Bayesian Methods

gistfile1.ipynb

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      "Probabilistic Programming\n",
      "=====\n",
      "and Bayesian Methods for Hackers \n",
      "========\n",
      "\n",
      "#####Version 0.1\n",
      "Welcome to *Bayesian Methods for Hackers*. The full Github repository, and additional chapters, is available at [github/Probabilistic-Programming-and-Bayesian-Methods-for-Hackers](https://github.com/CamDavidsonPilon/Probabilistic-Programming-and-Bayesian-Methods-for-Hackers). We hope you enjoy the book, and we encourage any contributions!"
     ]
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     "source": [
      "Chapter 1\n",
      "======\n",
      "***"
     ]
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      "The Philosophy of Bayesian Inference\n",
      "------\n",
      "  \n",
      "> You are a skilled programmer, but bugs still slip into your code. After a particularly difficult implementation of an algorithm, you decide to test your code on a trivial example. It passes. You test the code on a harder problem. It passes once again. And it passes the next, *even more difficult*, test too! You are starting to believe that there may be no bugs in this code...\n",
      "\n",
      "If you think this way, then congratulations, you already are a Bayesian practitioner! Bayesian inference is simply updating your beliefs after considering new evidence. A Bayesian can rarely be certain about a result, but he or she can be very confident. Just like in the example above, we can never be 100% sure that our code is bug-free unless we test it on every possible problem; something rarely possible in practice. Instead, we can test it on a large number of problems, and if it succeeds we can feel more *confident* about our code.  Bayesian inference works identically: we update our beliefs about an outcome; rarely can we be absolutely sure unless we rule out all other alternatives. \n"
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      "\n",
      "###The Bayesian state of mind\n",
      "\n",
      "\n",
      "Bayesian inference differs from more traditional statistical inference by preserving *uncertainty* about our beliefs. At first, this sounds like a bad statistical technique. Isn't statistics all about deriving *certainty* from randomness? To reconcile this, we need to start thinking like Bayesians. \n",
      "\n",
      "The Bayesian world-view interprets probability as measure of *believability in an event*, that is, how confident we are in an event occurring. In fact, we will see in a moment that this is the natural interpretation of probability. \n",
      "\n",
      "For this to be clearer, we consider an alternative interpretation of probability: *Frequentist* methods assume that probability is the long-run frequency of events (hence the bestowed title). For example, the *probability of plane accidents* under a frequentist philosophy is interpreted as the *long-term frequency of plane accidents*. This makes logical sense for many probabilities of events, but becomes more difficult to understand when events have no long-term frequency of occurrences. Consider: we often assign probabilities to outcomes of presidential elections, but the election itself only happens once! Frequentists get around this by invoking alternative realities and saying across all these universes, the frequency of occurrences defines the probability. \n",
      "\n",
      "Bayesians, on the other hand, have a more intuitive approach. Bayesians interpret a probability as measure of *belief*, or confidence, of an event occurring. An individual who assigns a belief of 0 to an event has no confidence that the event will occur; conversely, assigning a belief of 1 implies that the individual is absolutely certain of an event occurring. Beliefs between 0 and 1 allow for weightings of other outcomes. This definition agrees with the probability of a plane accident example, for having observed the frequency of plane accidents, an individual's belief should be equal to that frequency, excluding any outside information. Similarly, under this definition of probability being equal to beliefs, it is clear how we can speak about probabilities (beliefs) of presidential election outcomes: how confident are you candidate A will win?\n",
      "\n",
      "Notice in the paragraph above, I assigned the belief (probability) measure to an *individual*, not to Nature. This is very interesting, as this definition leaves room for conflicting beliefs between individuals. Again, this is appropriate for what naturally occurs: different individuals have different beliefs of events occurring, because they possess different *information* about the world. Consider the following examples demonstrating the relationship between individual beliefs and probabilities:\n",
      "\n",
      "- I flip a coin, and we both guess the result. We would both agree, assuming the coin is fair, that the probability of heads is 1/2. Assume, then, that I peek at the coin. Now I know for certain what the result is: I assign probability 1.0 to either heads or tails. Now what is *your* belief that the coin is heads? My knowledge of the outcome has not changed the coin's results. Thus we assign different probabilities to the result. \n",
      "\n",
      "-  Your code either has a bug in it or not, but we do not know for certain which is true. Though we have a belief about the presence or absence of a bug.  \n",
      "\n",
      "-  A medical patient is exhibiting symptoms $x$, $y$ and $z$. There are a number of diseases that could be causing all of them, but only a single disease is present. A doctor has beliefs about which disease.\n",
      "\n",
      "\n",
      "This philosophy of treating beliefs as probability is natural to humans. We employ it constantly as we interact with the world and only see partial evidence. Alternatively, you have to be *trained* to think like a frequentist. \n",
      "\n",
      "To align ourselves with traditional probability notation, we denote our belief about event $A$ as $P(A)$. We call this quantity the *prior probability*.\n",
      "\n",
      "John Maynard Keynes, a great economist and thinker, said \"When the facts change, I change my mind. What do you do, sir?\" This quote reflects the way a Bayesian updates his or her beliefs after seeing evidence. Even — especially — if the evidence is counter to what was initially believed, the evidence cannot be ignored. We denote our updated belief as $P(A |X )$, interpreted as the probability of $A$ given the evidence $X$. We call the updated belief the *posterior probability* so as to contrast it with the prior probability. For example, consider the posterior probabilities (read: posterior beliefs) of the above examples, after observing some evidence $X$.:\n",
      "\n",
      "1\\. $P(A): \\;\\;$ the coin has a 50 percent chance of being heads. $P(A | X):\\;\\;$ You look at the coin, observe a heads has landed, denote this information $X$, and trivially assign probability 1.0 to heads and 0.0 to tails.\n",
      "\n",
      "2\\.   $P(A): \\;\\;$  This big, complex code likely has a bug in it. $P(A | X): \\;\\;$ The code passed all $X$ tests; there still might be a bug, but its presence is less likely now.\n",
      "\n",
      "3\\.  $P(A):\\;\\;$ The patient could have any number of diseases. $P(A | X):\\;\\;$ Performing a blood test generated evidence $X$, ruling out some of the possible diseases from consideration.\n",
      "\n",
      "\n",
      "It's clear that in each example we did not completely discard the prior belief after seeing new evidence $X$, but we *re-weighted the prior* to incorporate the new evidence (i.e. we put more weight, or confidence, on some beliefs versus others). \n",
      "\n",
      "By introducing prior uncertainty about events, we are already admitting that any guess we make is potentially very wrong. After observing data, evidence, or other information, we update our beliefs, and our guess becomes *less wrong*. This is the alternative side of the prediction coin, where typically we try to be *more right*.\n"
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      "\n",
      "###Bayesian Inference in Practice\n",
      "\n",
      " If frequentist and Bayesian inference were programming functions, with inputs being statistical problems, then the two would be different in what they return to the user. The frequentist inference function would return a number, whereas the Bayesian function would return *probabilities*.\n",
      "\n",
      "For example, in our debugging problem above, calling the frequentist function with the argument \"My code passed all $X$ tests; is my code bug-free?\" would return a *YES*. On the other hand, asking our Bayesian function \"Often my code has bugs. My code passed all $X$ tests; is my code bug-free?\" would return something very different: a probabilities of *YES* and *NO*. The function might return:\n",
      "\n",
      "\n",
      ">    *YES*, with probability 0.8; *NO*, with probability 0.2\n",
      "\n",
      "\n",
      "\n",
      "This is very different from the answer the frequentist function returned. Notice that the Bayesian function accepted an additional argument:  *\"Often my code has bugs\"*. This parameter is the *prior*. By including the prior parameter, we are telling the Bayesian function to include our belief about the situation. Technically this parameter in the Bayesian function is optional, but we will see excluding it has its own consequences. \n",
      "\n",
      "\n",
      "####Incorporating evidence\n",
      "\n",
      "As we acquire more and more instances of evidence, our prior belief is *washed out* by the new evidence. This is to be expected. For example, if your prior belief is something ridiculous, like \"I expect the sun to explode today\", and each day you are proved wrong, you would hope that any inference would correct you, or at least align your beliefs better. Bayesian inference will correct this belief.\n",
      "\n",
      "\n",
      "Denote $N$ as the number of instances of evidence we possess. As we gather an *infinite* amount of evidence, say as $N \\rightarrow \\infty$, our Bayesian results align with frequentist results. Hence for large $N$, statistical inference is more or less objective. On the other hand, for small $N$, inference is much more *unstable*: frequentist estimates have more variance and larger confidence intervals. This is where Bayesian analysis excels. By introducing a prior, and returning probabilities (instead of a scalar estimate), we *preserve the uncertainty* that reflects the instability of statistical inference of a small $N$ dataset. \n",
      "\n",
      "One may think that for large $N$, one can be indifferent between the two techniques since they offer similar inference, and might lean towards the computational-simpler, frequentist methods. An individual in this position should consider the following quote by Andrew Gelman (2005)[1], before making such a decision:\n",
      "\n",
      "> Sample sizes are never large. If $N$ is too small to get a sufficiently-precise estimate, you need to get more data (or make more assumptions). But once $N$ is \"large enough,\" you can start subdividing the data to learn more (for example, in a public opinion poll, once you have a good estimate for the entire country, you can estimate among men and women, northerners and southerners, different age groups, etc.). $N$ is never enough because if it were \"enough\" you'd already be on to the next problem for which you need more data.\n",
      "\n",
      "### Are frequentist methods incorrect then? \n",
      "\n",
      "**No.**\n",
      "\n",
      "Frequentist methods are still useful or state-of-the-art in many areas. Tools like Least Squares linear regression, LASSO regression, EM algorithm etc. are all very powerful and incredibly fast. Bayesian methods are a compliment to solve the problems these solutions cannot or to gain further insight into the underlying system by offering more flexibility in modeling.\n",
      "\n",
      "\n",
      "#### A note on *Big Data*\n",
      "Paradoxically, big data's predictive analytic problems are actually solved by relatively simple algorithms [2][4]. Thus we can argue that big data's prediction difficulty does not lie in the algorithm used, but instead on the computational difficulties of storage and execution on big data. (One should also consider Gelman's quote from above and ask \"Do I really have big data?\" )\n",
      "\n",
      "The much more difficult analytic problems involve *medium data* and, especially troublesome, *really small data*. Using a similar argument as  Gelman's above, if big data problems are *big enough* to be readily solved, then we should be more interested in the *not-quite-big enough* datasets. \n"
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      "### Our Bayesian framework\n",
      "\n",
      "We are interested in beliefs, which can be interpreted as probabilities by thinking Bayesian. We have a *prior* belief in event $A$, beliefs formed by previous information, e.g., our prior belief about bugs being in our code before performing tests.\n",
      "\n",
      "Secondly, we observe our evidence. To continue our buggy-code example: if our code passes $X$ tests, we want to update our belief to incorporate this. We call this new belief the *posterior* probability. Updating our belief is done via the following equation, known as Bayes' Theorem, after its discoverer Thomas Bayes:\n",
      "\n",
      "\\begin{align}\n",
      " P( A | X ) = & \\frac{ P(X | A) P(A) } {P(X) } \\\\\\\\[5pt]\n",
      "& \\propto P(X | A) P(A)\\;\\; (\\propto \\text{is proportional to } )\n",
      "\\end{align}\n",
      "\n",
      "The above formula is not unique to Bayesian inference: it is a mathematical fact with uses outside Bayesian inference. Bayesian inference merely uses it to connect prior probabilities $P(A)$ with an updated posterior probabilities $P(A | X )$."
