elections.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Pandas, Statistics, And Elections"
   ]
  },
  {
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     "text": [
      "//anaconda/envs/py3l/lib/python3.6/site-packages/matplotlib/__init__.py:855: MatplotlibDeprecationWarning: \n",
      "examples.directory is deprecated; in the future, examples will be found relative to the 'datapath' directory.\n",
      "  \"found relative to the 'datapath' directory.\".format(key))\n",
      "//anaconda/envs/py3l/lib/python3.6/site-packages/matplotlib/__init__.py:846: MatplotlibDeprecationWarning: \n",
      "The text.latex.unicode rcparam was deprecated in Matplotlib 2.2 and will be removed in 3.1.\n",
      "  \"2.2\", name=key, obj_type=\"rcparam\", addendum=addendum)\n"
     ]
    }
   ],
   "source": [
    "%matplotlib inline\n",
    "import numpy as np\n",
    "import scipy as sp\n",
    "import matplotlib as mpl\n",
    "import matplotlib.cm as cm\n",
    "import matplotlib.pyplot as plt\n",
    "import pandas as pd\n",
    "import seaborn.apionly as sns # conda install seaborn or pip install seaborn"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Random Variables\n",
    "\n",
    "A **random variable** is a mapping from a sample space to the set of real numbers. It assigns a real number to each outcome in the sample space.\n",
    "\n",
    "For example, consider the event of a coin toss that we have seen before. There are two outcomes in the sample space, a heads and a tails. We can ask the question, whats the probability of a heads or a tails? For an unbiased coin, these are, by symmetry, 1/2 each. The random variable here is the number of heads, and its probability is P(0)=1/2, and P(1)=1/2.\n",
    "\n",
    "Another random variable is the number of heads in two coin tosses. There, as we have seen before, P(0)=1/4, P(1)=1/2, P(2)=1/4.\n",
    "\n",
    "Random variables provide the link from events and sample spaces to data, and it is their **probability distribution** that we are interested in.\n",
    "\n",
    "A random variable is called **discrete** if it has a countable number of values. The technical definition of countable is that there is a 1-1 correspondence with the integers 1,2,3... . The number of heads in 2 coin tosses is a discrete random variable.\n",
    "\n",
    "#### Bernoulli Random Variables\n",
    "\n",
    "The **Bernoulli Distribution** represents the distribution for coin flips. Let the random variable X represent such a coin flip, where X=1 is heads, and X=0 is tails. Let us further say that the probability of heads is p (p=0.5 is a fair coin). \n",
    "\n",
    "We then say:\n",
    "\n",
    "$$X \\sim Bernoulli(p),$$\n",
    "\n",
    "which is to be read as **X has distribution Bernoulli(p)**. The **probability distribution function (pdf)** or **probability mass function** associated with the Bernoulli distribution is\n",
    "\n",
    "\\begin{eqnarray}\n",
    "P(X = 1) &=& p \\\\\n",
    "P(X = 0) &=& 1 - p \n",
    "\\end{eqnarray}\n",
    "\n",
    "for p in the range 0 to 1. \n",
    "The **pdf**, or the probability that random variable $X=x$ may thus be written as \n",
    "\n",
    "$$P(X=x) = p^x(1-p)^{1-x}$$\n",
    "\n",
    "for x in the set {0,1}.\n",
    "\n",
    "The **mean**, or **expected value** of this distribution can be calculated analogously to the mean value of data by noting that $X=1$ happens with frequency $p*N$ and thus it is p. \n",
    "\n",
    "Let us engage in some term defining right now, since we will use these terms throught the book. $X$ is a random variable, and when we say $X=x$ we are asking \"*what if the random variable X takes the value x*. \n",
    "\n",
    "$P(X=x)$ asks: what is the probability that the random variable X takes the value x. \n",
    "\n",
    "Finally $p$ is a parameter of the Bernoulli distribution, and as we have seen, one of the things we want to do in data analysis is: having seen some data, what can we infer to be the values of p, so that we can make future predictions for X."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Dataframes with Pandas\n",
    "\n",
    "For reference, here is a useful [pandas cheat sheet](https://drive.google.com/folderview?id=0ByIrJAE4KMTtaGhRcXkxNHhmY2M&usp=sharing).\n",
    "\n",
    "Often data is stored in comma separated values (CSV) files. CSV files can be output by any spreadsheet software, and are plain text, hence are a great way to share data.\n",
    "\n",
    "Here we are reading in a spreadsheet of the number of electoral votes in the American Electoral College."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>State</th>\n",
       "      <th>Votes</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>California</td>\n",
       "      <td>55</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>Texas</td>\n",
       "      <td>38</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>New York</td>\n",
       "      <td>29</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>Florida</td>\n",
       "      <td>29</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>Illinois</td>\n",
       "      <td>20</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "        State  Votes\n",
       "0  California     55\n",
       "1       Texas     38\n",
       "2    New York     29\n",
       "3     Florida     29\n",
       "4    Illinois     20"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "electoral_votes = pd.read_csv(\"data/electoral_votes.csv\")\n",
