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     "source": [
      "Chapter 2\n",
      "======\n",
      "______\n",
      "\n",
      "This chapter introduces more PyMC syntax and design patterns, and ways to think about how to model a system from a Bayesian perspective. It also contains tips and data visualization techniques for assessing goodness-of-fit for your Bayesian model."
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "## A little more on PyMC\n",
      "\n",
      "### Parent and Child relationships\n",
      "\n",
      "To assist with describing Bayesian relationships, and to be consistent with PyMC's documentation, we introduce *parent and child* variables. \n",
      "\n",
      "*  *parent variables* are variables that influence another variable. \n",
      "\n",
      "*  *child variable* are variables that are affected by other variables, i.e. are the subject of parent variables. \n",
      "\n",
      "A variable can be both a parent and child. For example, consider the PyMC code below."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import pymc as pm\n",
      "\n",
      "\n",
      "parameter = pm.Exponential(\"poisson_param\", 1)\n",
      "data_generator = pm.Poisson(\"data_generator\", parameter)\n",
      "data_plus_one = data_generator + 1"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 1
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "`parameter` controls the parameter of `data_generator`, hence influences its values. The former is a parent of the latter. By symmetry, `data_generator` is a child of `parameter`.\n",
      "\n",
      "Likewise, `data_generator` is a parent to the variable `data_plus_one` (hence making `data_generator` both a parent and child variable). Although it does not look like one, `data_plus_one` should be treated as a PyMC variable as it is a *function* of another PyMC variable, hence is a child variable to `data_generator`.\n",
      "\n",
      "This nomenclature is introduced to help us describe relationships in PyMC modeling. You can access a variables children and parent variables using the `children` and `parents` attributes attached to variables."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "print \"Children of `parameter`: \"\n",
      "print parameter.children\n",
      "print \"\\nParents of `data_generator`: \"\n",
      "print data_generator.parents\n",
      "print \"\\nChildren of `data_generator`: \"\n",
      "print data_generator.children"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Children of `parameter`: \n",
        "set([<pymc.distributions.Poisson 'data_generator' at 0x1087e14d0>])\n",
        "\n",
        "Parents of `data_generator`: \n",
        "{'mu': <pymc.distributions.Exponential 'poisson_param' at 0x104efac50>}\n",
        "\n",
        "Children of `data_generator`: \n",
        "set([<pymc.PyMCObjects.Deterministic '(data_generator_add_1)' at 0x109119790>])\n"
       ]
      }
     ],
     "prompt_number": 2
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Of course a child can  have more than one parent, and a parent can have many children."
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "### PyMC Variables\n",
      "\n",
      "All PyMC variables also expose a `value` attribute. This method produces the *current* (possibly random) internal value of the variable. If the variable is a child variable, its value changes given the variable's parents' values. Using the same variables from before:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "print \"parameter.value =\", parameter.value\n",
      "print \"data_generator.value =\", data_generator.value\n",
      "print \"data_plus_one.value =\", data_plus_one.value"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "parameter.value = 0.0281609254306\n",
        "data_generator.value = 0\n",
        "data_plus_one.value = 1\n"
       ]
      }
     ],
     "prompt_number": 3
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "PyMC is concerned with two types of programming variables: `stochastic` and `deterministic`.\n",