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      "##### Example: Mandatory coin-flip example\n",
      "\n",
      "Every statistics text must contain a coin-flipping example, I'll use it here to get it out of the way. Suppose, naively, that you are unsure about the probability of heads in a coin flip (spoiler alert: it's 50%). You believe there is some true underlying ratio, call it $p$, but have no prior opinion on what $p$ might be. \n",
      "\n",
      "We begin to flip a coin, and record the observations: either $H$ or $T$. This is our observed data. An interesting question to ask is how our inference changes as we observe more and more data? More specifically, what do our posterior probabilities look like when we have little data, versus when we have lots of data. \n",
      "\n",
      "Below we plot a sequence of updating posterior probabilities as we observe increasing amounts of data (coin flips)."
     ]
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      "\"\"\"\n",
      "The book uses a custom matplotlibrc file, which provides the unique styles for matplotlib plots.\n",
      "If executing this book, and you wish to use the book's styling, provided are two options:\n",
      "    1. Overwrite your own matplotlibrc file with the rc-file provided in the book's styles/ dir.\n",
      "       See http://matplotlib.org/users/customizing.html\n",
      "    2. Also in the styles is  bmh_matplotlibrc.json file. This can be used to update the styles\n",
      "       in only this notebook. Try running the following code:\n",
      "\n",
      "        import json\n",
      "        s = json.load( open(\"../styles/bmh_matplotlibrc.json\") )\n",
      "        matplotlib.rcParams.update(s)\n",
      "\n",
      "\"\"\"\n",
      "\n",
      "#the code below can be passed over, as it is currently not important.\n",
      "%pylab inline\n",
      "figsize( 11, 9)\n",
      "\n",
      "import scipy.stats as stats\n",
      "\n",
      "dist = stats.beta\n",
      "n_trials = [0,1,2,3,4,5,8,15, 50, 500]\n",
      "data = stats.bernoulli.rvs(0.5, size = n_trials[-1] )\n",
      "x = np.linspace(0,1,100)\n",
      "\n",
      "for k, N in enumerate(n_trials):\n",
      "    sx = subplot( len(n_trials)/2, 2, k+1)\n",
      "    \n",
      "    plt.setp(sx.get_yticklabels(), visible=False)\n",
      "    heads = data[:N].sum()\n",
      "    y = dist.pdf(x, 1 + heads, 1 + N - heads )\n",
      "    plt.plot( x, y, label= \"observe %d tosses,\\n %d heads\"%(N,heads) )\n",
      "    plt.fill_between( x, 0, y, color=\"#348ABD\", alpha = 0.4 )\n",
      "    plt.vlines( 0.5, 0, 4, color = \"k\", linestyles = \"--\", lw=1 )\n",
      "    \n",
      "    leg = plt.legend()\n",
      "    leg.get_frame().set_alpha(0.4)\n",
      "    plt.autoscale(tight = True)\n",
      "\n",
      "\n",
      "plt.suptitle( \"Bayesian updating of posterior probabilities\", \n",
      "              y = 1.02,\n",
      "              fontsize = 14);\n",
      "\n",
      "plt.tight_layout()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "Welcome to pylab, a matplotlib-based Python environment [backend: module://IPython.zmq.pylab.backend_inline].\n",
        "For more information, type 'help(pylab)'.\n"
       ]
      },
      {
       "output_type": "display_data",
       "png": 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1Gl27dnX/l0eKpLRznhIpMUeTJ0/GihUrvB2GzNtzIG62tqE4dz6Is21gAUHk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1qwYAF2u53f/OY3eL1eQqEQBw8eZPfu3UBkxye73Y7VauXw4cM88cQT0Z+96qqrOHToEGvWrCEY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ITY2h6UgpWwp30+r2ztEvLi4+7UOvUY8LCwtxuVx4PB7/6zU1NWRnZzNu3DgWLlxIY2Nju7+v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\nQgTt/wPDC4KH3y6D3AAAAABJRU5ErkJggg==\n"
      }
     ],
     "prompt_number": 9
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "The posterior probabilities are represented by the curves, and our confidence is proportional to the height of the curve. As the plot above shows, as we start to observe data our posterior probabilities start to shift and move around. Eventually, as we observe more and more data (coin-flips), our probabilities will lump closer and closer around the true value of $p=0.5$ (marked by a dashed line). \n",
      "\n",
      "Notice that the plots are not always *peaked* at 0.5. There is no reason it should be: recall we assumed we did not have a prior opinion of what $p$ is. In fact, if we observe quite extreme data, say 8 flips and only 1 observed heads, our distribution would look very biased *away* from lumping around 0.5. As more data accumulates, we would see more and more probability being assigned at $p=0.5$.\n",
      "\n",
      "The next example is a simple demonstration of the mathematics of Bayesian inference. "
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "#####Example: Bug, or just sweet, unintended feature?\n",
      "\n",
      "\n",
      "Let $A$ denote the event that our code has **no bugs** in it. Let $X$ denote the event that the code passes all debugging tests. For now, we will leave the prior probability of no bugs as a variable, i.e. $P(A) = p$. \n",
      "\n",
      "We are interested in $P(A|X)$, i.e. the probability of no bugs, given our debugging tests $X$. To use the formula above, we need to compute some quantities.\n",
      "\n",
      "What is $P(X | A)$, i.e., the probability that the code passes $X$ tests *given* there are no bugs? Well, it is equal to 1, for a code with no bugs will pass all tests. \n",
      "\n",
      "$P(X)$ is a little bit trickier: The event $X$ can be divided into two possibilities, event $X$ occurring even though our code *indeed has* bugs (denoted $\\sim A\\;$, spoken *not $A$*), or event $X$ without bugs ($A$). $P(X)$ can be represented as:"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "\\begin{align}\n",
      "P(X ) & = P(X \\text{ and } A) + P(X \\text{ and } \\sim A) \\\\\\\\[5pt]\n",
      " & = P(X|A)P(A) + P(X | \\sim A)P(\\sim A)\\\\\\\\[5pt]\n",
      "& = P(X|A)p + P(X | \\sim A)(1-p)\n",
      "\\end{align}"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "We have already computed $P(X|A)$ above. On the other hand, $P(X | \\sim A)$ is subjective: our code can pass tests but still have a bug in it, though the probability there is a bug present is reduced. Note this is dependent on the number of tests performed, the degree of complication in the tests, etc. Let's be conservative and assign $P(X|\\sim A) = 0.5$. Then\n",
      "\n",
      "\\begin{align}\n",
      "P(A | X) & = \\frac{1\\cdot p}{ 1\\cdot p +0.5 (1-p) } \\\\\\\\\n",
      "& = \\frac{ 2 p}{1+p}\n",
      "\\end{align}\n",
      "This is the posterior probability. What does it look like as a function of our prior, $p \\in [0,1]$? "
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "figsize(12.5,4)\n",
      "p = np.linspace( 0,1, 50)\n",
      "plt.plot( p, 2*p/(1+p), color = \"#348ABD\", lw = 3 )\n",
      "#plt.fill_between( p, 2*p/(1+p), alpha = .5, facecolor = [\"#A60628\"])\n",
      "plt.scatter( 0.2, 2*(0.2)/1.2, s = 140, c =\"#348ABD\"  )\n",
      "plt.xlim( 0, 1)\n",
      "plt.ylim( 0, 1)\n",
      "plt.xlabel( \"Prior, $P(A) = p$\")\n",
      "plt.ylabel(\"Posterior, $P(A|X)$, with $P(A) = p$\")\n",
      "plt.title( \"Are there bugs in my code?\");"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "display_data",
       "png": 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zE3PmzIHRaOT89ERERBLVtLThVFmjqaDPq9ait1+nX+mfT+oo6v3VDuyfJ6Iu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\nRERkRv4fQx4Bwq/BWx0AAAAASUVORK5CYII=\n"
      }
     ],
     "prompt_number": 19
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "We can see the biggest gains if we observe the $X$ tests passed when the prior probability, $p$, is low. Let's settle on a specific value for the prior. I'm a strong programmer (I think), so I'm going to give myself a realistic prior of 0.20, that is, there is a 20% chance that I write code bug-free. To be more realistic, this prior should be a function of how complicated and large the code is, but let's pin it at 0.20. Then my updated belief that my code is bug-free is 0.33. \n",
      "\n",
      "Recall that the prior is a probability: $p$ is the prior probability that there *are no bugs*, so $1-p$ is the prior probability that there *are bugs*.\n",
      "\n",
      "Similarly, our posterior is also a probability, with $P(A | X)$ the probability there is no bug *given we saw all tests pass*, hence $1-P(A|X)$ is the probability there is a bug *given all tests passed*. What does our posterior probability look like? Below is a graph of both the prior and the posterior probabilities. \n"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "figsize( 12.5, 4 )\n",
      "colours = [\"#348ABD\", \"#A60628\"]\n",
      "\n",
      "prior = [0.20, 0.80]\n",
      "posterior =  [1./3, 2./3]\n",
      "plt.bar( [0,.7], prior ,alpha = 0.70, width = 0.25, \\\n",
      "            color = colours[0], label = \"prior distribution\",\n",
      "             lw = \"3\", edgecolor = colours[0])\n",
      "\n",
      "\n",
      "plt.bar( [0+0.25,.7+0.25], posterior ,alpha = 0.7, \\\n",
      "          width = 0.25, color =  colours[1], \n",
      "          label = \"posterior distribution\",\n",
      "          lw = \"3\", edgecolor = colours[1])\n",
      "\n",
      "plt.xticks( [0.20,.95], [\"Bugs Absent\", \"Bugs Present\"] )\n",
      "plt.title(\"Prior and Posterior probability of bugs present, prior = 0.2\")\n",
      "plt.ylabel(\"Probability\")\n",
      "plt.legend(loc=\"upper left\");"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "display_data",
       "png": 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vX2RkZGDhwoUYP348Tp8+LfeJiYnBu+++i7y8PHTp0qXa2GPHjkVAQABOnz6N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\nDiipbv7IxDoAAAAASUVORK5CYII=\n"
      }
     ],
     "prompt_number": 1
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Notice that after we observed $X$ occur, the probability of bugs being absent increased. By increasing the number of tests, we can approach confidence (probability 1) that there are no bugs present.\n",
      "\n",
      "This was a very simple example of Bayesian inference and Bayes rule. Unfortunately, the mathematics necessary to perform more complicated Bayesian inference only becomes more difficult, except for artificially constructed cases. We will later see that this type of mathematical analysis is actually unnecessary. First we must broaden our modeling tools. The next section deals with *probability distributions*. If you are already familiar, feel free to skip (or at least skim), but for the less familiar the next section is essential."