    "electoral_votes.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "`electoral_votes` is a dataframe."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The actual file looks something like this:\n",
    "\n",
    "```\n",
    "State,Votes\n",
    "California,55\n",
    "Texas,38\n",
    "New York,29\n",
    "Florida,29\n",
    "Illinois,20\n",
    "Pennsylvania,20\n",
    "```\n",
    "You can see that an index has been added, and its numerical, and starts at 0 (like in the lists). This index is not particularly useful, so lets set the state column as the index."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Votes</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>State</th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>California</th>\n",
       "      <td>55</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Texas</th>\n",
       "      <td>38</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>New York</th>\n",
       "      <td>29</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Florida</th>\n",
       "      <td>29</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Illinois</th>\n",
       "      <td>20</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "            Votes\n",
       "State            \n",
       "California     55\n",
       "Texas          38\n",
       "New York       29\n",
       "Florida        29\n",
       "Illinois       20"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "electoral_votes = electoral_votes.set_index('State')\n",
    "electoral_votes.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Notice how we used the `electoral_votes` variable twice in a line above. Pandas returns new objects in memory when we do something to a dataframe (here, setting the index). We relabel the new memory with the same label.\n",
    "\n",
    "What happens to the old memory? When nothing refers to it, Python \"garbage collects\" it."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### The Predictwise distribution revisited\n",
    "\n",
    "Let is go to Predictiwise election predictions. There, on OCt 8 2012, we took a set of probabilities, one per state that Predictwise gave us on October 12th to make a prediction of the \"empirical\" distribution of votes that Obama would get, come election day.\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "\n",
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       "\n",
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       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Obama</th>\n",
       "      <th>Romney</th>\n",
       "      <th>Votes</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>States</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>Alabama</th>\n",
       "      <td>0.000</td>\n",
       "      <td>1.000</td>\n",
       "      <td>9</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Alaska</th>\n",
       "      <td>0.000</td>\n",
       "      <td>1.000</td>\n",
       "      <td>3</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Arizona</th>\n",
       "      <td>0.062</td>\n",
       "      <td>0.938</td>\n",
       "      <td>11</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Arkansas</th>\n",
       "      <td>0.000</td>\n",
       "      <td>1.000</td>\n",
       "      <td>6</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>California</th>\n",
       "      <td>1.000</td>\n",
       "      <td>0.000</td>\n",
       "      <td>55</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "            Obama  Romney  Votes\n",
       "States                          \n",
       "Alabama     0.000   1.000      9\n",
       "Alaska      0.000   1.000      3\n",
       "Arizona     0.062   0.938     11\n",
       "Arkansas    0.000   1.000      6\n",
       "California  1.000   0.000     55"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "predictwise = pd.read_csv('data/predictwise.csv').set_index('States')\n",
    "predictwise.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "What we have now is a spreadsheet with indexed rows and named columns, called a dataframe in pandas.  \n",
    "\n",
    "`predictwise` is an instance of the pd.DataFrame class, created by calling the pd.read_csv \"constructor function\".\n",
    "\n",
    "`predictwise` is a dataframe object, and it has methods (functions) belonging to it. For example, `predictwise.head()` is a method that shows the first 5 rows of the dataframe.\n",
    "\n",
    "A pandas dataframe is a set of columns pasted together into a spreadsheet, as shown in the schematic below, which is taken from the cheatsheet above. The columns in pandas are called series objects.\n",
    "\n",
    "![](images/pandastruct.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Simulate an election"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "9957"
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     "execution_count": 5,
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   "source": [
    "def simulate_election(model, n_sim):\n",
    "    simulations = np.random.uniform(size=(51, n_sim))\n",
    "    obama_votes = (simulations < model.Obama.values.reshape(-1, 1)) * model.Votes.values.reshape(-1, 1)\n",
    "    #summing over rows gives the total electoral votes for each simulation\n",
    "    return obama_votes.sum(axis=0)\n",
    "result = simulate_election(predictwise, 10000)\n",
    "np.sum(result >= 269) #run multiple times to see result change"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let us parse the intent of the above code a bit. We run 10,000 simulations. In each one of these simulations, we toss 51 different biased coins, and assign the vote to obama is the output of `np.random.uniform` is less than the probablity of an obama win. \n",
