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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 is available at [github/Probabilistic-Programming-and-Bayesian-Methods-for-Hackers](https://github.com/CamDavidsonPilon/Probabilistic-Programming-and-Bayesian-Methods-for-Hackers). The other chapters can be found on the project's [homepage](camdavidsonpilon.github.io/Probabilistic-Programming-and-Bayesian-Methods-for-Hackers/). We hope you enjoy the book, and we encourage any contributions!"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Chapter 1\n",
      "======\n",
      "***"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "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 thinking Bayesian! 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, but still not certain.  Bayesian inference works identically: we update our beliefs about an outcome; rarely can we be absolutely sure unless we rule out all other alternatives. "
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      "\n",
      "### The Bayesian state of mind\n",
      "\n",
      "\n",
      "Bayesian inference differs from more traditional statistical inference by preserving *uncertainty*. 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*, known as the more *classical* version of statistics, 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 realities, 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. Simply, a probability is a summary of an opinion. 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 meaningful to 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. The existence of different beliefs does not imply that anyone is wrong. 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 (whichever it is). 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, but a second doctor may have slightly different beliefs. \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 truths, but gather evidence to form beliefs. 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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     "source": [
      "\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, representing an estimate (typically a summary statistic like the sample average etc.), 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: 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 (often) 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 computationally-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 such as least squares linear regression, LASSO regression, and expectation-maximization algorithms are all powerful and fast. Bayesian methods complement these techniques by solving problems that these approaches cannot, or by illuminating the underlying system with more flexible 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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     "source": [
      "### 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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     "source": [
      "##### 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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     "input": [
      "\"\"\"\n",
      "The book uses a custom matplotlibrc file, which provides the unique styles for\n",
      "matplotlib plots. If executing this book, and you wish to use the book's\n",
      "styling, provided are two options:\n",
      "    1. Overwrite your own matplotlibrc file with the rc-file provided in the\n",
      "       book's styles/ dir. See http://matplotlib.org/users/customizing.html\n",
      "    2. Also in the styles is  bmh_matplotlibrc.json file. This can be used to\n",
      "       update the styles 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, plus it\n",
      "# uses advanced topics we have not covered yet. LOOK AT PICTURE, MICHAEL!\n",
      "%matplotlib inline\n",
      "from IPython.core.pylabtools import figsize\n",
      "import numpy as np\n",
      "from matplotlib import pyplot as plt\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 the already prepared, I'm using Binomial's conj. prior.\n",
      "for k, N in enumerate(n_trials):\n",
      "    sx = plt.subplot(len(n_trials)/2, 2, k+1)\n",
      "    plt.xlabel(\"$p$, probability of heads\") \\\n",
      "        if k in [0, len(n_trials)-1] else None\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": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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X5PPCwIED0bJlSwCV54WqYl5gAUFEMi5fvgwPDw+jx7y8vJCRkSG1W7RoIf3s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\nxCwHOSnWYfs3KGsgxNnqWrvwZZ2Xvcc7+LLOQ1VL4LS1Cy6LkewUC9l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gAAAg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\nbEwgiIiIiIhINiYQREREREQk2/8HhO2oCkLEFsEAAAAASUVORK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0x104a21b90>"
       ]
      }
     ],
     "prompt_number": 1
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "The posterior probabilities are represented by the curves, and our uncertainty is proportional to the width 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 tighten 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 (with no prior opinion, how confident would you feel betting on a fair coin after observing 8 tails and 1 head). As more data accumulates, we would see more and more probability being assigned at $p=0.5$, though never all of it.\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": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 6,
       "text": [
        "<matplotlib.text.Text at 0x1051de650>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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mBX11s67X19jLZYj2dsZYv/ZifoyPC1SO7J8fqvizhaytXz8dkpKSEB8fj7ff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\nkQX5f5hZyxZq7GtyAAAAAElFTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0x10210d490>"
       ]
      }
     ],
     "prompt_number": 6
    },
    {
     "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 chart 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",
      "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\")\n",
      "plt.ylabel(\"Probability\")\n",