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "_______\n",
      "\n",
      "##Probability Distributions\n",
      "\n",
      "\n",
      "**Let's quickly recall what a probability distribution is:** Let $Z$ be some random variable. Then associated with $Z$ is a *probability distribution function* that assigns probabilities to the different outcomes $Z$ can take. Graphically, a probability distribution is a curve where the probability of an outcome is proportional to the height of the curve. You can see examples in the first figure of this chapter. \n",
      "\n",
      "We can divide random variables into three classifications:\n",
      "\n",
      "-   **$Z$ is discrete**: Discrete random variables may only assume values on a specified list. Things like populations, movie ratings, and number of votes are all discrete random variables. Discrete random variables become more clear when we contrast them with...\n",
      "\n",
      "-   **$Z$ is continuous**: Continuous random variable can take on arbitrarily exact values. For example, temperature, speed, time, color are all modeled as continuous variables because you can progressively make the values more and more precise.\n",
      "\n",
      "- **$Z$ is mixed**: Mixed random variables assign probabilities to both discrete and continuous random variables, i.e. it is a combination of the above two categories. \n",
      "\n",
      "###Discrete Case\n",
      "If $Z$ is discrete, then its distribution is called a *probability mass function*, which measures the probability $Z$ takes on the value $k$, denoted $P(Z=k)$. Note that the probability mass function completely describes the random variable $Z$, that is, if we know the mass function, we know how $Z$ should behave. There are popular probability mass functions that consistently appear: we will introduce them as needed, but let's introduce the first very useful probability mass function. We say $Z$ is *Poisson*-distributed if:\n",
      "\n",
      "$$P(Z = k) =\\frac{ \\lambda^k e^{-\\lambda} }{k!}, \\; \\; k=0,1,2, \\dots $$\n",
      "\n",
      "What is $\\lambda$? It is called the parameter, and it describes the shape of the distribution. For the Poisson random variable, $\\lambda$ can be any positive number. By increasing $\\lambda$, we add more probability to larger values, and conversely by decreasing $\\lambda$ we add more probability to smaller values. Unlike $\\lambda$, which can be any positive number, $k$ must be a non-negative integer, i.e., $k$ must take on values 0,1,2, and so on. This is very important, because if you wanted to model a population you could not make sense of populations with 4.25 or 5.612 members. \n",
      "\n",
      "If a random variable $Z$ has a Poisson mass distribution, we denote this by writing\n",
      "\n",
      "$$Z \\sim \\text{Poi}(\\lambda) $$\n",
      "\n",
      "One very useful property of the Poisson random variable, given we know $\\lambda$, is that its expected value is equal to the parameter, ie.:\n",
      "\n",
      "$$E\\large[ \\;Z\\; | \\; \\lambda \\;\\large] = \\lambda $$\n",
      "\n",
      "We will use this property often, so it's something useful to remember. Below we plot the probability mass distribution for different $\\lambda$ values. The first thing to notice is that by increasing $\\lambda$ we add more probability to larger values occurring. Secondly, notice that although the graph ends at 15, the distributions do not. They assign positive probability to every non-negative integer."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "figsize( 12.5, 4)\n",
      "\n",
      "import scipy.stats as stats\n",
      "a = np.arange( 16 )\n",
      "poi = stats.poisson\n",
      "lambda_ = [1.5, 4.25 ]\n",
      "\n",
      "plt.bar( a, poi.pmf( a, lambda_[0]), color=colours[0],\n",
      "        label = \"$\\lambda = %.1f$\"%lambda_[0], alpha = 0.60,\n",
      "        edgecolor = colours[0], lw = \"3\")\n",
      "\n",
      "plt.bar( a, poi.pmf( a, lambda_[1]), color=colours[1],\n",
      "         label = \"$\\lambda = %.1f$\"%lambda_[1], alpha = 0.60,\n",
      "          edgecolor = colours[1], lw = \"3\")\n",
      "\n",
      "plt.xticks( a + 0.4, a )\n",
      "plt.legend()\n",
      "plt.ylabel(\"probability of $k$\")\n",
      "plt.xlabel(\"$k$\")\n",
      "plt.title(\"Probability mass function of a Poisson random variable; differing \\\n",
      "$\\lambda$ values\");"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "display_data",
       "png": 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a2KekpHDffff5tI8///nPXHvttd43oxuLjY31vhm9bNkyRowYwbBhw4ILbyRs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\nIiIKAhzsiYiIiIiCwP8BIuWffYpP6wcAAAAASUVORK5CYII=\n"
      }
     ],
     "prompt_number": 48
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "###Continuous Case\n",
      "Instead of a probability mass function, a continuous random variable has a *probability density function*. This might seem like unnecessary nomenclature, but the density function and the mass function are very different creatures. An example of continuous random variable is a random variable with a *exponential density*. The density function for an exponential random variable looks like:\n",
      "\n",
      "$$f_Z(z | \\lambda) = \\lambda e^{-\\lambda z }, \\;\\; z\\ge 0$$\n",
      "\n",
      "Like the Poisson random variable, an exponential random variable can only take on non-negative values. But unlike a Poisson random variable, the exponential can take on *any* non-negative values, like 4.25 or 5.612401. This makes it a poor choice for count data, which must be integers, but a great choice for time data, or temperature data (measured in Kelvins, of course), or any other precise *and positive* variable. Below are two probability density functions with different $\\lambda$ value. \n",
      "\n",
      "When a random variable $Z$ has an exponential distribution with parameter $\\lambda$, we say *$Z$ is exponential* and write\n",
      "\n",
      "$$Z \\sim \\text{Exp}(\\lambda)$$\n",
      "\n",
      "Given a specific $\\lambda$, the expected value of an exponential random variable is equal to the inverse of $\\lambda$, that is:\n",
      "\n",
      "$$E[\\; Z \\;|\\; \\lambda \\;] = \\frac{1}{\\lambda}$$"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "a = np.linspace(0,4, 100)\n",
      "expo = stats.expon\n",
      "lambda_ = [0.5, 1]\n",
      "\n",
      "for l,c in zip(lambda_,colours):\n",
      "    plt.plot( a, expo.pdf( a, scale=1./l), lw=3, \n",
      "                color=c, label = \"$\\lambda = %.1f$\"%l)\n",
      "    plt.fill_between( a, expo.pdf( a, scale=1./l), color=c, alpha = .33)\n",
      "    \n",
      "plt.legend()\n",
      "plt.ylabel(\"PDF at $z$\")\n",
      "plt.xlabel(\"$z$\")\n",
      "plt.title(\"Probability density function of an Exponential random variable;\\\n",
      " differing $\\lambda$\");"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "display_data",
       "png": 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BQEAACgsLceDAAYwaNUrWfezKtGnTsHTpUmzbtg0jRozAtm3bkJycDBcXF82YnvbJwcEB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\nMY7jqPXr16uPPvpIZbNZtXXrVnX48OGSff70pz+pnTt3KqWU2rdvn9q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      }
     ],
     "prompt_number": 6
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "\n",
      "###But what is $\\lambda \\;$?\n",
      "\n",
      "\n",
      "**This question is what motivates statistics**. In the real world, $\\lambda$ is hidden from us. We only see $Z$, and must go backwards to try and determine $\\lambda$. The problem is so difficult because there is not a one-to-one mapping from $Z$ to $\\lambda$. Many different methods have been created to solve the problem of estimating $\\lambda$, but since $\\lambda$ is never actually observed, no one can say for certain which method is better! \n",
      "\n",
      "Bayesian inference is concerned with *beliefs* about what $\\lambda$ is. Rather than try to guess $\\lambda$ exactly, we can only talk about what $\\lambda$ is likely to be by assigning a probability distribution to $\\lambda$.\n",
      "\n",
      "This might seem odd at first: after all, $\\lambda$ is fixed, it is not (necessarily) random! How can we assign probabilities to a non-random event. Ah, we have fallen for the frequentist interpretation. Recall, under our Bayesian philosophy, we *can* assign probabilities if we interpret them as beliefs. And it is entirely acceptable to have *beliefs* about the parameter $\\lambda$. \n"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "\n",