    "\n",
    "The first thing to pick up on here is that `np.random.uniform` gives you a random number between 0 and 1, uniformly. In other words, the number is equally likely to be between 0 and 0.1, 0.1 and 0.2, and so on. This is a very intuitive idea, but it is formalized by the notion of the **Uniform Distribution**.\n",
    "\n",
    "We then say:\n",
    "\n",
    "$$X \\sim Uniform([0,1),$$\n",
    "\n",
    "which is to be read as **X has distribution Uniform([0,1])**. The **probability distribution function (pdf)** associated with the Uniform distribution is\n",
    "\n",
    "\\begin{eqnarray}\n",
    "P(X = x) &=& 1 \\, for \\, x \\in [0,1] \\\\\n",
    "P(X = x) &=& 0 \\, for \\, x \\notin [0,1]\n",
    "\\end{eqnarray}\n",
    "\n",
    "We use this trick of sampling from a Uniform distribution ti sumulate multiple draws from each of the 51 bernoulli distribitions we have, one for each state.\n",
    "\n",
    "Now for any Obama probability less than 1.0, there are simulations in which Obama wont win that state, and this will induce fluctuations and a distribution on the total number of electoral college votes that Obama gets (when we sum over all states). And this is what we see in the histogram below. "
   ]
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      "//anaconda/envs/py3l/lib/python3.6/site-packages/matplotlib/axes/_axes.py:6521: MatplotlibDeprecationWarning: \n",
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\n",
      "text/plain": [
       "<Figure size 921.6x633.6 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "def plot_simulation(simulation):    \n",
    "    plt.hist(simulation, bins=np.arange(200, 538, 1), \n",
    "             label='simulations', align='left', normed=True)\n",
    "    plt.axvline(332, 0, .5, color='r', label='Actual Outcome')\n",
    "    plt.axvline(269, 0, .5, color='k', label='Victory Threshold')\n",
    "    p05 = np.percentile(simulation, 5.)\n",
    "    p95 = np.percentile(simulation, 95.)\n",
    "    iq = int(p95 - p05)\n",
    "    pwin = ((simulation >= 269).mean() * 100)\n",
    "    plt.title(\"Chance of Obama Victory: %0.2f%%, Spread: %d votes\" % (pwin, iq))\n",
    "    plt.legend(frameon=False, loc='upper left')\n",
    "    plt.xlabel(\"Obama Electoral College Votes\")\n",
    "    plt.ylabel(\"Probability\")\n",
    "    sns.despine()\n",
    "with sns.plotting_context('poster'):\n",
    "    plot_simulation(result)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This is an empirical **Probability Mass Function** or **Probability Density Function**. The concept of Mass Function is used when the outcomes come from a discrete set, rather than a continuous set. The word **density** is strictly used when the random variable X takes on continuous values, as in the uniform distribution, rather than discrete values such as here, but we'll abuse the language and use the word probability distribution in both cases.\n",
    "\n",
    "Lets summarize: the way the density arose here that we did ran 10,000 tosses (for each state), and depending on the value, assigned the state to Obama or Romney, and then summed up the electoral votes over the states.\n",
    "\n",
    "There is a second, very useful question, we can ask of any such probability density: what is the probability that a random variable is less than some value. In other words: $P(X < x)$. This is *also* a probability distribution and is called the **Cumulative Distribution Function**, or CDF (sometimes just called the **distribution**, as opposed to the **density**). Its obtained by \"summing\" the probability density function for all $X$ less than $x$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Obama Win CDF at votes= 200  is  0.0\n",
      "Obama Win CDF at votes= 300  is  0.1445\n",
      "Obama Win CDF at votes= 320  is  0.4484\n",
      "Obama Win CDF at votes= 340  is  0.838\n",
      "Obama Win CDF at votes= 360  is  0.9971\n",
      "Obama Win CDF at votes= 400  is  1.0\n",
      "Obama Win CDF at votes= 500  is  1.0\n"
     ]
    }
   ],
   "source": [
    "CDF = lambda x: np.float(np.sum(result < x))/result.shape[0]\n",
    "for votes in [200, 300, 320, 340, 360, 400, 500]:\n",
    "    print(\"Obama Win CDF at votes=\", votes, \" is \", CDF(votes))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false,
    "figure_type": "m"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, 'probability of Obama win')"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "votelist=np.arange(0, 540, 5)\n",
    "plt.plot(votelist, [CDF(v) for v in votelist], '.-');\n",
    "plt.xlim([200,400])\n",
    "plt.xlabel(\"votes for Obama\")\n",
    "plt.ylabel(\"probability of Obama win\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### The Gaussian Distribution\n",
    "\n",
    "The sampling distribution of the mean itself has a mean $\\mu$ and variance $s^2 = \\frac{\\sigma^2}{N}$. This distribution is called the **Gaussian** or **Normal Distribution**, and is probably the most important distribution in all of statistics.\n",
    "\n",
    "The probability density of the normal distribution is given as:\n",
    "\n",
    "$$ N(x, \\mu, \\sigma) = \\frac{1}{s\\sqrt{2\\pi}} e^{ -\\frac{(x-\\mu)^2}{2s^2} } .$$\n",
    "\n",