      "plt.legend(loc=\"upper left\");"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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3b6+z/d0/dzT9PKuNgYhu4xV2IiNjZWUFHx8feHp6NjiDRkO6dOlSZxq0ffv2QZIkdOnS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\nuwBwyy23YLPZ+O6773jrrbd4+eWX3T5mZWUl6en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       "text": [
        "<matplotlib.figure.Figure at 0x1051e1290>"
       ]
      }
     ],
     "prompt_number": 7
    },
    {
     "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",
      "$\\lambda$ is called a parameter of the distribution, and it controls the distribution's shape. For the Poisson distribution, $\\lambda$ 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. One can describe $\\lambda$ as the *intensity* of the Poisson distribution. \n",
      "\n",
      "Unlike $\\lambda$, which can be any positive number, the value $k$ in the above formula 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 useful property of the Poisson distribution is that its expected value is equal to its parameter, i.e.:\n",
      "\n",
      "$$E\\large[ \\;Z\\; | \\; \\lambda \\;\\large] = \\lambda $$\n",
      "\n",
      "We will use this property often, so it's 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 of larger values occurring. Second, 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",
      "colours = [\"#348ABD\", \"#A60628\"]\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": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 8,
       "text": [
        "<matplotlib.text.Text at 0x105898110>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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VuTwxMZFHH300oH385S9/4aabbvK9IV1ddHQ0ffr0AWDZsmVcfPHF9OvXL7jw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\n9i2jw9oQXXiKZi2aUzEsBUbY+QEr4s/hk6XkHy0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       "text": [
        "<matplotlib.figure.Figure at 0x105211690>"
       ]
      }
     ],
     "prompt_number": 8
    },
    {
     "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 *exponential density*. The density function for an exponential random variable looks like this:\n",
      "\n",
      "$$f_Z(z | \\lambda) = \\lambda e^{-\\lambda z }, \\;\\; z\\ge 0$$\n",
      "\n",
      "Like a Poisson random variable, an exponential random variable can take on only non-negative values. But unlike a Poisson variable, the exponential can take on *any* non-negative values, including non-integral values such as 4.25 or 5.612401. This property makes it a poor choice for count data, which must be an integer, but a great choice for time data, temperature data (measured in Kelvins, of course), or any other precise *and positive* variable. The graph below shows two probability density functions with different $\\lambda$ values. \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.ylim(0,1.2)\n",
      "plt.title(\"Probability density function of an Exponential random variable;\\\n",
      " differing $\\lambda$\");"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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UFISrV6/it99+Q8+ePYXuY10GDx6MmTNnYvPmzejevTs2b96MhIQEuLu7G9ZpaJ+cnZ2x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\nXzJoEpT8JxelAAAAAElFTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0x1059ba590>"
       ]
      }
     ],
     "prompt_number": 12
    },
    {
     "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 see only $Z$, and must go backwards to try and determine $\\lambda$. The problem is difficult because there is no 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 best! \n",
      "\n",
      "Bayesian inference is concerned with *beliefs* about what $\\lambda$ might be. 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 values of a non-random variable? Ah, we have fallen for our old, frequentist way of thinking. Recall that under 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, one that concerns the rate at which a user sends and receives text messages:\n",
      "\n",
      ">  You are given a series of daily text-message counts from a user of your system. The data, plotted over time, appears in the chart below. You are curious to know if the user's text-messaging habits have 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": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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h4eGBPn36QAiBdevW4eTJk6aujyTSWu+WtWDu8jB7OZi7HMxdDuYuj9ayV3V3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\ne1WD9KioKJw/fx5Vq1Z9oo3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WLMC7776rakO7d+/GypUr8eyzz8LX1xcAMHv2bEyePBkD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\nRCTFKEkXEREREUkxStJFRERERFLMvwANW7VmJFIo4AAAAABJRU5ErkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0x1018653d0>"
       ]
      }
     ],
     "prompt_number": 2
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Before we start modeling, see what you can figure out just by looking at the chart above. Would you say there was a change in behaviour during this time period? \n",
      "\n",
      "How can we start to model this? Well, as we have conveniently already seen, a Poisson random variable is a very appropriate model for this type of *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 what the value of the $\\lambda$ parameter really is, however. Looking at the chart above, it appears that the rate might become higher late in the observation period, which is equivalent to saying that $\\lambda$ increases at some point during the observations. (Recall that a higher value of $\\lambda$ assigns more probability to larger outcomes. That is, there is a higher probability of many text messages having been sent on a given day.)\n",
      "\n",
      "How can we represent this observation mathematically? Let's assume that on some day during the observation period (call it $\\tau$), the parameter $\\lambda$ suddenly jumps to a higher value. So we really have two $\\lambda$ parameters: one for the period before $\\tau$, and one for the rest of the observation period. In the 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 $\\lambda_1 = \\lambda_2$, then 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 $\\lambda$ can be any positive number. As we saw earlier, the *exponential* distribution provides a continuous density function for positive numbers, so it might be a good choice for modeling $\\lambda_i$. But recall that the exponential distribution takes a parameter of its own, so we'll need to include that parameter in our model. Let's call that parameter $\\alpha$.\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 *parent variable*. In literal terms, it is a parameter that influences other parameters. Our initial guess at $\\alpha$ does not influence the model too strongly, so we have some flexibility in our choice.  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",
