",
       "5                 0.0  \n",
       "6                 0.0  "
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sl.hide_code_in_slideshow()\n",
    "# note that this data is available in 'data/HorseKicks.txt'\n",
    "horse_kicks = pd.DataFrame(\n",
    "data = np.array([\n",
    "[0, 108.67, 109],\n",
    "[1, 66.29, 65],\n",
    "[2, 20.22, 22],\n",
    "[3, 4.11, 3],\n",
    "[4, 0.63, 1],\n",
    "[5, 0.08, 0],\n",
    "[6, 0.01, 0]]),\n",
    "columns = [\"Number of Deaths Per Year\",\"Predicted Instances (Poisson)\",\"Observed Instances\"])\n",
    "horse_kicks"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div id=\"3dc23d621b4df25d\"></div>\n",
       "    <script type=\"text/javascript\">\n",
       "        $(function(){\n",
       "            var p = $(\"#3dc23d621b4df25d\");\n",
       "            if (p.length==0) return;\n",
       "\n",
       "            while (!p.hasClass(\"cell\")) {\n",
       "                p=p.parent();\n",
       "\n",
       "                if (p.prop(\"tagName\") ==\"body\") return;\n",
       "            }\n",
       "            var cell = p;\n",
       "            cell.find(\".input\").addClass(\"hide-in-slideshow\")\n",
       "        });\n",
       "    </script>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n"
     ]
    },
    {
     "data": {
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nkzU23WlSUhJmzZqF9u3bo0qVKrC3t4enpycaN26MDz74AOfOnTO5v8JMWZuUlIRPP/0U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\nxuPPbec6RUlrEeP+USOPetSjBv35vuSSS/Kxj30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pj/oAMEatwWmrV6+2fS4A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\nVQQlqamOo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      "text/plain": [
       "<matplotlib.figure.Figure at 0x118628400>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 377,
       "width": 542
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "sl.hide_code_in_slideshow()\n",
    "horse_kicks[[\"Predicted Instances (Poisson)\",\"Observed Instances\"]].plot.bar()\n",
    "plt.xlabel(\"Number of Deaths Per Year\",size=14)\n",
    "plt.ylabel(\"Count\",size=14)\n",
    "print('')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "The message here is that when events occur at random, we actually tend to perceive them as clustered.   \n",
    "\n",
    "Here is another example:\n",
    "\n",
    "![](figs/pinker-glow-worms-and-stars-plot.jpg)\n",
    "\n",
    "Which of these was generated by a random process ocurring equally likely everywhere?\n",
    "\n",
    "These images are from Steven Pinker’s book, _The Better Angels of our Nature._"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "In the left figure, the number of dots falling into regions of a given size follows the Poisson distribution."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "#### The Uniform Distribution"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "The uniform distribution models the case in which all outcomes are equally probable.  \n",
    "\n",
    "It can be a discrete or continuous distribution.\n",
    "\n",
    "We have already seen the uniform distribution in the case of rolls of a fair die:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div id=\"4b30886076e73280\"></div>\n",
       "    <script type=\"text/javascript\">\n",
       "        $(function(){\n",
       "            var p = $(\"#4b30886076e73280\");\n",
       "            if (p.length==0) return;\n",
       "\n",
       "            while (!p.hasClass(\"cell\")) {\n",
       "                p=p.parent();\n",
       "\n",
       "                if (p.prop(\"tagName\") ==\"body\") return;\n",
       "            }\n",
       "            var cell = p;\n",
       "            cell.find(\".input\").addClass(\"hide-in-slideshow\")\n",
       "        });\n",
       "    </script>"
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     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n"
     ]
    },
    {
     "data": {
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t7suX06S73z23FQMAAABb1nrcdeWlVfXKTC5P+S9JduX/DDi+nOSVSb4nye2T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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x105c2fb38>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 375,