    "$s$ is called the **standard error**."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Lets step back and try and think about what this all means. As an example, say I have a weight-watchers' study of 1000 people, whose average weight is 150 lbs with standard deviation of 30lbs. If I was to randomly choose many samples of 100 people each, the mean weights of those samples would cluster around 150lbs with a standard error of 30/$\\sqrt{100}$ = 3lbs. Now if i gave you a different sample of 100 people with an average weight of 170lbs, this weight would be more than 6 standard errors beyond the population mean, ^[this example is motivated by the crazy bus example in Charles Whelan's excellent Naked Statistics Book] and would thus be very unlikely to be from the weight watchers group."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The expected value of the Gaussian distribution is $E[X]=\\mu$ and the variance is $Var[X]=s^2$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 0, '$x$')"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x432 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "norm =  sp.stats.norm\n",
    "x = np.linspace(-5,5, num=200)\n",
    "colors=sns.color_palette()\n",
    "\n",
    "fig = plt.figure(figsize=(12,6))\n",
    "for mu, s, c in zip([0.5]*3, [0.2, 0.5, 0.8], colors):\n",
    "    plt.plot(x, norm.pdf(x, mu, s), lw=2, \n",
    "             c=c, label = r\"$\\mu = {0:.1f}, s={1:.1f}$\".format(mu, s))\n",
    "    plt.fill_between(x, norm.pdf(x, mu, s), color=c, alpha = .4)\n",
    "    \n",
    "    \n",
    "plt.xlim([-5,5])\n",
    "plt.legend(loc=0)\n",
    "plt.ylabel(\"PDF at $x$\")\n",
    "plt.xlabel(\"$x$\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### The Central Limit Theorem\n",
    "\n",
    "The reason for the distribution's importance is the Central Limit Theorem(CLT). The theorem is stated as thus, very similar to the law of large numbers:\n",
    "\n",
    "**Let $x_1,x_2,...,x_n$ be a sequence of independent, identically-distributed (IID) random variables from a random variable $X$. Suppose that $X$ has the finite mean $\\mu$ AND finite variance $\\sigma^2$. Then the average of the first n of them:**\n",
    "\n",
    "$$S_n = \\frac{1}{n} \\sum_{i=1}^{n} x_i ,$$\n",
    "\n",
    "**converges to a Gaussian Random Variable with mean $\\mu$ and variance $\\sigma^2/n$ as $n \\to \\infty$:**\n",
    "\n",
    "$$ S_n \\sim N(\\mu,\\frac{\\sigma^2}{n}) \\, as \\, n \\to \\infty. $$\n",
    "\n",
    "In other words:\n",
    "\n",
    "$$s^2 = \\frac{\\sigma^2}{N}.$$\n",
    "\n",
    "\n",
    "This is true, *regardless* of the shape of $X$, which could be binomial, poisson, or any other distribution."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Strictly speaking, under some conditions ^[REF :Lyapunov conditions], the variables $x_i$ dont have to be identically distributed, as long as $\\mu$ is the mean of the means and $\\sigma^2$ is the sum of the individual variances. This has major consequences, for the importance of this theorem.\n",
    "\n",
    "Many random variables can be thought of as having come from the sum of a large number of small and independent effects. For example human height or weight can be thought of as the sum as a large number of genetic and environmental factors, which add to increase or decrease height or weight respectively. Or think of a measurement of a height. There are lots of ways things could go wrong: frayed tapes, stretched tapes, smudged marks, bad lining up of the eye, etc. These are all independent and have no systematic error in one direction or the other.\n",
    "\n",
    "Then the sum of these factors, as long as there are a large number of them, will be distributed as a gaussian.\n",
    "\n",
    "As a rule of thumb, the CLT starts holding at $N \\sim 30$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "#### An application to elections: Binomial distribution in the large n, large k limit\n",
    "\n",
    "For example, consider the binomial distribution Binomial(n,k, p) in the limit of large n. The number of successes k in n trials can be ragarded as the sum of n IID Bernoulli variables with values 1 or 0. Obviously this is applicable to a large sequence of coin tosses, or to the binomial sampling issue that we encountered earlier in the case of the polling. \n",
    "\n",
    "Using the CLT we can replace the binomial distribution at large n by a gaussian where k is now a continuous variable, and whose mean is the mean of the binomial $np$ and whose variance is $np(1-p)$, since\n",
    "\n",
    "$$S_n \\sim N(p, \\frac{p(1-p)}{n}).$$\n",
    "\n",
    "The accuracy of this approximation depends on the variance. A large variance makes for a broad distribution spanning many discrete k, thus justifying the transition from a discrete to a continuous distribution.\n",
    "\n",
    "This approximation is used a lot in studying elections. For example, suppose I told you that I'd polled 1000 people in Ohio and found that 600 would vote Democratic, and 400 republican. Imagine that this 1000 is a \"sample\" drawn from the voting \"population\" of Ohio. Assume then that these are 1000 independent bernoulli trials with p=600/1000 = 0.6. Then we can say that, from the CLT, the mean of the sampling distribution of the mean of the bernoulli or equivalently the binomial is 0.6, with a variance of $0.6*0.4/1000 = 0.00024$. Thus the standard deviation is 0.015 for a mean of 0.6, or 1.5% on a mean of 60% voting Democratic.  This 1.5% if part of what pollsters quote as the margin of error of a candidates winning; they often include other factors such as errors in polling methodology.\n",