      "An alternative, and something I encourage the reader to try, would be to have two priors: one for each $\\lambda_i$. Creating two exponential distributions with different $\\alpha$ values reflects our prior belief that the rate changed at some point during the observations.\n",
      "\n",
      "What about $\\tau$? Because of the noisiness of the data, it's difficult to pick out a priori when $\\tau$ might have occurred. Instead, we can assign a *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 distribution for the unknown variables look like? Frankly, *it doesn't matter*. What we should understand is that it's an ugly, complicated mess involving symbols only a mathematician could love. And things will only get uglier the more complicated our models become. Regardless, all we really care about is the posterior distribution.\n",
      "\n",
      "We next turn to PyMC, a Python library for performing Bayesian analysis that is undaunted by 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 its documentation is lacking in certain areas, especially those that bridge the gap between beginner and 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 problem above using PyMC. 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; it is probabilistic in the sense that we create probability models using programming variables as the model's components. Model components are first-class primitives within the PyMC 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",
      "Because of the confusion engendered by the term *probabilistic programming*, I'll refrain from using it. Instead, I'll simply say *programming*, since that's what it really is. \n",
      "\n",
      "PyMC code is easy to read. The only novel thing should be the syntax. Simply remember that we are representing the model's components ($\\tau, \\lambda_1, \\lambda_2$ ) as variables.\n",
      "\n",
      "In the code below, we create the PyMC variables corresponding to $\\lambda_1$ and $\\lambda_2$. We assign them to PyMC's *stochastic variables*, so-called because they are treated by the back end as random number generators."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import pymc as pm\n",
      "\n",
      "with pm.Model() as model:\n",
      "    alpha = 1.0/count_data.mean()  # Recall count_data is the\n",
      "                                   # variable that holds our txt counts\n",
      "    lambda_1 = pm.Exponential(\"lambda_1\", alpha)\n",
      "    lambda_2 = pm.Exponential(\"lambda_2\", alpha)\n",
      "    \n",
      "    tau = pm.DiscreteUniform(\"tau\", lower=0, upper=n_count_data)\n",
      "\n",
      "    #def lambda_(tau=tau, lambda_1=lambda_1, lambda_2=lambda_2):\n",
      "    #    out = np.zeros(n_count_data)\n",
      "    #    out[:tau] = lambda_1  # lambda before tau is lambda1\n",
      "    #    out[tau:] = lambda_2  # lambda after (and including) tau is lambda2\n",
      "    #    return out\n",
      "    idx = np.arange( n_count_data )\n",
      "    \n",
      "    # the following code is equivilant to \n",
      "    # def switch(tau, lambda_1, lambda_2):\n",
      "    #    out = np.zeros(n_count_data)\n",
      "    #    out[:tau] = lambda_1  # lambda before tau is lambda1\n",
      "    #    out[tau:] = lambda_2  # lambda after (and including) tau is lambda2\n",
      "    #    return out\n",
      "    # lambda_ = switch( tau, lambda_1, lambda_2 )\n",
      "    lambda_ = pm.switch( tau >= idx, lambda_1, lambda_2 )\n",
      "    \n",
      "    observation = pm.Poisson(\"obs\", lambda_, observed=count_data)\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 40
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "This code creates a new function `lambda_`, but really we can 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."
     ]
    },
    {
     "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 `observed` keyword. \n",
      "\n",
      "The code below will be explained in Chapter 3, but I show it here so you can see where our results come from. One can think of it as a *learning* step. The machinery being employed is called *Markov Chain Monte Carlo* (MCMC), which I also delay explaining until Chapter 3. This technique 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 distributions look like. Below, we collect the samples (called *traces* in the MCMC literature) into histograms."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "### Mysterious code to be explained in Chapter 3.\n",
      "with model:\n",
      "    step = pm.Metropolis(model.free_RVs)\n",
      "    trace = pm.sample(10000, tune=5000,step=step)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [----             11%                  ] 1106 of 10000 complete in 0.5 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [---------        23%                  ] 2391 of 10000 complete in 1.0 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [--------------   37%                  ] 3708 of 10000 complete in 1.5 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [-----------------50%                  ] 5043 of 10000 complete in 2.0 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [-----------------63%----              ] 6352 of 10000 complete in 2.5 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [-----------------76%---------         ] 7685 of 10000 complete in 3.0 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [-----------------89%--------------    ] 8970 of 10000 complete in 3.5 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [-----------------100%-----------------] 10000 of 10000 complete in 3.9 sec"
       ]
      }
     ],
     "prompt_number": 34
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "lambda_1_samples = trace['lambda_1']\n",
      "lambda_2_samples = trace['lambda_2']\n",
      "tau_samples = trace['tau']"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 38
    },
    {