      "\n",
      "*  *stochastic variables* are variables that are not deterministic, i.e., even if you knew all the values of the variables' parents (if it even has any parents), it would still be random. Included in this category are instances of classes `Poisson`, `DiscreteUniform`, and `Exponential`.\n",
      "\n",
      "*  *deterministic variables* are variables that are not random if the variables' parents were known. This might be confusing at first: a quick mental check is *if I knew all of variable `foo`'s parent variables, I could determine what `foo`'s value is.* \n",
      "\n",
      "We will detail each below.\n",
      "\n",
      "#### Initializing Stochastic variables\n",
      "\n",
      "Initializing a stochastic variable requires a `name` argument, plus additional parameters that are class specific. For example:\n",
      "\n",
      "`some_variable = pm.DiscreteUniform(\"discrete_uni_var\", 0, 4)`\n",
      "\n",
      "where 0, 4 are the `DiscreteUniform`-specific lower and upper bound on the random variable. The [PyMC docs](http://pymc-devs.github.com/pymc/distributions.html) contain the specific parameters for stochastic variables. (Or use `??` if you are using IPython!)\n",
      "\n",
      "The `name` attribute is used to retrieve the posterior distribution later in the analysis, so it is best to use a descriptive name. Typically, I use the Python variable's name as the `name`.\n",
      "\n",
      "For multivariable problems, rather than creating a Python array of stochastic variables, addressing the `size` keyword in the call to a `Stochastic` variable creates multivariate array of (independent) stochastic variables. The array behaves like a Numpy array when used like one, and references to its `value` attribute return Numpy arrays.  \n",
      "\n",
      "The `size` argument also solves the annoying case where you may have many variables $\\beta_i, \\; i = 1,...,N$ you wish to model. Instead of creating arbitrary names and variables for each one, like:\n",
      "\n",
      "    beta_1 = pm.Uniform(\"beta_1\", 0, 1)\n",
      "    beta_2 = pm.Uniform(\"beta_2\", 0, 1)\n",
      "    ...\n",
      "\n",
      "we can instead wrap them into a single variable:\n",
      "\n",
      "    betas = pm.Uniform(\"betas\", 0, 1, size=N)\n",
      "\n",
      "#### Calling `random()`\n",
      "We can also call on a stochastic variable's `random()` method, which (given the parent values) will generate a new, random value. Below we demonstrate this using the texting example from the previous chapter."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "lambda_1 = pm.Exponential(\"lambda_1\", 1)  # prior on first behaviour\n",
      "lambda_2 = pm.Exponential(\"lambda_2\", 1)  # prior on second behaviour\n",
      "tau = pm.DiscreteUniform(\"tau\", lower=0, upper=10)  # prior on behaviour change\n",
      "\n",
      "print \"lambda_1.value = %.3f\" % lambda_1.value\n",
      "print \"lambda_2.value = %.3f\" % lambda_2.value\n",
      "print \"tau.value = %.3f\" % tau.value\n",
      "print\n",
      "\n",
      "lambda_1.random(), lambda_2.random(), tau.random()\n",
      "\n",
      "print \"After calling random() on the variables...\"\n",
      "print \"lambda_1.value = %.3f\" % lambda_1.value\n",
      "print \"lambda_2.value = %.3f\" % lambda_2.value\n",
      "print \"tau.value = %.3f\" % tau.value"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "lambda_1.value = 0.539\n",
        "lambda_2.value = 1.858\n",
        "tau.value = 1.000\n",
        "\n",
        "After calling random() on the variables...\n",
        "lambda_1.value = 0.343\n",
        "lambda_2.value = 0.316\n",
        "tau.value = 6.000\n"
       ]
      }
     ],
     "prompt_number": 4
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "The call to `random` stores a new value into the variable's `value` attribute. In fact, this new value is stored in the computer's cache for faster recall and efficiency."