    "\n",
    "If one has results from multiple pollsters, one can treat them as independent samples from the voting population. Then the average from these samples will approach the average in the population, with the sample means distributed normally around it."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### What does this all mean?\n",
    "\n",
    "The sample mean, or mean of the random variables $x_{mi}$ in the sample $m$, has a sampling distribution with mean $\\mu$ and variance $\\frac{\\sigma^2}{N}$, as shown before. Now for large sample sizes we can go further and use the CLT theorem to say that this distribution is the normal distribution,\n",
    "\n",
    "$$S_N \\sim N(\\mu, \\frac{\\sigma^2}{N})$$.\n",
    "\n",
    "The preciseness of saying that we have a gaussian is a huge gain in our expository power. For example, for the case of the weight-watchers program above, a separation of 20lbs is more than 3 standard errors away, which corresponds to being way in the tail of a gaussian distribution. Because we can now quantify the area under the curve, we can say that 99.7\\% of the sample means lie within 9lbs of 150. Thus you can way easily reject the possibility that the new sample is from the weight-watchers program with 99.7\\% confidence. \n",
    "\n",
    "Indeed, the CLT allows us to take the reduction in variance we get from large samples, and make statements in different cases that are quite strong:\n",
    "\n",
    "1. if we know a lot about the population, and randomly sampled 100 points from it, the sample mean would be with 99.7\\% confidence within $0.3\\sigma$ of the population mean. And thus, if $\\sigma$ is small, the sample mean is quite representative of the population mean.\n",
    "2. The reverse: if we have a well sampled 100 data points, we could make strong statements about the population as a whole. This is indeed how election polling and other sampling works. \n",
    "3. we can infer, as we just did, if a sample is consistent with a population\n",
    "4. by the same token, you can compare two samples and infer if they are from the same population."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### An application: Gallup Party Affiliation Poll\n",
    "\n",
    "Earlier we had used the Predictwise probabilities from Octover 12th to create a predictive model for the elections. This time, armed with what we have learnt in this chapter, we will try to **estimate** our own win probabilities to plug into our predictive model.\n",
    "\n",
    "We will start with a simple forecast model. We will try to predict the outcome of the election based the estimated proportion of people in each state who identify with one one political party or the other.\n",
    "\n",
    "Gallup measures the political leaning of each state, based on asking random people which party they identify or affiliate with. [Here's the data](http://www.gallup.com/poll/156437/heavily-democratic-states-concentrated-east.aspx#2) they collected from January-June of 2012:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Democrat</th>\n",
       "      <th>Republican</th>\n",
       "      <th>Dem_Adv</th>\n",
       "      <th>N</th>\n",
       "      <th>Unknown</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>State</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>Alabama</th>\n",
       "      <td>36.0</td>\n",
       "      <td>49.6</td>\n",
       "      <td>-13.6</td>\n",
       "      <td>3197</td>\n",
       "      <td>14.4</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Alaska</th>\n",
       "      <td>35.9</td>\n",
       "      <td>44.3</td>\n",
       "      <td>-8.4</td>\n",
       "      <td>402</td>\n",
       "      <td>19.8</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Arizona</th>\n",
       "      <td>39.8</td>\n",
       "      <td>47.3</td>\n",
       "      <td>-7.5</td>\n",
       "      <td>4325</td>\n",
       "      <td>12.9</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Arkansas</th>\n",
       "      <td>41.5</td>\n",
       "      <td>40.8</td>\n",
       "      <td>0.7</td>\n",
       "      <td>2071</td>\n",
       "      <td>17.7</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>California</th>\n",
       "      <td>48.3</td>\n",
       "      <td>34.6</td>\n",
       "      <td>13.7</td>\n",
       "      <td>16197</td>\n",
       "      <td>17.1</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "            Democrat  Republican  Dem_Adv      N  Unknown\n",
       "State                                                    \n",
       "Alabama         36.0        49.6    -13.6   3197     14.4\n",
       "Alaska          35.9        44.3     -8.4    402     19.8\n",
       "Arizona         39.8        47.3     -7.5   4325     12.9\n",
       "Arkansas        41.5        40.8      0.7   2071     17.7\n",
       "California      48.3        34.6     13.7  16197     17.1"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "gallup_2012=pd.read_csv(\"data/g12.csv\").set_index('State')\n",
    "gallup_2012[\"Unknown\"] = 100 - gallup_2012.Democrat - gallup_2012.Republican\n",
    "gallup_2012.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Each row lists a state, the percent of surveyed individuals who identify as Democrat/Republican, the percent whose identification is unknown or who haven't made an affiliation yet, the margin between Democrats and Republicans (`Dem_Adv`: the percentage identifying as Democrats minus the percentage identifying as Republicans), and the number `N` of people surveyed."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can construct sub-dataframes by using an array-like indexing syntax"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Dem_Adv</th>\n",