     "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\n",
      "    $\\lambda_1,\\;\\lambda_2,\\;\\tau$\"\"\")\n",
      "plt.xlim([15, 30])\n",
      "plt.xlabel(\"$\\lambda_1$ value\")\n",
      "\n",
      "ax = plt.subplot(312)\n",
      "ax.set_autoscaley_on(False)\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",
      "\n",
      "plt.subplot(313)\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=2.)\n",
      "plt.xticks(np.arange(n_count_data))\n",
      "\n",
      "plt.legend(loc=\"upper left\")\n",
      "plt.ylim([0, .75])\n",
      "plt.xlim([35, len(count_data)-20])\n",
      "plt.xlabel(r\"$\\tau$ (in days)\")\n",
      "plt.ylabel(\"probability\");"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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6WaUREREREamOlDnyOp0O7dq1w44dO+Dq6oru3bsjOjoavr6++jELFixAcXEx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       "text": [
        "<matplotlib.figure.Figure at 0x106746050>"
       ]
      }
     ],
     "prompt_number": 39
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "### Interpretation\n",
      "\n",
      "Recall that 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 wider the distribution, the less certain our posterior belief should be. We can also see what the plausible values for the parameters are: $\\lambda_1$ is around 18 and $\\lambda_2$ is around 23. The posterior distributions of the two $\\lambda$s are clearly distinct, indicating that it is indeed likely that there was a change in the user's text-message behaviour.\n",
      "\n",
      "What other observations can you make? If you look at the original data again, do these results seem reasonable? \n",
      "\n",
      "Notice also that the posterior distributions for the $\\lambda$s do not look like exponential distributions, even though our priors for these variables were exponential. In fact, the posterior distributions are not really of any form that we recognize from the original model. But that's OK! This is one of the benefits of taking a computational point of view. If we had instead done this analysis using mathematical approaches, we would have been stuck with an analytically intractable (and messy) distribution. Our use of a computational approach makes us indifferent to mathematical tractability.\n",
      "\n",
      "Our analysis also returned a distribution for $\\tau$. Its posterior distribution looks a little different from the other two because it is a discrete random variable, so it doesn't assign probabilities to intervals. We can see that near day 45, there was a 50% chance that the user's behaviour changed. Had no change occurred, or had the change been gradual over time, the posterior distribution of $\\tau$ would have been more spread out, reflecting that many days were plausible candidates for $\\tau$. By contrast, in the actual results we see that only three or four days make any sense as potential transition points. "
     ]
    },
    {
     "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 that it will lead us to some amazing results. For now, let's end this chapter with one more example.\n",
      "\n",
      "We'll use the posterior samples to answer the following question: what is the expected number of texts at day $t, \\; 0 \\le t \\le 70$ ? Recall that the expected value of a Poisson variable is equal to its parameter $\\lambda$. Therefore, the question is equivalent to *what is the expected value of $\\lambda$ at time $t$*?\n",
      "\n",
      "In the code below, 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 has not yet occurred), else we use $\\lambda_i = \\lambda_{2,i}$. "
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "figsize(12.5, 5)\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\n",
      "    # \"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",
      "         label=\"expected number of text-messages received\")\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, 60)\n",
      "plt.bar(np.arange(len(count_data)), count_data, color=\"#348ABD\", alpha=0.65,\n",
      "        label=\"observed texts per day\")\n",
      "\n",
      "plt.legend(loc=\"upper left\");"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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h+P3334X1JyQkID09Hb169aryPTpnzhxoaWkhISEB69atw+7du2vFMDJCCCG1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\n+y+490+5AAAAAElFTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0x1068764d0>"
       ]
      }
     ],
     "prompt_number": 41
    },
    {
     "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 that the change was sudden rather than gradual (as demonstrated by $\\tau$'s strongly peaked posterior distribution). We can speculate what might have caused this: a cheaper text-message rate, a recent weather-to-text subscription, or perhaps a new relationship. (In fact, 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": 25
    },
    {
     "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 this 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": 26
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "3\\. What is the mean of $\\lambda_1$ **given** that we know $\\tau$ is less than 45.  That is, suppose we have been given new information that the change in behaviour occurred prior to 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": [],
     "prompt_number": 17
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "### References\n",
      "\n",
      "\n",
      "-  [1] Gelman, Andrew. N.p.. Web. 22 Jan 2013. [N is never large enough](http://andrewgelman.com/2005/07/n_is_never_large).\n",
      "-  [2] Norvig, Peter. 2009. [The Unreasonable Effectiveness of Data](http://static.googleusercontent.com/media/research.google.com/en//pubs/archive/35179.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://9dbb143991406a7c655e-aa5fcb0a5a4ec34cff238a2d56ca4144.r56.cf5.rackcdn.com/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: 22pt;\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"
       ],
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 1,
       "text": [
        "<IPython.core.display.HTML at 0x10f034850>"
       ]
      }
     ],
     "prompt_number": 1
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [],
     "language": "python",
     "metadata": {},
     "outputs": []
    }
   ],
   "metadata": {}
  }
 ]
}