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "### **Warning**: *Don't update stochastic variables' values in-place.*\n",
      "\n",
      "\n",
      "Straight from the PyMC docs, we quote [4]:\n",
      "\n",
      "> `Stochastic` objects' values should not be updated in-place. This confuses PyMC's caching scheme... The only way a stochastic variable's value should be updated is using statements of the following form:\n",
      "\n",
      "        A.value = new_value\n",
      "\n",
      "> The following are in-place updates and should **never** be used:\n",
      "\n",
      "    \n",
      "        A.value += 3\n",
      "        A.value[2,1] = 5\n",
      "        A.value.attribute = new_attribute_value\n",
      "    "
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "#### Deterministic variables\n",
      "\n",
      "Since most variables you will be modeling are stochastic, we distinguish deterministic variables with a `pymc.deterministic` wrapper. (If you are unfamiliar with Python wrappers (also called decorators), that's no problem. Just prepend the `pymc.deterministic` decorator before the variable declaration and you're good to go. No need to know more. ) The declaration of a deterministic variable uses a Python function:\n",
      "\n",
      "    @pm.deterministic\n",
      "    def some_deterministic_var(v1=v1,):\n",
      "         #jelly goes here.\n",
      "\n",
      "For all purposes, we can treat the object `some_deterministic_var` as a variable and not a Python function. \n",
      "\n",
      "Prepending with the wrapper is the easiest way, but not the only way, to create deterministic variables. This is not completely true: elementary operations, like addition, exponentials etc. implicitly create deterministic variables. For example, the following returns a deterministic variable:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "type(lambda_1 + lambda_2)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 5,
       "text": [
        "pymc.PyMCObjects.Deterministic"
       ]
      }
     ],
     "prompt_number": 5
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "The use of the `deterministic` wrapper was seen in the previous chapter's text-message example.  Recall the model for $\\lambda$ looked like: \n",
      "\n",
      "$$\n",
      "\\lambda = \n",
      "\\cases{\n",
      "\\lambda_1  & \\text{if } t \\lt \\tau \\cr\n",
      "\\lambda_2 & \\text{if } t \\ge \\tau\n",
      "}\n",
      "$$\n",
      "\n",
      "And in PyMC code:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import numpy as np\n",
      "n_data_points = 5  # in CH1 we had ~70 data points\n",
      "\n",
      "\n",
      "@pm.deterministic\n",
      "def lambda_(tau=tau, lambda_1=lambda_1, lambda_2=lambda_2):\n",
      "    out = np.zeros(n_data_points)\n",
      "    out[:tau] = lambda_1  # lambda before tau is lambda1\n",
      "    out[tau:] = lambda_2  # lambda after tau is lambda1\n",
      "    return out"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 7
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Clearly, if $\\tau, \\lambda_1$ and $\\lambda_2$ are known, then $\\lambda$ is known completely, hence it is a deterministic variable. \n",
      "\n",
      "Inside the deterministic decorator, the `Stochastic` variables passed in behave like scalars or Numpy arrays (if multivariable), and *not* like `Stochastic` variables. For example, running the following:\n",
      "\n",
      "    @pm.deterministic\n",
      "    def some_deterministic(stoch=some_stochastic_var):\n",
      "        return stoch.value**2\n",
      "\n",
      "\n",
      "will return an `AttributeError` detailing that `stoch` does not have a `value` attribute. It simply needs to be `stoch**2`. During the learning phase, it's the variable's `value` that is repeatedly passed in, not the actual variable.  \n",
      "\n",
      "Notice in the creation of the deterministic function we added defaults to each variable used in the function. This is a necessary step, and all variables *must* have default values. "
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "### Including observations in the Model\n",
      "\n",
      "At this point, it may not look like it, but we have fully specified our priors. For example, we can ask and answer questions like \"What does my prior distribution of $\\lambda_1$ look like?\" "
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%matplotlib inline\n",
      "from IPython.core.pylabtools import figsize\n",
      "from matplotlib import pyplot as plt\n",
      "figsize(12.5, 4)\n",
      "\n",
      "\n",
      "samples = [lambda_1.random() for i in range(20000)]\n",
      "plt.hist(samples, bins=70, normed=True, histtype=\"stepfilled\")\n",
      "plt.title(\"Prior distribution for $\\lambda_1$\")\n",
      "plt.xlim(0, 8);"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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uVHV1tZYtW6a8vLwGazIzM7VmzRpJ0meffaZ//OMf6tu371mUjpY69aoWQodsbZGvHbK1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\nAACM0XQDAAAAxmi6AQAAAGP/Hwc/8FsEqXMRAAAAAElFTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0x108b23910>"
       ]
      }
     ],
     "prompt_number": 10
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "To frame this in the notation of the first chapter, though this is a slight abuse of notation, we have specified $P(A)$. Our next goal is to include data/evidence/observations $X$ into our model. \n",