      "##### Example: Inferring behaviour from text-message data\n",
      "\n",
      "Let's try to model a more interesting example, concerning text-message rates:\n",
      "\n",
      ">  You are given a series of text-message counts from a user of your system. The data, plotted over time, appears in the graph below. You are curious if the user's text-messaging habits changed over time, either gradually or suddenly. How can you model this? (This is in fact my own text-message data. Judge my popularity as you wish.)\n"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "figsize( 12.5, 3.5 )\n",
      "count_data = np.loadtxt(\"data/txtdata.csv\")\n",
      "n_count_data = len(count_data)\n",
      "plt.bar( np.arange( n_count_data ), count_data, color =\"#348ABD\"  )\n",
      "plt.xlabel( \"Time (days)\")\n",
      "plt.ylabel(\"count of text-msgs received\")\n",
      "plt.title(\"Did the user's texting habits change over time?\")\n",
      "plt.xlim( 0, n_count_data );"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "display_data",
       "png": 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qt1QN0tPT01G5cmVT10IWRIu9W9aAucvD7OVg7nIwdzmYuzxazL7IQfqGDRsw\nevRoAMDGjRuhKIrBciEEFEXB+PHjTVshEREREVE5U2RP+qZNm/T/v2HDhgL/Nm7ciA0bNpilSDI/\nLfZuWQPmLg+zl4O5y8Hc5WDu8mgx+yLPpP/000/6/9+/f785aiEiIiIiIpTiFow3b97E+vXrsXTp\nUgDA1atXceXKFZMVRnJpsXfLGjB3eZi9HMxdDuYuB3OXR4vZqxqkR0VFoWnTpvjvf/+L+fPnAwAu\nXLiAN954w6TFERERERGVR6oG6VOnTsXmzZsRFhaGihUfd8h07NgRR44cMWlxJI8We7esAXOXh9nL\nwdzlYO5yMHd5tJi9qkF6cnIyevToYTDP1tYWubm5JimKiIiIiKg8UzVIb968OcLCwgzmRUREwNvb\n2yRFkXxa7N2yBsxdHmYvB3OXg7nLwdzl0WL2qr7MaPny5ejXrx/69OmD7OxsTJo0CTt37sT27dtN\nXR8RERERUbmj6kx6x44dERcXBy8vL4wbNw4NGzbEsWPH0L59e9Ubun37Nl566SU0b94cLVq0wJEj\nR5CRkYGgoCA0adIEPXv2xO3bt8v8Qsi4tNi7ZQ2YuzzMXg7mLgdzl4O5y6PF7FWdSc/OzoaLiwtm\nzJihn5eTk4Ps7GxUqVJF1YamTp2KPn36YOvWrXj06BHu3r2LhQsXIigoCNOnT8eSJUsQEhKCkJCQ\nsr0SIiIiIiIroWqQHhQUhGXLlqFjx476eSdOnMAHH3yg6ouO/vjjDxw4cAChoaGPN1qxImrUqIEd\nO3YgKioKABAcHIyAgIBCB+mTJ0+Gu7s7AMDBwQHe3t763qL834w4zWlrmM6fZ87tJ968B8AFAJCV\nGAsAsG/kCwCIPXoIWc7VLCYfU0536dLFouopT9P5LKUetdOxRw8hK/Gq/vPy9OdHdn3c3y1zOp+l\n1FNepvPnyawnPj4emZmZAICUlBRMmDABxVGEEKLYRwBwdHRERkYGbGz+7I7Jzc2Fs7OzqhaV2NhY\nvPbaa2jRogXi4uLQpk0bfPrpp6hbty5u3boFABBCwMnJST+dLyIiAq1bty5xG0RUNnGpWfjrjxcL\nXbasryd8atmbuSIibeBnh4ieRUxMDAIDA4tcrqon3dHREenp6Qbzrl27hurVq6sq4tGjR4iJicGb\nb76JmJgY2NnZFThjrigKFEVRtT4yvad/4yfzYO7yMHs5mLsczF0O5i6PFrNXNUgfMmQIRo4cifj4\neNy7dw/qg8tfAAAgAElEQVS//vorRo8ejZdfflnVRurWrYu6deuiXbt2AICXXnoJMTExcHNzQ1pa\nGgAgNTUVrq6uZXwZRERERETWQ9UgfcGCBWjevDk6dOiA6tWro2PHjmjWrBkWL16saiNubm6oV68e\nEhISAAB79+6Fl5cX+vfvr+9TDw0NxaBBg8r4MsjYnuzhIvNh7vIwezmYuxzMXQ7mLo8Ws6+o5kFV\nq1bFF198gVWrVuHmzZtwdnY26E9XY9WqVRg5ciRycnLQqFEjrF27Frm5uRg6dCjWrFkDDw8PbNmy\npUwvgoiIiIjImqgeaZ89exYLFizARx99BBsbG5w7dw6//vqr6g35+Pjg2LFjiIuLw/fff48aNWrA\nyckJe/fuRUJCAsLDw+Ho6FimF0HGp8XeLWvA3OVh9nIwdzmYuxzMXR4tZq9qkP7tt9/i+eefx9Wr\nV7F+/XoAQFZWFt59912TFkdEREREVB6paneZM2cO9uzZA19fX31Liq+vL2JjY01aHMlj7t6t1MwH\nuHY3p8jlrnaVUMuhshkrkkOLPXPWgtnLwdzlYO5yMHd5tJi9qkH69evX0apVqwLzS9uXTlSUa3dz\nirzfMPD4nsPlYZBOREREBKhsd2ndujU2bNhgMO+bb75B+/btTVIUyafF3i1rwNzlYfZyMHc5mLsc\nzF0eLWav6kz6qlWrEBQUhDVr1uDevXvo2bOn/mJPIiIiIiIyrhIH6UIIVKpUCadOnUJYWBj69esH\nd3d39OvXT/U3jpL2aLF3yxowd3mYvRzMXQ7mLgdzl0eL2as6k96yZUvcuXMHw4YNM3U9RERERETl\nXok96YqiwM/PD+fPnzdHPWQhtNi7ZQ2YuzzMXg7mLgdzl4O5y6PF7FWdSe/WrRt69+6NsWPHol69\nelAUBUIIKIqC8ePHm7pGIiIiIqJyRdUgPTo6Gh4eHoiKiiqwjIN066TF3i1rwNzlYfZyMHc5mLsc\nzF0eLWavapC+f/9+E5dBRERExeGXvhGVL/w2IiqUFnu3rAFzl4fZy8Hc1cv/0rei/hU3gH8ac5eD\nucujxew5SCciIiIisjAcpFOhtNi7ZQ2YuzzMXg7mLgdzl4O5y6PF7DlIJyIiIiKyMKoG6adPn0Za\nWhoAICsrCx9++CHmzZuHe/fuqd6Qh4cHWrVqBT8/P7Rv3x4AkJGRgaCgIDRp0gQ9e/bE7du3y/AS\nyBS02LtlDZi7PMxeDuYuB3OXg7nLo8XsVQ3SR4wYgT/++AMA8P777+PAgQM4fPgwXnvtNdUbUhQF\n+/fvx8mTJ3H06FEAQEhICIKCgpCQkIDAwECEhISU4SUQEREREVkXVbdgTE5ORtOmTZGXl4fvv/8e\nZ86cQbVq1eDh4VGqjQkhDKZ37Nihv/d6cHAwAgICOFC3EFrs3bIGzF0eZi8Hc5eDucvB3OXRYvaq\nBulVqlRBZmYmzp49i/r168PFxQUPHz5Edna26g0pioIePXqgQoUKeO211zBx4kSkp6dDp9MBAHQ6\nHdLT0wt97uTJk+Hu7g4AcHBwgLe3tz7s/D9fcFrb0/aNfAAAWYmx/5v2NZgGPC2qXmuaTrx5D4AL\ngIL5xx49hCznahZVL6c5bSnTsUcPISvxaoHjVf60ubfHzyunOW3Z0/Hx8cjMzAQApKSkYMKECSiO\nIp4+vV2IadOm4cCBA8jKysJbb72FKVOm4MiRI5g0aRLi4uJKejoAIDU1FbVq1cL169cRFBSEVatW\nYcCAAbh165b+MU5OTsjIyDB4XkREBFq3bq1qG2Q80dHR+h3LHOJSs/DXHy8WuXxZX0/41LI3Wz2y\nmDt3oPjsy0vugJzsSdu5m/uzY8zjpJZz1zLmLo8lZh8TE4PAwMAil1dUs5Lly5cjPDwctra26N69\nOwCgQoUKWLFihepCatWqBQBwcXHB4MGDcfToUeh0OqSlpcHNzQ2pqalwdXVVvT4iIiJLx28JJaKy\nUjVIVxQFvXr1MpjXtm1b1Ru5d+8ecnNzYW9vj7t37yI8PBxz587FgAEDEBoaihkzZiA0NBSDBg0q\nXfVkMpb222Z5wdzlYfZyWHvu+d8SWpRlfT2lDNKtPXdLxdzl0WL2qgbpXbt2haIoBhd+KoqCSpUq\noV69ehg8eDAGDBhQ5PPT09MxePBgAMCjR48wcuRI9OzZE23btsXQoUOxZs0aeHh4YMuWLc/4coiI\niIiItE/VLRj9/f2RlJSEgIAAjBo1Cv7+/khOTkbbtm3h6uqKCRMmYMmSJUU+v0GDBoiNjUVsbCxO\nnTqFDz74AMDjHvS9e/ciISEB4eHhcHR0NM6romeWf8EDmRdzl4fZy8Hc5WDucjB3ebSYvaoz6eHh\n4di9ezeaN2+unzdq1CgEBwfjyJEjGDJkCIYPH44ZM2aYrFAiIiIiovJC1Zn08+fPo0GDBgbz6tev\nj3PnzgEA2rVrV+TtE0mbtNi7ZQ2YuzzMXg7mLgdzl4O5y6PF7FUN0p9//nmMHz8eFy5cQHZ2Ni5c\nuIBXX30VXbt2BQDEx8ejdu3aJi2UiIiIiKi8UDVIX7duHfLy8uDl5YVq1arBy8sLubm5WLduHQCg\ncuXK2LRpkynrJDPTYu+WNWDu8jB7OZi7HMxdDuYujxazV9WT7uzsjM2bNyM3NxfXr1+Hq6srbGz+\nHN83bdrUZAUSEREREZU3qs6knz59GmlpaahQoQLs7Ozw0UcfYd68ebh3756p6yNJtNi7ZQ2YuzzM\nXg7mLgdzl4O5y6PF7FUN0keMGIE//vgDAPD+++/jwIEDOHz4MF577TWTFkdEREREVB6pGqQnJyej\nadOmyMvLw/fff48tW7Zg69atCAsLM3V9JIkWe7esAXOXh9nLwdzlYO5yMHd5tJi9qp70KlWqIDMz\nE2fPnkX9+vXh4uKChw8fIjs729T1ERERERGVO6oG6a+88gq6d++OrKwsvPXWWwCAmJgYNGzY0KTF\nkTxa7N2yBsxdHmYvB3OXg7nLwdzl0WL2qgbpK1aswO7du2Fra4vu3bsDACpUqIAVK1aYtDgiIiIi\novJIVU86APTq1Us/QAeAtm3bGkyTddFi75Y1YO7yMHs5mLsczF0O5i6PFrNXdSY9OTkZ8+bNw8mT\nJ3Hnzh39fEVRkJCQYLLiiIiIiIjKI1WD9JdffhnNmzfH/PnzUaVKFVPXRBZAi71b1oC5y8Ps5WDu\ncjB3OZi7PFrMXtUg/fz58zh06BAqVKhg6nqIiIiIiMo9VT3p/fr1Q1RU1DNvLDc3F35+fujfvz8A\nICMjA0FBQWjSpAl69uyJ27dvP/M2yDi02LtlDZi7PMxeDuYuB3OXg7nLo8XsVZ1JX7lyJTp16oQm\nTZrA1dVVP19RFHz11VeqN7Zy5Uq0aNECWVlZAICQkBAEBQVh+vTpWLJkCUJCQhASElLKl0BERERE\nZF1UnUkfP348KlWqhObNm6NOnTqoW7cu6tSpgzp16qje0JUrV/DTTz/h1VdfhRACALBjxw4EBwcD\nAIKDg7Ft27YyvAQyBS32blkD5i4Ps5eDucvB3OVg7vJoMXtVZ9IjIyNx9epVODg4lHlD06ZNw7Jl\ny5CZmamfl56eDp1OBwDQ6XRIT08v9LmTJ0+Gu7s7AMDBwQHe3t76sPP/fMFpbU/bN/IBAGQlxv5v\n2tdgGvC0qHqtaTrx5j0ALgAK5h979BCynKtZVL2c5rSlTMcePYSsxKsFjlf50yV9vrISYxF79Dp8\nBvY0yvb4eeU0py17Oj4+Xj8OTklJwYQJE1AcReSf1i7Gc889h40bN6JBgwYlPbRQP/zwA3bt2oUv\nvvgC+/fvxyeffIKdO3eiZs2auHXrlv5xTk5OyMjIMHhuREQEWrduXabtUtlFR0frdyxziEvNwl9/\nvFjk8mV9PeFTy95s9chi7tyB4rMvL7kDcrInbeeu5rNjzGObMdel5dy1jLnLY4nZx8TEIDAwsMjl\nFdWspHv37ujVqxfGjRunP/MthICiKBg/fnyJzz948CB27NiBn376CdnZ2cjMzMTo0aOh0+mQlpYG\nNzc3pKamGvS7ExERERGVV6oG6QcOHEDt2rURHh5eYJmaQfqiRYuwaNEiAEBUVBQ+/vhjbNiwAdOn\nT0doaChmzJiB0NBQDBo0qJTlk6lY2m+b5QVzl4fZy8Hc5WDucjD30knNfIBrd3MKXeZqVwm1HCqr\nXpcWs1c1SN+/f79RN6ooCgBg5syZGDp0KNasWQMPDw9s2bLFqNshIiIiIm26djen2Jay0gzStUjV\n3V2e9Ky3SPT398eOHTsAPO5B37t3LxISEhAeHg5HR8dnWjcZT/4FD2RezF0eZi8Hc5eDucvB3OXR\nYvalHqQvXLjQFHUQEREREdH/qGp3ofJHi71b1oC5y8Ps5WDucjB3OZi78RXXtw782buuxexLPUgf\nOXKkKeogIiIiIiqV4vrWAW33rqtqd/n444/1///Pf/5T///Lly83fkVkEbTYu2UNmLs8zF4O5i4H\nc5eDucujxexVDdLnzZtX6Pz58+cbtRgiIiIiIiqh3WXfvn0QQiA3Nxf79u0zWJaYmAgHBweTFkfy\naLF3yxowd3mYvRzMXQ7mLgdzl0eL2Rc7SB8/fjwURcGDBw8wYcIE/XxFUaDT6bBq1SqTF6hlxrwJ\nPxERERmX2osOiWQodpCelJQEABg9ejQ2bNhgjnqsipZvwh8dHa3J3zq1jrnLw+zlYO5yMPfHzH3R\nIXOXR4vZq+pJnz17dqHzf/nlF6MWQ0REREREKgfpnTp1wj/+8Q/9dE5ODmbMmIHBgwebrDCSS2u/\nbVoL5i4Ps5eDucvB3OVg7vJoMXtVg/TIyEisXr0affr0QUREBNq1a4e4uDjExcWZuj4iIiIionJH\n1SDdx8cHR48exeXLlxEUFIR27dohLCwMtWrVMnV9JIkW7ydqDZi7PMxeDuYuB3OXg7nLo8XsVQ3S\nr1y5gn79+qFy5cpYuXIltm/fjg8++ACPHj0ydX1EREREROWOqkG6n58fOnXqhMOHD2PKlCmIjY3F\n8ePH0a5dO1PXR5JosXfLGjB3eZi9HMxdDuYuB3OXR4vZF3sLxnzbt29H586d9dN16tRBeHg4Pvvs\nM5MVRkSWg/cSJiIiMi9VZ9I7d+6MmzdvYv369Vi6dCkA4Pfff8eLL75o0uJIHi32blkDS809/17C\nRf0rbgCvFZaavbVj7nIwdzmYuzxazF7VmfSoqCgMGTIEbdu2xS+//ILp06fjwoUL+OSTT7Bz584S\nn5+dnQ1/f388ePAAOTk5GDhwIBYvXoyMjAwMGzYMycnJ8PDwwJYtW+Do6PjML4qIiIieDf+CZh34\n7efapWqQPnXqVGzevBk9evRAzZo1AQAdO3bEkSNHVG2kSpUqiIyMRLVq1fDo0SN06dIF0dHR2LFj\nB4KCgjB9+nQsWbIEISEhCAkJKfurIaPRYu+WNWDu8jB7OZi7HGpyN/e3cZYHMvZ3LX/7uTFp8Vij\nqt0lOTkZPXr0MJhna2uL3Nxc1RuqVq0agMdfhJSbm4uaNWtix44dCA4OBgAEBwdj27ZtqtdHRERE\nRGStVJ1Jb968OcLCwvDCCy/o50VERMDb21v1hvLy8tC6dWskJibijTfegJeXF9LT06HT6QAAOp0O\n6enphT538uTJcHd3BwA4ODjA29tb/xtRfo+RpU5nJcYCAOwb+RpMA54WUV9R0/nzzLU9+0Y+ms7L\nWNOrV682+/6dePMeABcABfOPPXoIWc7VysX78/S+L7ue8jIdHx+PN954w2LqKc107NFDyEq8WuDz\nkD9d0ucrKzEWsUevw2dgT6NsL//zaqz93Zjbs9RpY74/lrq/F3f8zn99qZkPEB4ZBQDwbd8JwOP3\nN3/a1a4SEn89ZpZ6TfXzScbP16en4+PjkZmZCQBISUnBhAkTUBxFCCGKfQSAw4cPo1+/fujTpw++\n/fZbjB49Gjt37sT27dvRvn37kp5u4I8//kCvXr2wePFivPjii7h165Z+mZOTEzIyMgweHxERgdat\nW5dqG5YiLjWr2D8x+dSyN3NF6kVHR+t3LHMoLivA8vMyFnPnDqjbT8vD+yMje9J27ub+7BhzXWpy\nLw+fe3O/Rh7jS8eYtVvisSYmJgaBgYFFLq+oZiUdO3ZEXFwcNm7ciOrVq8Pd3R3Hjh1D3bp1S11Q\njRo10LdvX5w4cQI6nQ5paWlwc3NDamoqXF1dS70+Mg1L25FNwRIvpikPuVsqZi8Hc5eDucvB3OXR\nYvaqBukff/wx3n//fcyYMcNg/vLly/Huu++W+PwbN26gYsWKcHR0xP3797Fnzx7MnTsXAwYMQGho\nKGbMmIHQ0FAMGjSobK+CqAx4MQ0RERFZKlUXjs6bN6/Q+fPnz1e1kdTUVHTv3h2+vr7o0KED+vfv\nj8DAQMycORN79uxBkyZNsG/fPsycOVN95WRST/Yrkvkwd3mYvRzMXQ7mLgdzl0eL2Rd7Jn3fvn0Q\nQiA3Nxf79u0zWJaYmAgHBwdVG/H29kZMTEyB+U5OTti7d28pyiUiIiIisn7FDtLHjx8PRVHw4MED\ngytQFUWBTqfDqlWrTF4gyaHF3i1rwNzlYfZyMHc5mLsczF0eLWZf7CA9KSkJADB69Ghs2LDBHPUQ\nEUlhiRcSExFpDY+lxqPqwlEO0MsfS7xVUXnA3OUJj4zC19ddCl3GC4lNh/u8HMxdjvKQu6XelEGL\n2au6cJSIiIiIiMyHg3QqlNZ+27QWzF2e/G/ZI/PiPi8Hc5eDucujxeyLHKTv2LFD//8PHz40SzFE\nRERERFTMIH3kyJH6/3d2djZLMWQ5tHg/UWvA3OWJPXpIdgnlEvd5OZi7HMxdHi1mX+SFo25ubli1\nahVatGiBR48eFbhPer7u3bubrDgiIiIiovKoyEH6unXr8OGHH+Kzzz4rcJ/0J/32228mK06t4m73\nA5Tulj/GXJeWabF3yxowd3l823fC10XckYBMh/u8HMxdDuYujxazL3KQ/txzzyEiIgIA0KhRIyQm\nJpqtqNIq7nY/QOlu+WPMdRERERERlYWqu7vkD9BTUlJw6NAhpKSkmLQokk+LvVvWgLnLw550ObjP\ny8Hc5WDu8mgxe1VfZpSamorhw4fj0KFDcHZ2xs2bN9GxY0ds3rwZtWvXNnWNRERlxhY2IjIHftMm\nGZuqQfrrr78OHx8f/PTTT7Czs8Pdu3cxa9YsvP766wa3aiTrocXeLWvA3I1PbQsbe9Ll4D4vB3M3\nPjXftMnc5dFi9qoG6dHR0fj2229RqVIlAICdnR2WLl3Ks+hWTM3ZRwA8Q2lkPOtLRM+KZ3SJ5DPG\n51DVIN3JyQlnzpyBr6+vft65c+dQs2ZNlaWS1oRHRuHr6y5FLl/W1xMAeJGtkanJnZmaxuOe9KKz\nJ9OIjo7W5BkuS6bmjC5zl4O5y2Pu7NV8DkuiapA+ffp0BAUFYcKECahfvz6SkpKwdu1azJ8/X1Wh\nly9fxpgxY3Dt2jUoioJJkybh7bffRkZGBoYNG4bk5GR4eHhgy5YtcHR0VLVOIiIiIiJrperuLhMn\nTsQ333yD69evY+fOnbh58yY2bdqE1157TdVGbG1tsWLFCpw+fRqHDx/GF198gbNnzyIkJARBQUFI\nSEhAYGAgQkJCnunFkPH4tu8ku4RyibnLw+zl4FlFORq1aoe41Kwi/6VmPpBdolXi/i6PFrNXdSYd\nePzNomX9dlE3Nze4ubkBAKpXr47mzZvj6tWr2LFjB6KiogAAwcHBCAgI4ECdiIjIxNRcUE1Ecqke\npBtLUlISTp48iQ4dOiA9PR06nQ4AoNPpkJ6eXuhzJk+eDHd3dwCAg4MDvL299b8RRUdHI/HmPeT3\nkmYlxgIA7Bv56qdjj16Hz8Ce+scDMHj+k9OxRw8hK/GqwfOfXF/s0UPIcq5W5POfni6snsc8VT1f\n1nR+piXVX9Ty/Gm127Nv5CMlL0t7f7auX4Os2zWMtv+pmS7u85O/PVnvj6lf35PHh/zPfnGvb3t4\nJG7ff6g/655/b3Xf9p3galcJib8ek/56tTYdHx+PN954w2LqKc10ST8vZP18Ku7zqmZ/N1ifEX8e\nGmu6Uat2uHY3x+Dzl18PAPTs5q/vuy9pfeZ8f2Tt72r2h6KWP12/Mbdn7p9Pq1evLjB+NEXexe0P\n936/iNzsu1iX5IScW+mYMGECiqMIIUSxjzCiO3fuwN/fH3PmzMGgQYNQs2ZN3Lp1S7/cyckJGRkZ\nBs+JiIhA69ati11vXGpWiWcEfGrZq6rRXOsqzXpkCN0ebpQLR2XkrpYlvj9qcpeRg4z3x1jU1l5c\n9mpysOQMLJmWL6Qz92dH7brU1GXuY7wxaflnvoz93ZL209LuM8as3dzZq6k9JiYGgYGBRa7DbGfS\nHz58iCFDhmD06NEYNGgQgMdnz9PS0uDm5obU1FS4urqaqxwqgZbvGW3u2xgac3tazl0GY95qjtnL\nYYkD9PJwK1Rj7u+85aN6lri/lxdazF7VIP3jjz/G+++/X2D+8uXL8e6775b4fCEEJkyYgBYtWuCd\nd97Rzx8wYABCQ0MxY8YMhIaG6gfvRM9C7ZfXaHV79Cdj3OKK6Gn8TJcOP4dEpqHq7i7z5s0rdL7a\nWzD+8ssv2LhxIyIjI+Hn5wc/Pz+EhYVh5syZ2LNnD5o0aYJ9+/Zh5syZ6isnk8rv7SPzYu7yMHs5\n8vs4yby4v8vB/V0eLWZf7Jn0ffv2QQiB3Nxc7Nu3z2BZYmIiHBwcVG2kS5cuyMvLK3TZ3r17VZZK\nRKVRHv5kT0TWha0zRH8qdpA+fvx4KIqCBw8eGFyBqigKdDodVq1aZfICSQ7258phzNz5J/vS4T4v\nhxb7RK2Bpe7v1t46w/1dHi1mX+wgPSkpCQAwevRobNiwwRz1EBGVCzxjSKQNxvyrJP/CSaWh6sLR\nJwfoT7et2NioamsnjXncr1j07bnINJi7PObO3trPGKql5VswahmPNeoZ86+S4ZFRJd76srx89s1N\ni8caVSPsEydOoFOnTqhWrRoqVqyo/2dra2vq+oiIiIiIyh1Vg/Tg4GB069YNx48fx6VLl/T/EhMT\nTV0fSZL/DW5kXsxdHmavXmrmA8SlZhX6LzXzQanWpbUzW9aC+7sczF0eLR5rVLW7pKSkYOHChVAU\nxdT1EBGRhWOrDhGR6akapA8ePBi7d+/GCy+8YOp66BkY84IU9ivKwdzlYfbGpfZ4ZMw+UTUX46qp\nqzzg/i4Hc5dHiz3pqgbp9+/fx+DBg9G1a1fodDr9fEVRsH79epMVR6XDW+4RkaWQcTxSc4ZfTV1E\nRJZAVU96ixYtMGPGDHTu3BmNGjUy+EfWiX1zcjB3eZi9HFo7s2UtuL/Lwdzl0eKxRtWZ9I8++sjE\nZZRfvGcqEZkDjzVERMWztOOkqkH6vn37ilzWvXt3oxVTHllqiwr75uRg7vJYe/aWeqzRYp+oNbD2\n/d1SMXd51BxrLO04qWqQPn78eIM7u1y/fh0PHjxAvXr1cOnSJZMVly8uNavQ+TzzQ2SdLO1shizM\ngYgsBY9Hj5kzB1WD9KSkJIPp3NxcLFiwANWrVzdKESXhrb7Mz7d9J3xdzG+TZBrM/TEZZzMsMXtL\nO6tjCjyLLocl7u/lgZZz1/rxyFjHGnPmoOrC0adVqFABs2bNwtKlS41SBBERERER/UnVmfTC7Nmz\nBxUqVDBmLWRB2DdnfGru4aw2dzXrotLhPi8He9LlKA/7uyUeJ8tD7pZKi8caVYP0evXqGUzfu3cP\n2dnZ+Mc//mGSooiskTG/pZHf+EhEVDweJ0nrVA3SN2zYYDBtZ2eHJk2aoEaNGqo2Mn78ePz4449w\ndXVFfHw8ACAjIwPDhg1DcnIyPDw8sGXLFjg6Opay/PLDmGcE1KzLmH1z5q5dy7Tcr6h1zF4OrZ3Z\nshbm3t950eFjPM7Io8VjjapBekBAAAAgLy8P6enp0Ol0sLFR384+btw4TJkyBWPGjNHPCwkJQVBQ\nEKZPn44lS5YgJCQEISEhpau+HNHyWVgt105ERM9O6xcdEsmgaqSdmZmJMWPGoEqVKqhTpw6qVKmC\nMWPG4I8//lC1ka5du6JmzZoG83bs2IHg4GAAQHBwMLZt21bk83/7Zgl+3xOK3/eEIv3AVmQlxuqX\nRUdH/6/H67GsxFiD5VmJsQbLo6OjER0dXeR07NFDBZ7/5HTs0UPFPv/p6cLqeXp9pdleSa+vpO2V\nlFf+9vIfU9L6jLU9tesrKa/S7g9q6i/p/Tbm9rauX2OR+0Np1leaz4epPz+leX/y1/Ws25NxfEjN\nfIC41CyEbg9H6PZwxKVm6ae3h0eq3p4x6i/t/rd69eoyb7+0x29jf16NvT1j/3wy9f5u6ccjS9wf\ntq5fo3p75jieGvP1lXZ/eNafr6XdH1avXm3Wn+eF5ZV+YCt+3xOKdV+swOTJk1ESVWfSp0yZgrt3\n7+LUqVNwd3dHSkoKZs2ahSlTpmD9+vVqVlFA/hl5ANDpdEhPTy/ysQ2GzShyWZcuXWCfmqX/85F9\nI1+D5faNfOHb3tPg8U8//0m+7TvB/vqfv+0/vT7f9p3gU8te9foKq6cs28u/V3xJr6+k7ZWUV/72\nEreHq1qfsbZX3Ot7+vHF5VXa/UFN/SVNG3N7ns1a4Mh1lyKXy9of1L4/avJSM22p+4Oa7ZVm2pjH\nh8dnKR/vO3/+Od0Fy/oad38Hin9/jP35Ks20Je4PMn4+Gev9sdSfT1o+PiTevIcj14teX2n2B3N/\nXo29Pzzrz9fS7g/e3t4G2zD1z/PC8sp/zNi+nvCpZY+YmBgUR9WZ9LCwMKxfvx5NmjRBlSpV0KRJ\nE6xbtw5hYWFqnl4iRVEMviyJ5PNt30l2CeUSc5eH2cuhxT5Ra8D9XQ7mLo8WjzWqzqRXrVoV169f\nh52dnX7ejRs3UKVKlTJvWKfTIS0tDW5ubkhNTYWrq2uZ10VE8vHCMCIiIuNRNUh/9dVXERQUhPfe\ne5o/R4sAAA64SURBVA/169dHUlISVqxYgYkTJ5Z5wwMGDEBoaChmzJiB0NBQDBo0qMzrIuPjvVzl\n0HLuWr8wTMvZa5kW711sDbi/y8Hc5dHisUbVIH3WrFmoXbs2vv76a6SmpqJ27dqYMWMGxo8fr2oj\nI0aMQFRUFG7cuIF69erh73//O2bOnImhQ4dizZo1+lswmpq1376PiIiIiKyDqkG6jY0Nxo8fr3pQ\n/rRNmzYVOn/v3r1lWl9Z8fZ96vFernIwd3mYvRxaO7NlLbi/y8Hc5dHisUbVhaNTpkzBwYMHDeYd\nPHgQ77zzjkmKIiIiIiIqz1SdSd+0aRM+/vhjg3mtW7fGwIED8emnn5qkMEtWHi6QY9+cHOUhd0tt\nOysP2Vui7eGR8PBuW+gyaziWqmXuzwX3dzmYuzxW25NuY2ODvLw8g3l5eXkQQpikKEun9QvkiGRi\n2xk96fb9h9wfwM8FERWkqt2lS5cumD17tn6gnpubi7lz56Jr164mLY7k4b1cH8v/Jsei/qVmPjDq\n9pi7PMbK3tz7jLEVV78pauc+Lwdzl4O5y6O1s+iAyjPpK1euRL9+/eDm5ob69esjJSUFtWrVws6d\nO01dH5FUav5qQvQkrf+ljWd0iYgsg6pBer169RATE4OjR4/i8uXLqFevHjp06AAbG1Un4kmD2Dcn\nB3OXh9nLwdzlYO5yMHd5rLYnHQAqVKiATp06oVMn/qmGiIiIiLTj5r2HiEvNKnSZpV6kzlPhVCj2\nzcnB3OVh9nIwdzmYuxzMXR4P77b4648XC/1X3B37ZFJ9Jp2IiIiITM9Sb1VL5sVBOhWKfXNyMHd5\nmL0czF0O5i6H2tx5AbfxaXGfZ7sLEREREZGF4SCdCsW+OTmYuzzMXg7mLgdzl4O5y6PF7DlIJyIi\nIiKyMOxJp0JpsXfLGjB3eZi9HGpyL+4iOoAX0pUF93c5jJk7Pxelo8V9noN0KtTFc2cAZ3/ZZZQ7\nzF0eZi+Hmty1/i2uloj7uxzGzJ2fi9LR4j4vvd0lLCwMzZo1Q+PGjbFkyRLZ5dD/3MnKlF1CucTc\n5WH2cjB3OZi7HMxdHi1mL3WQnpubi7feegthYWE4c+YMNm3ahLNnz8osiYiIiIhIOqmD9KNHj8LT\n0xMeHh6wtbXF8OHDsX37dpkl0f+kXb0iu4RyibnLw+zlYO5yMHc5mLs8WsxeEUIIWRvfunUrdu/e\njS+//BIAsHHjRhw5cgSrVq3SPyYiIkJWeUREREREJhMYGFjkMqkXjiqKUuJjiiueiIiIiMgaSW13\nqVOnDi5fvqyfvnz5MurWrSuxIiIiIiIi+aQO0tu2bYsLFy4gKSkJOTk5+OabbzBgwACZJRERERER\nSSe13aVixYr4/PPP0atXL+Tm5mLChAlo3ry5zJKIiIiIiKSTfp/03r174/z587h48SI++OADg2W8\nh7p5jB8/HjqdDt7e3vp5GRkZCAoKQpMmTdCzZ0/cvn1bYoXW6fLly+jWrRu8vLzQsmVLfPbZZwCY\nvallZ2ejQ4cO8PX1RYsWLfTHHeZuPrm5ufDz80P//v0BMHtz8PDwQKtWreDn54f27dsDYO7mcPv2\nbbz00kto3rw5WrRogSNHjjB3Ezt//jz8/Pz0/2rUqIHPPvtMk7lLH6QXhfdQN59x48YhLCzMYF5I\nSAiCgoKQkJCAwMBAhISESKrOetna2mLFihU4ffo0Dh8+jC+++AJnz55l9iZWpUoVREZGIjY2Fr/+\n+isiIyMRHR3N3M1o5cqVaNGihf7mAcze9BRFwf79+3Hy5EkcPXoUAHM3h6lTp6JPnz44e/Ysfv31\nVzRr1oy5m1jTpk1x8uRJnDx5EidOnEC1atUwePBgbeYuLNTBgwdFr1699NOLFy8WixcvlliRdfvt\nt99Ey5Yt9dNNmzYVaWlpQgghUlNTRdOmTWWVVm4MHDhQ7Nmzh9mb0d27d0Xbtm3FqVOnmLuZXL58\nWQQGBop9+/aJfv36CSF4vDEHDw8PcePGDYN5zN20bt++LRo0aFBgPnM3n927d4suXboIIbSZu8We\nSb969Srq1aunn65bty6uXr0qsaLyJT09HTqdDgCg0+mQnp4uuSLrlpSUhJMnT6JDhw7M3gzy8vLg\n6+sLnU6nbzli7uYxbdo0LFu2DDY2f/74YfampygKevTogbZt2+q/m4S5m9Zvv/0GFxcXjBs3Dq1b\nt8bEiRNx9+5d5m5GmzdvxogRIwBoc3+32EG6mnuok3koisL3w4Tu3LmDIUOGYOXKlbC3tzdYxuxN\nw8bGBrGxsbhy5Qp+/vlnREZGGixn7qbxww8/wNXVFX5+fhBFfI8eszeNX375BSdPnsSuXbvwxRdf\n4MCBAwbLmbvxPXr0CDExMXjzzTcRExMDOzu7Ai0WzN10cnJysHPnTrz88ssFlmkld4sdpPMe6nLp\ndDqkpaUBAFJTU+Hq6iq5Iuv08OFDDBkyBKNHj8agQYMAMHtzqlGjBvr27YsTJ04wdzM4ePAgduzY\ngQYNGmDEiBHYt28fRo8ezezNoFatWgAAFxcXDB48GEePHmXuJla3bl3UrVsX7dq1AwC89NJLiImJ\ngZubG3M3g127dqFNmzZwcXEBoM2frRY7SOc91OUaMGAAQkNDAQChoaH6ASQZjxACEyZMQIsWLfDO\nO+/o5zN707px44b+qv779+9jz5498PPzY+5msGjRIly+fBm//fYbNm/ejO7du2PDhg3M3sTu3buH\nrKwsAMDdu3cRHh4Ob29v5m5ibm5uqFevHhISEgAAe/fuhZeXF/r378/czWDTpk36VhdAoz9bZTfF\nF+enn34STZo0EY0aNRKLFi2SXY7VGj58uKhVq5awtbUVdevWFV999ZW4efOmCAwMFI0bNxZBQUHi\n1q1bssu0OgcOHBCKoggfHx/h6+srfH19xa5du5i9if3666/Cz89P+Pj4CG9vb7F06VIhhGDuZrZ/\n/37Rv39/IQSzN7VLly4JHx8f4ePjI7y8vPQ/T5m76cXGxoq2bduKVq1aicGDB4vbt28zdzO4c+eO\ncHZ2FpmZmfp5WsxdEaKIxkAiIiIiIpLCYttdiIiIiOj/27vfkKa3B47j75hOB9O5ZQ7TcNGDoEKw\nfBAGGZZBYGCYGtSa4AMNhCQIIhjUox5p0LOkB1GuolB8MBZkRRMCMWigrT+GlIJWiK2vs4wt9