       "      <th>Unknown</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>State</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>Alabama</th>\n",
       "      <td>-13.6</td>\n",
       "      <td>14.4</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Alaska</th>\n",
       "      <td>-8.4</td>\n",
       "      <td>19.8</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Arizona</th>\n",
       "      <td>-7.5</td>\n",
       "      <td>12.9</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Arkansas</th>\n",
       "      <td>0.7</td>\n",
       "      <td>17.7</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>California</th>\n",
       "      <td>13.7</td>\n",
       "      <td>17.1</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "            Dem_Adv  Unknown\n",
       "State                       \n",
       "Alabama       -13.6     14.4\n",
       "Alaska         -8.4     19.8\n",
       "Arizona        -7.5     12.9\n",
       "Arkansas        0.7     17.7\n",
       "California     13.7     17.1"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "gallup_2012[['Dem_Adv', 'Unknown']].head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The most obvious source of error in the Gallup data is the finite sample size -- Gallup did not poll *everybody* in America, and thus the party affilitions are subject to sampling errors. How much uncertainty does this introduce? Lets estimate the sampling error using what we learnt in the last section"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Democrat</th>\n",
       "      <th>Republican</th>\n",
       "      <th>Dem_Adv</th>\n",
       "      <th>N</th>\n",
       "      <th>Unknown</th>\n",
       "      <th>SE_percentage</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>State</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>Alabama</th>\n",
       "      <td>36.0</td>\n",
       "      <td>49.6</td>\n",
       "      <td>-13.6</td>\n",
       "      <td>3197</td>\n",
       "      <td>14.4</td>\n",
       "      <td>0.848926</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Alaska</th>\n",
       "      <td>35.9</td>\n",
       "      <td>44.3</td>\n",
       "      <td>-8.4</td>\n",
       "      <td>402</td>\n",
       "      <td>19.8</td>\n",
       "      <td>2.392562</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Arizona</th>\n",
       "      <td>39.8</td>\n",
       "      <td>47.3</td>\n",
       "      <td>-7.5</td>\n",
       "      <td>4325</td>\n",
       "      <td>12.9</td>\n",
       "      <td>0.744298</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Arkansas</th>\n",
       "      <td>41.5</td>\n",
       "      <td>40.8</td>\n",
       "      <td>0.7</td>\n",
       "      <td>2071</td>\n",
       "      <td>17.7</td>\n",
       "      <td>1.082709</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>California</th>\n",
       "      <td>48.3</td>\n",
       "      <td>34.6</td>\n",
       "      <td>13.7</td>\n",
       "      <td>16197</td>\n",
       "      <td>17.1</td>\n",
       "      <td>0.392646</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "            Democrat  Republican  Dem_Adv      N  Unknown  SE_percentage\n",
       "State                                                                   \n",
       "Alabama         36.0        49.6    -13.6   3197     14.4       0.848926\n",
       "Alaska          35.9        44.3     -8.4    402     19.8       2.392562\n",
       "Arizona         39.8        47.3     -7.5   4325     12.9       0.744298\n",
       "Arkansas        41.5        40.8      0.7   2071     17.7       1.082709\n",
       "California      48.3        34.6     13.7  16197     17.1       0.392646"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "gallup_2012[\"SE_percentage\"]=100.0*np.sqrt((gallup_2012.Democrat/100.)*((100. - gallup_2012.Democrat)/100.)/(gallup_2012.N))\n",
    "gallup_2012.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "On their [webpage](http://www.gallup.com/poll/156437/heavily-democratic-states-concentrated-east.aspx#2) discussing these data, Gallup notes that the sampling error for the states is between 3 and 6%, with it being 3% for most states. This is more than what we find, so lets go with what Gallup says.\n",
    "\n",
    "We now use Gallup's estimate of 3% to build a Gallup model with some uncertainty. We will, using the CLT, assume that the sampling distribution of the Obama win percentage is a gaussian with mean the democrat percentage and standard error the sampling error of 3\\%. \n",
    "\n",
    "We'll build the model in the function `uncertain_gallup_model`, and return a forecast where the probability of an Obama victory is given by the probability that a sample from the `Dem_Adv` Gaussian is positive.\n",
    "\n",
    "To do this we simply need to find the area under the curve of a Gaussian that is on the positive side of the x-axis.\n",
    "The probability that a sample from a Gaussian with mean $\\mu$ and standard deviation $\\sigma$ exceeds a threhold $z$ can be found using $1$ minus the Cumulative Distribution Function, or the survival function of a Gaussian:\n",
    "\n",
    "$$ SF(z) = 1 - CDF(z) $$\n",
    "\n",
    "$$\n",
    "1 - CDF(z) = \\frac1{2}\\left(1 + {\\mathrm erf}\\left(\\frac{z - \\mu}{\\sqrt{2 \\sigma^2}}\\right)\\right) \n",