       "width": 541
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "sl.hide_code_in_slideshow()\n",
    "plt.figure()\n",
    "x = np.arange(7)\n",
    "plt.plot(x, 7*[1/6.], 'bo', ms=8)\n",
    "plt.vlines(x, 0, 1/6., colors='b', lw=5, alpha=0.6)\n",
    "plt.xlim([-0.5,6.5])\n",
    "plt.ylim([0,1.1])\n",
    "plt.xlabel('Number of points showing',size=14)\n",
    "plt.ylabel(r'$P[X = x]$',size=14)\n",
    "print('')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "There is an important relationship between the uniform and Poisson distributions.\n",
    "\n",
    "__When the time an event occurs is uniformly distributed, the number of events in a time interval is Poisson distributed.__\n",
    "\n",
    "You can replace \"time\" with \"location\", and so on.\n",
    "\n",
    "Also, the reverse statment is true as well.\n",
    "\n",
    "So a simple way to generate a picture like the scattered points above is to select the $x$ and $y$ coordinates of each point uniformly distributed over the picture size."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "#### The Gaussian Distribution\n",
    "\n",
    "The Gaussian Distribution is also called the Normal Distribution."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "We will make __extensive__ use of Gaussian distribution, for a number of reasons.\n",
    "\n",
    "One of reasons we will use it so much is that it is a good guess for how errors are distributed in data.\n",
    "\n",
    "This comes from the celebrated __Central Limit Theorem__.   Informally, \n",
    "\n",
    ">_The sum of a large number of independent observations from any\n",
    ">distribution with finite variance tends to have a Gaussian\n",
    "> distribution._"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "As a special case, the sum of $n$ independent Gaussian variates is Gaussian.\n",
    "Thus Gaussian processes remain Gaussian after passing through linear\n",
    "systems.   \n",
    "\n",
    "If $X_1$ and $X_2$ are Gaussian, then $X_3 = aX_2 + bX_3$ is Gaussian."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "Thus we can see that one way of thinking of the Gaussian is that it is the\n",
    "limit of the Binomial when $n$ is large, that is, the limit of\n",
    "the sum of many Bernoulli trials.    However many other\n",
    "sums of random variables (not just Bernoulli trials) converge to the\n",
    "Gaussian as well."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "The _standard Gaussian_ distribution has mean zero and a variance (and standard deviation)\n",
    "of 1.   The pdf of the standard Gaussian is:\n",
    "\n",
    "$$ p(x) = \\frac{1}{\\sqrt{2 \\pi}} e^{-x^2/2}. $$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "For an arbitrary Gaussian distribution with mean $\\mu$ and variance\n",
    "$\\sigma^2$, the pdf is simply the standard Gaussian that is relocated to\n",
    "have its center at $\\mu$ and its width scaled by $\\sigma$:\n",
    "\n",
    "$$ p_{\\mu,\\sigma}(x) = \\frac{1}{\\sigma \\sqrt{2 \\pi}} e^{-\\frac{1}{2}\\left(\\frac{x-\\mu}{\\sigma}\\right)^2}. $$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
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beGnLMS8cLakSEYdSiontOEysdwMvzswr6oxVkiRJ/SMilgEHUkb7bNcouK0u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\nAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x114cb5d68>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 398,
       "width": 554
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "sl.hide_code_in_slideshow()\n",
    "from scipy.stats import norm\n",
    "plt.figure()\n",
    "x = np.linspace(norm.ppf(0.001), norm.ppf(0.999), 100)\n",
    "plt.plot(x, norm.pdf(x),'b-', lw=5, alpha=0.6)\n",
    "plt.title(r'Standard Gaussian PDF.  $\\mu = 0, \\sigma = 1$',size=14)\n",
    "plt.xlabel('x',size=14)\n",
    "plt.ylabel(r'$p(x)$',size=14)\n",
    "print('')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div id=\"6ae00990f7205cac\"></div>\n",
       "    <script type=\"text/javascript\">\n",
       "        $(function(){\n",
       "            var p = $(\"#6ae00990f7205cac\");\n",
       "            if (p.length==0) return;\n",