D6I\n++V6r/d3f/fevG31eT3y7BzPOZxHnx3OzpGflUK6iIiIiEiKUUgXEREREUkxCukiIiIiIilGIV1E\nJMVt2bKFgYGB/2Ssp0+fmvc6L6epqQm/379i4w8PD7Njx44V619EJF1kfO8JiIj87Ox2u/n63ceP\nH8nOzsZisQDQ1dXFkydP/rO5+P1+Tp48+af1K/1SX2lpKXl5eQSDQWpqalZsHBGRVKeddBGR72xu\nbo54PE48HqekpIRgMGiWf/sYx0p78+YNDx48+MtHPlb65t7Dhw9z8eLFFR1DRCTVKaSLiKQ4j8fD\n/fv3AThz5gz19fV4vV5yc3MpLS3l5cuXnDt3DrfbTUlJCf39/eb/GoZBc3Mza9eupbi4GL/fz8LC\nwrLj9Pf3s23bNqxWq/lZJBJh69at5ObmcujQIT5//mzWxWIxampqKCgowOVysX//fiYnJwG4desW\n5eXlS/rv7Ow0vwCEQiE2b95Mbm4uxcXFdHR0mO0qKyu5d+8eyWTyX66ciEj6UkgXEUlxvz9eEgwG\nOXr0KLFYjLKyMqqrqwGYmprC7/fT0tJitm1qasJqtTI2NkYkEuHOnTtcunRp2XFGRkbYuHGjWU4k\nEtTW1uLz+YjFYtTX19PT02POZ3FxkebmZiYmJpiYmMBms9HW1gZ8fYL71atXPH/+3Ozv6tWr+Hw+\nAJqbm+nq6mJ2dpZoNEpVVZXZrqioiMzMTF68ePFvlk1EJK0ppIuIpJmdO3dSXV2NxWLh4MGDzMzM\ncOrUKSwWC42Njbx+/ZrZ2VnevXvH7du3OX/+PDabjTVr1tDe3s6NGzeW7dcwDOx2u1keHBzky5cv\nHD9+HIvFQl1d3ZIflbpcLg4cOEB2djZ2u53Tp08TDocByMrKoqGhge7ubgCi0Sjj4+PmOXOr1Uo0\nGmV2dhaHw0FZWdmSueTk5PDhw4dvum4iIulEIV1EJM0UFBSYf9tsNvLz883dbZvNBnw95z4+Pk4y\nmaSwsBCn04nT6aS1tZXp6ell+3U6ncTjcbM8NTVFUVHRkjYlJSXmmfRPnz7R0tKCx+PB4XBQWVmJ\nYRhmvc/n49q1a8DXXfTGxkYyMzMB6OnpIRQK4fF42LVrF4ODg0vGicfj5OXl/eM1EhFJdwrpIiI/\nqHXr1pGVlcXMzAyxWIxYLIZhGIyMjCzbvrS0lNHRUbNcWFhonjH/1fj4uPmFoKOjg9HRUYaGhjAM\ng3A4zOLiohnSt2/fjtVqZWBggOvXr+P1es1+ysvL6evrY3p6mtraWhoaGsy6yclJEonEkqM3IiI/\nG4V0EZEfVGFhIXv37uXEiRPE43EWFhYYGxv70zvX9+zZw+PHj0kkEgBUVFSQkZHBhQsXSCaT9Pb2\n8ujRI7P93NwcNpsNh8PB+/fvOXv27B/69Hq9tLW1YbVaqaioACCZTBIIBDAMA4vFQk5OjnnlJEA4\nHGb37t3mrruIyM9IIV1EJI0sd0/5/ypfuXKFRCLBpk2bcLlc1NfX8/bt22X7drvdVFVV0dfXB0Bm\nZia9vb1cvnyZ1atXc/PmTerq6sz27e3tzM/Pk5+fT0VFBfv27fvDXLxeL9FolCNHjiz5vLu7m/Xr\n1+NwOOjq6iIQCJh1gUCA1tbWv7EqIiI/nlWLK33hrYiIpI1nz57h8/kYGhr6Jv3Nz8/jdruJRCJs\n2LDhL9sPDw9z7NgxHj58+E3GFxFJVwrpIiKyYjo7OwmFQty9e/d7T0VEJK1kfO8JiIjIj8nj8bBq\n1Srz+IyIiPz/tJMuIiIiIpJi9MNREREREZEUo5AuIiIiIpJiFNJFRERERFKMQrqIiIiISIpRSBcR\nERERSTEK6SIiIiIiKeYXoHCqALgxt0IAAAAASUVORK5CYII=\n"
      }
     ],
     "prompt_number": 2
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Before we begin, with respect to the plot above, would you say there was a change in behaviour\n",
      "during the time period? \n",
      "\n",
      "How can we start to model this? Well, as I conveniently already introduced, a Poisson random variable would be a very appropriate model for this *count* data. Denoting day $i$'s text-message count by $C_i$, \n",
      "\n",
      "$$ C_i \\sim \\text{Poisson}(\\lambda)  $$\n",
      "\n",
      "We are not sure about what the $\\lambda$ parameter is though. Looking at the chart above, it appears that the rate might become higher at some later date, which is equivalently saying the parameter $\\lambda$ increases at some later date (recall a higher $\\lambda$ means more probability on larger outcomes, that is, higher probability of many texts.).\n",
      "\n",
      "How can we mathematically represent this? We can think, that at some later date (call it $\\tau$), the parameter $\\lambda$ suddenly jumps to a higher value. So we create two $\\lambda$ parameters, one for behaviour before the $\\tau$, and one for behaviour after. In literature, a sudden transition like this would be called a *switchpoint*:\n",
      "\n",
      "$$\n",
      "\\lambda = \n",
      "\\begin{cases}\n",
      "\\lambda_1  & \\text{if } t \\lt \\tau \\cr\n",
      "\\lambda_2 & \\text{if } t \\ge \\tau\n",
      "\\end{cases}\n",
      "$$\n",
      "\n",
      "\n",
      " If, in reality, no sudden change occurred and indeed $\\lambda_1 = \\lambda_2$, the $\\lambda$'s posterior distributions should look about equal.\n",
      "\n",
      "We are interested in inferring the unknown $\\lambda$s. To use Bayesian inference, we need to assign prior probabilities to the different possible values of $\\lambda$. What would be good prior probability distributions for $\\lambda_1$ and $\\lambda_2$? Recall that $\\lambda_i, \\; i=1,2,$ can be any positive number. The *exponential* random variable has a density function for any positive number. This would be a good choice to model $\\lambda_i$. But, we need a parameter for this exponential distribution: call it $\\alpha$.\n",
      "\n",
      "\\begin{align}\n",
      "&\\lambda_1 \\sim \\text{Exp}( \\alpha ) \\\\\\\n",
      "&\\lambda_2 \\sim \\text{Exp}( \\alpha )\n",
      "\\end{align}\n",
      "\n",
      "$\\alpha$ is called a *hyper-parameter*, or a *parent-variable*, literally a parameter that influences other parameters. The influence is not too strong, so we can choose $\\alpha$ liberally.  A good rule of thumb is to set the exponential parameter equal to the inverse of the average of the count data, since we're modeling $\\\\lambda$ using an Exponential distribution we can use the expected value identity shown earlier to get:\n",
      "\n",
      "$$\\frac{1}{N}\\sum_{i=0}^N \\;C_i \\approx E[\\; \\lambda \\; |\\; \\alpha ] = \\frac{1}{\\alpha}$$ \n",
      "\n",
      "Alternatively, and something I encourage the reader to try, is to have two priors: one for each $\\lambda_i$; creating two exponential distributions with different $\\alpha$ values reflects a prior belief that the rate changed after some period.\n",
      "\n",
      "What about $\\tau$? Well, due to the randomness, it is too difficult to pick out when $\\tau$ might have occurred. Instead, we can assign an *uniform prior belief* to every possible day. This is equivalent to saying\n",
      "\n",
      "\\begin{align}\n",
      "& \\tau \\sim \\text{DiscreteUniform(1,70) }\\\\\\\\\n",
      "& \\Rightarrow P( \\tau = k ) = \\frac{1}{70}\n",
      "\\end{align}\n",
      "\n",
      "So after all this, what does our overall prior for the unknown variables look like? Frankly, *it doesn't matter*. What we should understand is that it would be an ugly, complicated, mess involving symbols only a mathematician would love. And things would only get uglier the more complicated our models become. Regardless, all we really care about is the posterior distribution. We next turn to PyMC, a Python library for performing Bayesian analysis, that is agnostic to the mathematical monster we have created. \n",
      "\n",
      "\n",
      "Introducing our first hammer: PyMC\n",
      "-----\n",
      "\n",
      "PyMC is a Python library for programming Bayesian analysis [3]. It is a fast, well-maintained library. The only unfortunate part is that documentation can be lacking in areas, especially the bridge between beginner to hacker. One of this book's main goals is to solve that problem, and also to demonstrate why PyMC is so cool.\n",
      "\n",
      "We will model the above problem using the PyMC library. This type of programming is called *probabilistic programming*, an unfortunate misnomer that invokes ideas of randomly-generated code and has likely confused and frightened users away from this field. The code is not random. The title is given because we create probability models using programming variables as the model's components, that is, model components are first-class primitives in this framework. \n",
      "\n",
      "B. Cronin [5] has a very motivating description of probabilistic programming:\n",
      "\n",
      ">   Another way of thinking about this: unlike a traditional program, which only runs in the forward directions, a probabilistic program is run in both the forward and backward direction. It runs forward to compute the consequences of the assumptions it contains about the world (i.e., the model space it represents), but it also runs backward from the data to constrain the possible explanations. In practice, many probabilistic programming systems will cleverly interleave these forward and backward operations to efficiently home in on the best explanations.\n",
      "\n",
      "Due to its poorly understood title, I'll refrain from using the name *probabilistic programming*. Instead, I'll simply use *programming*, as that is what it really is. \n",
      "\n",
      "The PyMC code is easy to follow along: the only novel thing should be the syntax, and I will interrupt the code to explain sections. Simply remember we are representing the model's components ($\\tau, \\lambda_1, \\lambda_2$ ) as variables:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import pymc as mc\n",
      "\n",
      "n = count_data.shape[0]\n",
      "\n",
      "alpha = 1.0/count_data.mean() #recall count_data is \n",
      "                              #the variable that holds our txt counts\n",
      "\n",
      "lambda_1 = mc.Exponential( \"lambda_1\",  alpha )\n",