    "$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "#from scipy.special import erf\n",
    "def uncertain_gallup_model(gallup):\n",
    "    sigma = 3\n",
    "    #prob =  .5 * (1 + erf(gallup.Dem_Adv / np.sqrt(2 * sigma**2)))\n",
    "    prob = norm.sf(0, gallup.Dem_Adv, sigma)\n",
    "    return pd.DataFrame(dict(Obama=prob), index=gallup.index)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We now have two dataframes with state names as an index. Lets **join** these to produce a wider one with all the data we have. This is identical to a SQL inner join."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "model = uncertain_gallup_model(gallup_2012)\n",
    "model = model.join(electoral_votes)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Obama</th>\n",
       "      <th>Votes</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>State</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>Alabama</th>\n",
       "      <td>0.000003</td>\n",
       "      <td>9</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Alaska</th>\n",
       "      <td>0.002555</td>\n",
       "      <td>3</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Arizona</th>\n",
       "      <td>0.006210</td>\n",
       "      <td>11</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Arkansas</th>\n",
       "      <td>0.592249</td>\n",
       "      <td>6</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>California</th>\n",
       "      <td>0.999998</td>\n",
       "      <td>55</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "               Obama  Votes\n",
       "State                      \n",
       "Alabama     0.000003      9\n",
       "Alaska      0.002555      3\n",
       "Arizona     0.006210     11\n",
       "Arkansas    0.592249      6\n",
       "California  0.999998     55"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "You can make simple plots very easily with pandas:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "model.Votes.hist(bins=15);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 648x1296 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(9, 18))\n",
    "gallup_2012.sort_values('Dem_Adv')['Dem_Adv'].plot(kind=\"barh\", color=\"r\");"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "What exactly is in a Pandas Series? Lets see:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "State\n",
       "Alabama                  9\n",
       "Alaska                   3\n",
       "Arizona                 11\n",
       "Arkansas                 6\n",
       "California              55\n",
       "Colorado                 9\n",
       "Connecticut              7\n",
       "Delaware                 3\n",
       "District of Columbia     3\n",
       "Florida                 29\n",
       "Georgia                 16\n",
       "Hawaii                   4\n",
       "Idaho                    4\n",
       "Illinois                20\n",
       "Indiana                 11\n",
       "Iowa                     6\n",
       "Kansas                   6\n",
       "Kentucky                 8\n",
       "Louisiana                8\n",
       "Maine                    4\n",
       "Maryland                10\n",
       "Massachusetts           11\n",
       "Michigan                16\n",
       "Minnesota               10\n",
       "Mississippi              6\n",
       "Missouri                10\n",
       "Montana                  3\n",
       "Nebraska                 5\n",
       "Nevada                   6\n",
       "New Hampshire            4\n",
       "New Jersey              14\n",
       "New Mexico               5\n",
       "New York                29\n",
       "North Carolina          15\n",
       "North Dakota             3\n",
       "Ohio                    18\n",
       "Oklahoma                 7\n",
       "Oregon                   7\n",
       "Pennsylvania            20\n",
       "Rhode Island             4\n",
       "South Carolina           9\n",
       "South Dakota             3\n",
       "Tennessee               11\n",
       "Texas                   38\n",
       "Utah                     6\n",
       "Vermont                  3\n",
       "Virginia                13\n",
       "Washington              12\n",
       "West Virginia            5\n",
       "Wisconsin               10\n",
       "Wyoming                  3\n",
       "Name: Votes, dtype: int64"
      ]
     },
     "execution_count": 34,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "votes_series = model.Votes\n",
    "votes_series"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "pandas.core.series.Series"
      ]
     },
     "execution_count": 35,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "type(votes_series)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We might want to get back to numpy:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 9,  3, 11,  6, 55,  9,  7,  3,  3, 29, 16,  4,  4, 20, 11,  6,  6,\n",
       "        8,  8,  4, 10, 11, 16, 10,  6, 10,  3,  5,  6,  4, 14,  5, 29, 15,\n",
       "        3, 18,  7,  7, 20,  4,  9,  3, 11, 38,  6,  3, 13, 12,  5, 10,  3])"
      ]
     },
     "execution_count": 36,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "votes_series.values"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[2.90300406e-06, 9.00000000e+00],\n",
       "       [2.55513033e-03, 3.00000000e+00],\n",
       "       [6.20966533e-03, 1.10000000e+01],\n",
       "       [5.92248712e-01, 6.00000000e+00],\n",