       "\n",
       "            while (!p.hasClass(\"cell\")) {\n",
       "                p=p.parent();\n",
       "\n",
       "                if (p.prop(\"tagName\") ==\"body\") return;\n",
       "            }\n",
       "            var cell = p;\n",
       "            cell.find(\".input\").addClass(\"hide-in-slideshow\")\n",
       "        });\n",
       "    </script>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n"
     ]
    },
    {
     "data": {
      "image/png": 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SM6YGU48p9Rffitx0em3yP6sl5OTFk+S7I0+1Ia7xwF7kL+1TyF/0ngJuSCm9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\nC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      "text/plain": [
       "<matplotlib.figure.Figure at 0x114bf5978>"
      ]
     },
     "metadata": {
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       "width": 545
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "sl.hide_code_in_slideshow()\n",
    "plt.figure()\n",
    "x = np.linspace(norm.ppf(0.001), norm.ppf(0.999), 100)\n",
    "plt.plot(x, norm.cdf(x),'b-', lw=5, alpha = 0.6)\n",
    "plt.title(r'Standard Gaussian CDF.  $\\mu = 0, \\sigma = 1$',size=14)\n",
    "plt.xlabel('x',size=14)\n",
    "plt.ylabel(r'$P[X\\leq x]$',size=14)\n",
    "print('')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Heavy Tails"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "Earlier we discussed high- and low-variability.   \n",
    "\n",
    "All of the distributions we have discussed so far have \"light tails\", meaning that they show low variability.\n",
    "\n",
    "In other words, extremely large observations are essentially impossible."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "However in other cases, extremely large observations can occur.   Distributions that capture this property are called \"heavy tailed\".\n",
    "\n",
    "Some examples of data that can be often modeled using heavy-tailed distributions:\n",
    "\n",
    "* The sizes of files in a file system\n",
    "* The sizes of objects transferred over the Internet\n",
    "* The execution time of jobs on a computer system\n",
    "* The degree of nodes in a network (eg, social network).\n",
    "\n",
    "In practice, random variables that follow heavy tailed distributions\n",
    "are characterized as exhibiting many small observations mixed in with\n",
    "a few large observations.  \n",
    "\n",
    "In such datasets, most of the observations\n",
    "are small, but most of the contribution to the sample mean or variance\n",
    "comes from the rare, large observations."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "#### The Pareto Distribution"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "The Pareto distribution is the simplest continuous heavy-tailed\n",
    "distribution.    \n",
    "\n",
    "Pareto was an Italian economist who studied income distributions.\n",
    "(In fact, income distributions typically show heavy tails.)\n",
    "\n",
    "Its pdf is:\n",
    "\n",
    "$$ p(x) = \\alpha k^{\\alpha} x^{-\\alpha-1}\\;\\;\\; k \\leq x,\\; \\;0 < \\alpha\n",
    "\\leq 2. $$\n",
    "\n",
    "It takes on values in the range $[k, \\infty]$. \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
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       "        $(function(){\n",
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      "\n"
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ZJA9qrX1tlmPs3Lkzxx577Jo/P+aY5G1vm/y+ghEAAIDtYffu3dm9e/SH6Tt3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\nYGoJRgAAAICpJRgBAAAAptb/AQewPP3RW31CAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x118621b70>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 397,
       "width": 547
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "sl.hide_code_in_slideshow()\n",
    "from scipy.stats import pareto\n",
    "alpha = 1.3\n",
    "x = np.linspace(pareto.ppf(0.005,alpha), pareto.ppf(0.995,alpha), 100)\n",
    "plt.plot(x, pareto.pdf(x,alpha),'b-', lw=5, alpha=0.6, label='pareto pdf')\n",
    "plt.title(r'Pareto PDF.  $\\alpha$ = {}'.format(alpha),size=14)\n",
    "plt.xlabel(r'x',size=14)\n",
    "plt.ylabel(r'p(x)',size=14)\n",