      "lambda_2 = mc.Exponential( \"lambda_2\", alpha )\n",
      "\n",
      "tau = mc.DiscreteUniform( \"tau\", lower = 0, upper = n )"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 5
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "In the above code, we create the PyMC variables corresponding to $\\lambda_1, \\; \\lambda_2$. We assign them to PyMC's *stochastic variables*, called stochastic variables because they are treated by the backend as random number generators. We can test this by calling their built-in `random()` method."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "print \"Random output:\", tau.random(),tau.random(), tau.random()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Random output: 13 12 54\n"
       ]
      }
     ],
     "prompt_number": 6
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "@mc.deterministic\n",
      "def lambda_( tau = tau, lambda_1 = lambda_1, lambda_2 = lambda_2 ):\n",
      "    out = np.zeros( n )  \n",
      "    out[:tau] = lambda_1 #lambda before tau is lambda1\n",
      "    out[tau:] = lambda_2 #lambda after tau is lambda2\n",
      "    return out"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 7
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "This code is creating a new function `lambda_`, but really we think of it as a random variable: the random variable $\\lambda$ from above. Note that because `lambda_1`, `lambda_2` and `tau` are random, `lambda_` will be random. We are **not** fixing any variables yet. The `@mc.deterministic` is a decorator to tell PyMC that this is a deterministic function, i.e., if the arguments were deterministic (which they are not), the output would be deterministic as well. "
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "observation = mc.Poisson( \"obs\", lambda_, value = count_data, observed = True)\n",
      "\n",
      "model = mc.Model( [observation, lambda_1, lambda_2, tau] )"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 8
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "The variable `observation` combines our data, `count_data`, with our proposed data-generation scheme, given by the variable `lambda_`, through the `value` keyword. We also set `observed = True` to tell PyMC that this should stay fixed in our analysis. Finally, PyMC wants us to collect all the variables of interest and create a `Model` instance out of them. This makes our life easier when we try to retrieve the results.\n",
      "\n",
      "The below code will be explained in the Chapter 3, but this is where our results come from. One can think of it as a *learning* step. The machinery being employed is called *Monte Carlo Markov Chains* (which I delay explaining until Chapter 3). It returns thousands of random variables from the posterior distributions of $\\lambda_1, \\lambda_2$ and $\\tau$. We can plot a histogram of the random variables to see what the posterior distribution looks like. Below, we collect the samples (called *traces* in MCMC literature) in histograms."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "### Mysterious code to be explained in Chapter 3.\n",
      "mcmc = mc.MCMC(model)\n",
      "mcmc.sample( 35000, 5000, 1 )"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " \r",
        "[****************100%******************]  35000 of 35000 complete"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n"
       ]
      }
     ],
     "prompt_number": 9
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "lambda_1_samples = mcmc.trace( 'lambda_1' )[:]\n",
      "lambda_2_samples = mcmc.trace( 'lambda_2' )[:]\n",
      "tau_samples = mcmc.trace( 'tau' )[:]"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 10
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "figsize(12.5, 10)\n",
      "#histogram of the samples:\n",
      "\n",
      "ax = plt.subplot(311)\n",
      "ax.set_autoscaley_on(False)\n",
      "\n",
      "plt.hist( lambda_1_samples, histtype='stepfilled', bins = 30, alpha = 0.85, \n",
      "        label = \"posterior of $\\lambda_1$\", color = \"#A60628\",normed = True )\n",
      "plt.legend(loc = \"upper left\")\n",
      "plt.title(r\"Posterior distributions of the variables $\\lambda_1,\\;\\lambda_2,\\;\\tau$\")\n",
      "plt.xlim([15,30])\n",
      "plt.xlabel(\"$\\lambda_2$ value\")\n",
      "plt.ylabel(\"probability\")\n",
      "\n",
      "ax = plt.subplot(312)\n",
      "ax.set_autoscaley_on(False)\n",
      "\n",
      "plt.hist( lambda_2_samples,histtype='stepfilled', bins = 30, alpha = 0.85, \n",
      "          label = \"posterior of $\\lambda_2$\",color=\"#7A68A6\", normed = True )\n",
      "plt.legend(loc = \"upper left\")\n",
      "plt.xlim([15,30])\n",
      "plt.xlabel(\"$\\lambda_2$ value\")\n",
      "plt.ylabel(\"probability\")\n",
      "\n",
      "plt.subplot(313)\n",
      "\n",
      "\n",
      "w = 1.0/ tau_samples.shape[0] * np.ones_like( tau_samples )\n",
      "plt.hist( tau_samples, bins = n_count_data, alpha = 1, \n",
      "         label = r\"posterior of $\\tau$\",\n",
      "         color=\"#467821\", weights=w, rwidth =1. )\n",
      "\n",
      "plt.legend(loc = \"upper left\");\n",
      "plt.ylim([0,.75])\n",
      "plt.xlim([35, len(count_data)-20])\n",
      "plt.xlabel(\"days\")\n",
      "plt.ylabel(\"probability\");"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "display_data",
       "png": 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3sG4J/58i0cy2rZa9gKyYnbj8f+u1ruv+8yI85e5cr3USERERGVpdvxBK56w1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      }
     ],
     "prompt_number": 11
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "### Interpretation\n",
      "\n",
      "Recall that the Bayesian methodology returns a *distribution*, hence we now have distributions to describe the unknown $\\lambda$'s and $\\tau$. What have we gained? Immediately we can see the uncertainty in our estimates: the more variance in the distribution, the less certain our posterior belief should be. We can also say what a plausible value for the parameters might be: $\\lambda_1$ is around 18 and $\\lambda_2$ is around 23. What other observations can you make? Look at the data again, do these seem reasonable? The distributions of the two $\\\\lambda$s are positioned very differently, indicating that it's likely there was a change in the user's text-message behaviour.\n",
      "\n",
      "Also notice that the posterior distributions for the $\\lambda$'s do not look like any exponential distributions, though we originally started modeling with exponential random variables. They are really not anything we recognize. But this is OK. This is one of the benefits of taking a computational point-of-view. If we had instead done this mathematically, we would have been stuck with a very analytically intractable (and messy) distribution. Via computations, we are agnostic to the tractability.\n",
      "\n",
      "Our analysis also returned a distribution for what $\\tau$ might be. Its posterior distribution looks a little different from the other two because it is a discrete random variable, hence it doesn't assign probabilities to intervals. We can see that near day 45, there was a 50% chance the users behaviour changed. Had no change occurred, or the change been gradual over time, the posterior distribution of $\\tau$ would have been more spread out, reflecting that many values are likely candidates for $\\tau$. On the contrary, it is very peaked. "
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "###Why would I want samples from the posterior, anyways?\n",
      "\n",
      "\n",
      "We will deal with this question for the remainder of the book, and it is an understatement to say we can perform amazingly useful things. For now, let's end this chapter with one more example. We'll use the posterior samples to answer the following question: what is the expected number of texts at day $t, \\; 0 \\le t \\le70$? Recall that the expected value of a Poisson is equal to its parameter $\\lambda$, then the question is equivalent to *what is the expected value of $\\lambda$ at time $t$*?\n",
      "\n",
      "In the code below, we are calculating the following: Let $i$ index samples from the posterior distributions. Given a day $t$, we average over all possible $\\lambda_i$ for that day $t$, using $\\lambda_i = \\lambda_{1,i}$ if $t \\lt \\tau_i$ (that is, if the behaviour change hadn't occurred yet), else we use $\\lambda_i = \\lambda_{2,i}$. \n",
      "\n",