       "       [9.99997522e-01, 5.50000000e+01],\n",
       "       [4.15182197e-02, 9.00000000e+00],\n",
       "       [9.99999858e-01, 7.00000000e+00],\n",
       "       [9.99999997e-01, 3.00000000e+00],\n",
       "       [1.00000000e+00, 3.00000000e+00],\n",
       "       [5.92248712e-01, 2.90000000e+01],\n",
       "       [9.12112197e-02, 1.60000000e+01],\n",
       "       [1.00000000e+00, 4.00000000e+00],\n",
       "       [2.76210947e-24, 4.00000000e+00],\n",
       "       [9.99986654e-01, 2.00000000e+01],\n",
       "       [1.27634855e-02, 1.10000000e+01],\n",
       "       [7.25746882e-01, 6.00000000e+00],\n",
       "       [8.83796687e-09, 6.00000000e+00],\n",
       "       [5.53035117e-01, 8.00000000e+00],\n",
       "       [5.47992917e-02, 8.00000000e+00],\n",
       "       [9.28766623e-01, 4.00000000e+00],\n",
       "       [1.00000000e+00, 1.00000000e+01],\n",
       "       [1.00000000e+00, 1.10000000e+01],\n",
       "       [9.99892200e-01, 1.60000000e+01],\n",
       "       [9.99663071e-01, 1.00000000e+01],\n",
       "       [9.81532863e-03, 6.00000000e+00],\n",
       "       [9.68004846e-02, 1.00000000e+01],\n",
       "       [2.47770531e-06, 3.00000000e+00],\n",
       "       [1.19960226e-10, 5.00000000e+00],\n",
       "       [8.07566592e-02, 6.00000000e+00],\n",
       "       [3.08537539e-01, 4.00000000e+00],\n",
       "       [9.99936791e-01, 1.40000000e+01],\n",
       "       [8.84930330e-01, 5.00000000e+00],\n",
       "       [1.00000000e+00, 2.90000000e+01],\n",
       "       [5.26576464e-01, 1.50000000e+01],\n",
       "       [5.41254391e-06, 3.00000000e+00],\n",
       "       [8.84930330e-01, 1.80000000e+01],\n",
       "       [8.64165209e-04, 7.00000000e+00],\n",
       "       [9.96533026e-01, 7.00000000e+00],\n",
       "       [9.58481780e-01, 2.00000000e+01],\n",
       "       [1.00000000e+00, 4.00000000e+00],\n",
       "       [3.64424071e-05, 9.00000000e+00],\n",
       "       [2.27501319e-02, 3.00000000e+00],\n",
       "       [2.55513033e-03, 1.10000000e+01],\n",
       "       [2.65975740e-02, 3.80000000e+01],\n",
       "       [1.64628831e-39, 6.00000000e+00],\n",
       "       [9.99998201e-01, 3.00000000e+00],\n",
       "       [1.58655254e-01, 1.30000000e+01],\n",
       "       [9.99455891e-01, 1.20000000e+01],\n",
       "       [8.71462851e-01, 5.00000000e+00],\n",
       "       [8.24676055e-01, 1.00000000e+01],\n",
       "       [1.06633208e-23, 3.00000000e+00]])"
      ]
     },
     "execution_count": 38,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model[['Obama', 'Votes']].values # get 2d"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Simulate!\n",
    "\n",
    "We plot a map of these probabilities as before, run the simulation, and display the results"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([326, 333, 329, ..., 320, 294, 313])"
      ]
     },
     "execution_count": 39,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "prediction = simulate_election(model, 10000)\n",
    "prediction"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x648 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from statesplot import make_map, load_states_geom\n",
    "s2p = load_states_geom(\"data/us-states.json\")\n",
    "make_map(s2p, model.Obama, \"P(Obama): Gallup\");"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [],
   "source": [
    "def plot_simulation(simulation):    \n",
    "    plt.hist(simulation, bins=np.arange(200, 538, 1), \n",
    "             label='simulations', align='left', normed=True)\n",
    "    plt.axvline(332, 0, .5, color='r', label='Actual Outcome')\n",
    "    plt.axvline(269, 0, .5, color='k', label='Victory Threshold')\n",
    "    p05 = np.percentile(simulation, 5.)\n",
    "    p95 = np.percentile(simulation, 95.)\n",
    "    iq = int(p95 - p05)\n",
    "    pwin = ((simulation >= 269).mean() * 100)\n",
    "    plt.title(\"Chance of Obama Victory: %0.2f%%, Spread: %d votes\" % (pwin, iq))\n",
    "    plt.legend(frameon=False, loc='upper left')\n",
    "    plt.xlabel(\"Obama Electoral College Votes\")\n",
    "    plt.ylabel(\"Probability\")\n",
    "    sns.despine()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "//anaconda/envs/py3l/lib/python3.6/site-packages/matplotlib/axes/_axes.py:6521: MatplotlibDeprecationWarning: \n",
      "The 'normed' kwarg was deprecated in Matplotlib 2.1 and will be removed in 3.1. Use 'density' instead.\n",
      "  alternative=\"'density'\", removal=\"3.1\")\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 921.6x633.6 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "with sns.plotting_context('poster'):\n",
    "    plot_simulation(prediction)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The predictive distribution is consistent with the real data -- the real outcome seems like a typical outcome according to the model. The accuracy is not very good as the center of the distribution falls fairly far from the observed outcome, but the precision is only marginally worse than in the predictwise case.\n",
    "\n",
    "But note that we used the Gallup voter self-identification from January to June to predict this, so we do not expect to do too well. And even though this is probably not a very unbiased sample, it still makes us wonder: at 97\\% of simulations showing a win for Obama, why did Romney ever think he had a chance?"
   ]
  }
 ],
 "metadata": {
  "celltoolbar": "Edit Metadata",
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.6.8"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}