    "print('')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "The variance of the Pareto distribution is infinite.  (The corresponding\n",
    "integral diverges.)\n",
    "\n",
    "In practice, this means that a new observation that significantly\n",
    "changes the sample variance is _always_ possible, no matter how many samples\n",
    "of the random variable have already been taken."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "The mean of the Pareto is $\\frac{k\\alpha}{\\alpha-1}$, for $\\alpha > 1$.  \n",
    "\n",
    "But\n",
    "note that as $\\alpha$ decreases, the variability of the Pareto\n",
    "increases.  \n",
    "\n",
    "In fact, for $\\alpha \\leq 1$, the Pareto distribution has\n",
    "_infinite mean._  Again, in practice this means that a swamping\n",
    "observation for the mean is always possible.   \n",
    "\n",
    "Hence the running average\n",
    "of a series of Pareto observations with $\\alpha \\leq 1$ will never\n",
    "converge to a fixed value, and the mean itself is not a useful\n",
    "statistic in this case."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Statistics"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "Statistics: \"The collection, analysis, interpretation, and presentation of masses of data.\""
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Bayes' Rule"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "Bayes' Rule is a simple way of manipulating conditional probabilities in a way that can be very useful."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "Start with a situation in which we are interested in two events, $A_1$ and $A_2$.  These are exhaustive, meaning that in any experiment either $A_1$ or $A_2$ must occur. (They form a partition of $\\Omega$.)\n",
    "\n",
    "Now:\n",
    "\n",
    "$$ P[A_1|B] = \\frac{P[A_1 \\cap B]}{P[B]}$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
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     "slide_type": "fragment"
    }
   },
   "source": [
    "$$ = \\frac{P[A_1 \\cap B]}{P[B|A_1] + P[B|A_2]}$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "$$ = \\frac{P[B|A_1]\\,P[A_1]}{P[B|A_1] + P[B|A_2]}$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "(This is easy to extend to the case where $A_1, A_2, ..., A_n$ form a partition of $\\Omega$.)\n",
    "\n",
    "This formula is useful because often the probabilities $P[B|A_i]$ can be\n",
    "estimated, while the probabilties $P[A_i|B]$ may be hard to estimate."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "We interpret this transformation as updating our estimate of the probability of each $A_i$\n",
    "based on new information, namely, that $B$ is true.   \n",
    "\n",
    "This update\n",
    "transforms the __prior__ probabilities $P[A_i]$ into the \n",
    "__posterior__ probabilities $P[A_i|B]$.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "__Example.__\n",
    "\n",
    "Empirical evidence suggests that amongs sets of twins,\n",
    "about 1/3 are identical.  \n",
    "\n",
    "Assume therefore that probability of a pair of\n",
    "twins being identical to be 1/3.  \n",
    "\n",
    "Now, consider how a couple might\n",
    "update this probability after they get an ultrasound that shows that the\n",
    "twins are of the same gender.   \n",
    "\n",
    "What is their new estimate of the\n",
    "probability that their twins are identical?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "Let $I$ be the event that the twins are identical.  Let $G$ be the event\n",
    "that gender is the same via ultrasound.  \n",
    "\n",
    "The prior probabilities here\n",
    "is $P[I]$.\n",
    "\n",
    "What we want to calculate is the\n",
    "posterior probability $P[I\\,|\\,G]$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "First, we note:\n",
    "\n",
    "$$P[G\\,|\\,I] = 1 $$\n",
    "\n",
    "(Surprisingly, people are sometimes confused about that fact!)   \n",
    "\n",
    "Note that this conditional probability is easy to estimate."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "Also,\n",
    "we assume that if the twins are not identical, they are like any two\n",
    "siblings, _i.e.,_ their probability of being same gender is 1/2: \n",