      "\n"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "\n",
      "___________________"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "figsize( 12.5, 4)\n",
      "# tau_samples, lambda_1_samples, lambda_2_samples contain\n",
      "# N samples from the corresponding posterior distribution\n",
      "N = tau_samples.shape[0]\n",
      "expected_texts_per_day = np.zeros(n_count_data)\n",
      "for  day in range(0, n_count_data):\n",
      "    # ix is a bool index of all tau samples corresponding to\n",
      "    # the switchpoint occurring prior to value of 'day'\n",
      "    ix = day < tau_samples\n",
      "    # Each posterior sample corresponds to a value for tau.\n",
      "    # for each day, that value of tau indicates whether we're \"before\" \n",
      "    # (in the lambda1 \"regime\") or\n",
      "    #  \"after\" (in the lambda2 \"regime\") the switchpoint.\n",
      "    # by taking the posterior sample of lambda1/2 accordingly, we can average\n",
      "    # over all samples to get an expected value for lambda on that day.\n",
      "    # As explained, the \"message count\" random variable is Poisson distributed, \n",
      "    # and therefore lambda (the poisson parameter) is the expected value of \"message count\"\n",
      "    expected_texts_per_day[day] = (lambda_1_samples[ix].sum() \n",
      "                                    + lambda_2_samples[~ix].sum() ) /N\n",
      "\n",
      "    \n",
      "plt.plot( range( n_count_data), expected_texts_per_day, lw =4, color = \"#E24A33\" )\n",
      "plt.xlim( 0, n_count_data )\n",
      "plt.xlabel( \"Day\" )\n",
      "plt.ylabel( \"Expected # text-messages\" )\n",
      "plt.title( \"Expected number of text-messages received\")\n",
      "#plt.ylim( 0, 35 )\n",
      "plt.bar( np.arange( len(count_data) ), count_data, color =\"#348ABD\", alpha = 0.5,\n",
      "            label=\"observed texts per day\")\n",
      "\n",
      "plt.legend(loc=\"upper left\");"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "display_data",
       "png": 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REVHr+yYiIqLGi1fSdcDd3R2XL1/WagBevHhR62rx3Q3e27dvIzc3F+7u7gCA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\nigAAAABJRU5ErkJggg==\n"
      }
     ],
     "prompt_number": 49
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Our analysis shows strong support for believing the user's behavior did change ($\\lambda_1$ would have been close in value to $\\lambda_2$ had this not been true), and the change was sudden rather then gradual (demonstrated by $\\tau$'s strongly peaked posterior distribution). We can speculate what might have caused this: a cheaper text-message rate, a recent weather-2-text subscription, or a new relationship. (The 45th day corresponds to Christmas, and I moved away to Toronto the next month leaving a girlfriend behind.)\n"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "##### Exercises\n",
      "\n",
      "1\\.  Using `lambda_1_samples` and `lambda_2_samples`, what is the mean of the posterior distributions of $\\lambda_1$ and $\\lambda_2$?"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#type your code here."
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 17
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "2\\.  What is the expected percentage increase in text-message rates? `hint:` compute the mean of `lambda_1_samples/lambda_2_samples`. Note that quantity is very different from `lambda_1_samples.mean()/lambda_2_samples.mean()`."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#type your code here."
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 16
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "3\\. Looking at the posterior distribution graph of $\\tau$, why do you think there is a small number of posterior $\\tau$ samples near 0? `hint:` Look at the data again."
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "4\\. What is the mean of $\\lambda_1$ **given** we know $\\tau$ is less than 45.  That is, suppose we have new information as we know for certain that the change in behaviour occurred before day 45. What is the expected value of $\\lambda_1$ now? (You do not need to redo the PyMC part, just consider all instances where `tau_samples<45`. )"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#type your code here."
     ],
     "language": "python",
     "metadata": {},
     "outputs": []
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "### References\n",
      "\n",
      "\n",
      "-  [1] Gelman, Andrew. N.p.. Web. 22 Jan 2013. <http://andrewgelman.com/2005/07/n_is_never_larg/>.\n",
      "-  [2] Norvig, Peter. 2009. [*The Unreasonable Effectiveness of Data*](http://www.csee.wvu.edu/~gidoretto/courses/2011-fall-cp/reading/TheUnreasonable EffectivenessofData_IEEE_IS2009.pdf).\n",
      "- [3] Patil, A., D. Huard and C.J. Fonnesbeck. 2010. \n",
      "PyMC: Bayesian Stochastic Modelling in Python. Journal of Statistical \n",
      "Software, 35(4), pp. 1-81. \n",
      "- [4] Jimmy Lin and Alek Kolcz. Large-Scale Machine Learning at Twitter. Proceedings of the 2012 ACM SIGMOD International Conference on Management of Data (SIGMOD 2012), pages 793-804, May 2012, Scottsdale, Arizona.\n",
      "- [5] Cronin, Beau. \"Why Probabilistic Programming Matters.\" 24 Mar 2013. Google, Online Posting to Google . Web. 24 Mar. 2013. <https://plus.google.com/u/0/107971134877020469960/posts/KpeRdJKR6Z1>."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from IPython.core.display import HTML\n",
      "def css_styling():\n",
      "    styles = open(\"../styles/custom.css\", \"r\").read()\n",
      "    return HTML(styles)\n",
      "css_styling()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "html": [
        "<style>\n",
        "    @font-face {\n",
        "        font-family: \"Computer Modern\";\n",
        "        src: url('http://mirrors.ctan.org/fonts/cm-unicode/fonts/otf/cmunss.otf');\n",
        "    }\n",
        "    div.cell{\n",
        "        width:800px;\n",
        "        margin-left:16% !important;\n",
        "        margin-right:auto;\n",
        "    }\n",
        "    h1 {\n",
        "        font-family: Helvetica, serif;\n",
        "    }\n",
        "    h4{\n",
        "        margin-top:12px;\n",
        "        margin-bottom: 3px;\n",
        "       }\n",
        "    div.text_cell_render{\n",
        "        font-family: Computer Modern, \"Helvetica Neue\", Arial, Helvetica, Geneva, sans-serif;\n",
        "        line-height: 145%;\n",
        "        font-size: 130%;\n",
        "        width:800px;\n",
        "        margin-left:auto;\n",
        "        margin-right:auto;\n",
        "    }\n",
        "    .CodeMirror{\n",
        "            font-family: \"Source Code Pro\", source-code-pro,Consolas, monospace;\n",
        "    }\n",
        "    .prompt{\n",
        "        display: None;\n",
        "    }\n",
        "    .text_cell_render h5 {\n",
        "        font-weight: 300;\n",
        "        font-size: 16pt;\n",
        "        color: #4057A1;\n",
        "        font-style: italic;\n",
        "        margin-bottom: .5em;\n",
        "        margin-top: 0.5em;\n",
        "        display: block;\n",
        "    }\n",
        "    \n",
        "    .warning{\n",
        "        color: rgb( 240, 20, 20 )\n",
        "        }  \n",
        "</style>\n",
        "<script>\n",
        "    MathJax.Hub.Config({\n",
        "                        TeX: {\n",
        "                           extensions: [\"AMSmath.js\"]\n",
        "                           },\n",
        "                tex2jax: {\n",
        "                    inlineMath: [ ['$','$'], [\"\\\\(\",\"\\\\)\"] ],\n",
        "                    displayMath: [ ['$$','$$'], [\"\\\\[\",\"\\\\]\"] ]\n",
        "                },\n",
        "                displayAlign: 'center', // Change this to 'center' to center equations.\n",
        "                \"HTML-CSS\": {\n",
        "                    styles: {'.MathJax_Display': {\"margin\": 4}}\n",
        "                }\n",
        "        });\n",
        "</script>"
       ],
       "output_type": "pyout",
       "prompt_number": 3,
       "text": [
        "<IPython.core.display.HTML at 0x50cf0f0>"
       ]
      }
     ],
     "prompt_number": 3
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [],
     "language": "python",
     "metadata": {},
     "outputs": []
    }
   ],
   "metadata": {}
  }
 ]
}