    "\n",
    "$$P[G\\,|\\,\\bar{I}] = 1/2 $$\n",
    "\n",
    "Again, easy to estimate."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "And we know from observing the population at large that among all sets\n",
    "of twins, about 1/3 are identical:\n",
    "\n",
    "$$ P[I] = 1/3 $$\n",
    "\n",
    "Note that this statistic is easy to obtain from data."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true,
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "Then:\n",
    "\n",
    "$$ P[I\\,|\\,G] = \\frac{P[G\\,|\\,I]\\; P[I]}{P[G\\,|\\,I]\\,P[I] + P[G\\,|\\,\\bar{I}]\\,P[\\bar{I}]} $$\n",
    "\n",
    "$$ = \\frac{1 \\cdot 1/3}{(1 \\cdot 1/3) + (1/2 \\cdot 2/3)} = \\frac{1}{2}$$\n",
    "\n",
    "So we have updated our estimate of the twins being identical from 1/3\n",
    "(prior probability) to 1/2 (posterior probability).\n",
    "\n",
    "We did this in a way that used quantities that were relatively easy to obtain or measure."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Confidence Intervals"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "Say you are concerned with some data that we take as coming from a random process.\n",
    "\n",
    "You want to characterize it as accurately as possible.   You measure it, yielding a\n",
    "single value.  \n",
    "\n",
    "How much does that value tell you?   Can you rely on it as a description of the random process?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "Let's say you have a dataset and you compute its average value.   \n",
    "\n",
    "How certain are you that the average would be the same if you took another dataset from the same source (i.e., the same random process)?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "We think of the hypothetical data source as a random variable with a true mean $\\mu$.\n",
    "\n",
    "We would like to find a range within which we are 90% sure that the\n",
    "true mean $\\mu$ lies.  \n",
    "\n",
    "In other words, we want the probability that the true mean lies in\n",
    "the interval to be 0.9.  This interval is then called the 90% confidence interval."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "To be more precise:  A confidence interval at level $\\gamma$ for a fixed\n",
    "but unknown parameter $m$ is an interval $(a,b)$ such that\n",
    "\n",
    "$$ P[a < m < b] \\geq \\gamma. $$\n",
    "\n",
    "Note that $m$ is fixed --- it is not random.  What is random is the\n",
    "interval $(a, b)$.  This interval is constructed based on the\n",
    "data, which (by assumption) are random."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "![](figs/confidence-intervals.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true,
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Confidence Intervals for the Mean"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "Imagine we have a set of $n$ samples of a random variable,\n",
    "$x_1, x_2, ..., x_n$ Let's assume that the random variable has mean\n",
    "$\\mu$ and variance $\\sigma^2$.\n",
    "\n",
    "An estimate of $\\mu$ is the empirical average of the samples, $\\bar{x}$.   "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "Now, the Central Limit Theorem tells us that the sum of a\n",
    "large number $n$ of random variables, each with mean $\\mu$ and variance\n",
    "$\\sigma^2$, yields a Gaussian random variable with mean\n",
    "$n\\mu$ and variance $n \\sigma^2$.   So the distribution of the average\n",
    "would be normal with mean $\\mu$ and variance $\\sigma^2 / n$.  That\n",
    "is, \n",
    "\n",
    "$$ \\bar{x} \\sim N(\\mu, \\sigma/\\sqrt{n}) $$\n",
    "\n",
    "We usually assume that the number of samples should be 30 or more for\n",
    "the CLT to hold.   While the specific value 30 is a bit shaky, we will usually be\n",
    "using very large samples (datasets) in this course for which this assumption is \n",
    "valid."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "The standard deviation of the sample mean is called the standard error.\n",
    "\n",
    "Notice that the standard error decreases as we increase the sample size, according to $1/\\sqrt{n}.$\n",
    "\n",
    "So it will turn out that using $\\bar{x}$, we can get\n",
    "increasingly \"tight\" estimates of $\\mu$ as we increase the number of\n",
    "samples $n$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "Now, remember that the true mean $\\mu$ is a constant, while the\n",
    "empirical mean $\\bar{x}$ is a random variable.   \n",
    "\n",
    "Let us assume for a\n",
    "moment that we know the true $\\mu$ and $\\sigma$, and that we accept that\n",
    "$\\bar{x}$ has a $N(\\mu, \\sigma/\\sqrt{n})$ distribution.   "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "Then it is\n",
    "true that \n",
    "\n",
    "$$ P[\\mu-k\\sigma/\\sqrt{n} < \\bar{x} < \\mu+k\\sigma/\\sqrt{n}] = P[-k < S <\n",
    "k]$$\n",
    "\n",
    "where $S$ is the standard Gaussian random variable (having distribution $N(0,1)$)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "We write $z_{1-\\alpha/2}$ to be the $1-\\alpha/2$ quantile of the\n",
    "unit normal.  That is, \n",
    "\n",
    "$$ P[-z_{1-\\alpha/2} < S < z_{1-\\alpha/2}] = 1-\\alpha.$$\n",
    "\n",
    "So to form a 90% probability interval for $S$ (centered on\n",
    "zero) we choose $k = z_{0.95}$.  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
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HpQuUHUY4EU4u+w2i5klFln91onxL9NxKuEP4he1JuMB6Py+ebRtwjKTaPnnz/Dlvv30A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bfeyTaOJLUwiyqSpIo0diy8+27NArUvADvgx54kFVsA/ptrf4vzznMXIEmti98uJUkV6eabY0Hv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\nRZIkSZIkqQeTKpIkSZIkST38H+9cwqtPsMtbAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1132e34a8>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 397,
       "width": 554
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "sl.hide_code_in_slideshow()\n",
    "from scipy.stats import norm\n",
    "plt.figure()\n",
    "x = np.linspace(norm.ppf(0.001), norm.ppf(0.999), 100)\n",
    "x90 = np.linspace(norm.ppf(0.05), norm.ppf(0.95), 100)\n",
    "plt.plot(x, norm.pdf(x),'b-')\n",
    "plt.fill_between(x90, 0, norm.pdf(x90))\n",
    "plt.title(r'90% region for Standard Gaussian',size=14)\n",
    "plt.xlabel('x',size=14)\n",
    "plt.ylabel(r'$p(x)$',size=14)\n",
    "print('')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "Turning back to $\\bar{x}$, the\n",
    "90% probability interval on $\\bar{x}$ would be:\n",
    "\n",
    "$$ \\mu-z_{0.95}\\sigma/\\sqrt{n} < \\bar{x} <\n",
    "\\mu+z_{0.95}\\sigma/\\sqrt{n}. $$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "The last step: by a simple argument, we can show that the sample mean is \n",
    "in some fixed-size interval centered on the true mean, if and only if the true\n",
    "mean is also in\n",
    "a fixed-size interval (of the same size) centered on the sample mean."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "This means that:\n",
    "\\begin{eqnarray*}\n",
    "  1-\\alpha & = & P[\\mu-z_{1-\\alpha/2}\\sigma/\\sqrt{N} < \\bar{x} <\n",
    "\\mu+z_{1-\\alpha/2}\\sigma/\\sqrt{N}]\\\\\n",
    "& = & P[\\bar{x}-k\\sigma\\sqrt{N} < \\mu < \\bar{x}+k\\sigma/\\sqrt{N}].\n",
    "\\end{eqnarray*}\n",
    "This latter expression defines the __$1-\\alpha$ confidence interval\n",
    "  for the mean.__"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "We are done, except for estimating $\\sigma$.  We do this\n",
    "directly from the data: $\\hat{\\sigma} = s$\n",
    "(where $s$ is the sample standard deviation, $s = \\sqrt{1/(n-1) \\sum (x_i\n",
    "- \\bar{x})^2}$)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "To summarize: by the argument presented here, a 100(1-$\\alpha$)%\n",
    "confidence interval for the population mean is given by\n",
    "\n",
    "$$\\bar{x} \\pm  z_{1-\\alpha/2} \\, \\frac{s}{\\sqrt{n}}. $$\n",
    "\n",
    "As an example, a 95% confidence interval for the mean is the sample average plus or minus two standard errors."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
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   "source": [
    "### Confidence Intervals for the Median"
   ]
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   "source": [
    "A $p$th percentile of a distribution is the value $m_p$ such that $P[X <\n",
    "m_p] = p$.   For example, the median is the 50th percentile."
   ]
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   "source": [
    "Say we start with a set of $n$ i.i.d. observations of an RV $X$. \n",
    "\n",
    "The true $p$th percentile of $X$ is $m_p$ by definition.  "
   ]
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   "source": [
    "Each observation\n",
    "$X_i$ therefore has probability $p$ of being below the corresponding\n",
    "percentile $m_p$.  \n",
    "\n",
    "What is the probability that exactly $j$ of the\n",
    "observations are less than $m_p$?  "
   ]
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    "This is a standard coin-flipping\n",
    "problem --- it is given by the Binomial: $B_{n,p}(j)$.\n",
    "\n",
    "$$ P[\\mbox{exactly }j\\mbox{ observations are less than } m_p] = B_{n,p}(j). $$"
   ]
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   "source": [
    "  \n",
    "We can write this compactly using _order statistics._  For a set\n",
    "of values $X_1, X_2, ..., X_n$ the order statistics are obtained by\n",
    "simply sorting the set.  This yields $X_{(1)}, X_{(2)}, ..., X_{(n)}$ ---\n",
    "so that, for example, $X_{(1)}$ is the smallest of the values and\n",
    "$X_{(n)}$ is the largest."
   ]
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   "cell_type": "markdown",
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   "source": [
    "Then the above expression can be written:\n",
    "\n",
    "$$ P[X_{(j)} < m_p \\leq X_{(j+1)}] = B_{n,p}(j). $$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
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     "slide_type": "fragment"
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   "source": [
    "Now we can string consecutive intervals together if we like, yielding:\n",
    "\n",
    "$$ P[X_{(j)} < m_p \\leq X_{(k)}] = \\sum_{i=j}^k B_{n,p}(i). $$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "Now look at this from another standpoint.  \n",
    "\n",
    "The above expression also\n",
    "can be read as giving the probability that the $p$th percentile lies between\n",
    "$X_{(j)}$ and $X_{(k)}$.   "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
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     "slide_type": "fragment"
    }
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   "source": [
    "Let's say the sum on the right evaluates to\n",
    "$\\gamma$.   \n",
    "\n",
    "Then we have shown that $(X_{(j)}, X_{(k)})$ is a confidence\n",
    "interval at level $\\gamma$ for $m_p$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "To use this in practice, let's say we have a set of $n$ measurements and\n",
    "we want to find the $\\gamma$ confidence interval for $p$th percentile.\n",
    "\n",
    "Then we just \n",
    "need to find integers $j$ and $k$ so that \n",
    "\n",
    "$$ \\sum_{i=j}^k B_{n,p}(i) \\geq \\gamma. $$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "This can be aided if we have a table of the cumulative distribution of\n",
    "the binomial $F_{n,p}(k)$.   Then we need to find $j$ and $k$ such that\n",
    "\n",
    "$$ F_{n,p}(k) -  F_{n,p}(j) \\geq \\gamma. $$\n",
    "\n",
    "(Remember also that when $np$ is large, we can approximate the binomial\n",
    "by the Normal distribution)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "__Example.__  Let's say we want the 95% confidence interval for the\n",
    "median, based on the following dataset:\n",
    "\n",
    "3, 1, 9, 7, 11, 15, 12, 4, 17, 10.\n",
    "\n",
    "We can compute that for $n = 10$ and $p = 0.5$,  $F_{n,p}(9) -\n",
    "F_{n,p}(2) \\geq 0.95$.  The order statistics are:\n",
    "\n",
    "1, 3, 4, 7, 9, 10, 11, 12, 15, 17.\n",
    "\n",
    "Then our estimate of the median is 9.5, and the confidence interval is (3,\n",
    "15)."
   ]
  }
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