      "\n",
      "PyMC stochastic variables have a keyword argument `observed` which accepts a boolean (`False` by default). The keyword `observed` has a very simple role: fix the variable's current value, i.e. make `value` immutable. We have to specify an initial `value` in the variable's creation, equal to the observations we wish to include, typically an array (and it should be an Numpy array for speed). For example:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "data = np.array([10, 5])\n",
      "fixed_variable = pm.Poisson(\"fxd\", 1, value=data, observed=True)\n",
      "print \"value: \", fixed_variable.value\n",
      "print \"calling .random()\"\n",
      "fixed_variable.random()\n",
      "print \"value: \", fixed_variable.value"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "value:  [10  5]\n",
        "calling .random()\n",
        "value:  [10  5]\n"
       ]
      }
     ],
     "prompt_number": 11
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "This is how we include data into our models: initializing a stochastic variable to have a *fixed value*. \n",
      "\n",
      "To complete our text message example, we fix the PyMC variable `observations` to the observed dataset. "
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# We're using some fake data here\n",
      "data = np.array([10, 25, 15, 20, 35])\n",
      "obs = pm.Poisson(\"obs\", lambda_, value=data, observed=True)\n",
      "print obs.value"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "[10 25 15 20 35]\n"
       ]
      }
     ],
     "prompt_number": 12
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "### Finally...\n",
      "\n",
      "We wrap all the created variables into a `pm.Model` class. With this `Model` class, we can analyze the variables as a single unit. This is an optional step, as the fitting algorithms can be sent an array of the variables rather than a `Model` class. I may or may not use this class in future examples ;)"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "model = pm.Model([obs, lambda_, lambda_1, lambda_2, tau])"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 13
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "## Modeling approaches\n",
      "\n",
      "A good starting thought to Bayesian modeling is to think about *how your data might have been generated*. Position yourself in an omniscient position, and try to imagine how *you* would recreate the dataset. \n",
      "\n",
      "In the last chapter we investigated text message data. We begin by asking how our observations may have been generated:\n",
      "\n",
      "1.  We started by thinking \"what is the best random variable to describe this count data?\" A Poisson random variable is a good candidate because it can represent count data. So we model the number of sms's received as sampled from a Poisson distribution.\n",
      "\n",
      "2.  Next, we think, \"Ok, assuming sms's are Poisson-distributed, what do I need for the Poisson distribution?\" Well, the Poisson distribution has a parameter $\\lambda$. \n",
      "\n",
      "3.  Do we know $\\lambda$? No. In fact, we have a suspicion that there are *two* $\\lambda$ values, one for the earlier behaviour and one for the latter behaviour. We don't know when the behaviour switches though, but call the switchpoint $\\tau$.\n",
      "\n",
      "4. What is a good distribution for the two $\\lambda$s? The exponential is good, as it assigns probabilities to positive real numbers. Well the exponential distribution has a parameter too, call it $\\alpha$.\n",
      "\n",
      "5.  Do we know what the parameter $\\alpha$ might be? No. At this point, we could continue and assign a distribution to $\\alpha$, but it's better to stop once we reach a set level of ignorance: whereas we have a prior belief about $\\lambda$, (\"it probably changes over time\", \"it's likely between 10 and 30\", etc.), we don't really have any strong beliefs about $\\alpha$. So it's best to stop here. \n",
      "\n",
      "    What is a good value for $\\alpha$ then? We think that the $\\lambda$s are between 10-30, so if we set $\\alpha$ really low (which corresponds to larger probability on high values) we are not reflecting our prior well. Similar, a too-high alpha misses our prior belief as well. A good idea for $\\alpha$ as to reflect our belief is to set the value so that the mean of $\\lambda$, given $\\alpha$, is equal to our observed mean. This was shown in the last chapter.\n",
      "\n",
      "6. We have no expert opinion of when $\\tau$ might have occurred. So we will suppose $\\tau$ is from a discrete uniform distribution over the entire timespan.\n",
      "\n",
      "\n",
      "Below we give a graphical visualization of this, where arrows denote `parent-child` relationships. (provided by the [Daft Python library](http://daft-pgm.org/) )\n",
      "\n",
      "<img src=\"http://i.imgur.com/7J30oCG.png\" width = 700/>\n",
      "\n",
      "\n",
      "PyMC, and other probabilistic programming languages, have been designed to tell these data-generation *stories*. More generally, B. Cronin writes [5]:\n",
      "\n",
      "> Probabilistic programming will unlock narrative explanations of data, one of the holy grails of business analytics and the unsung hero of scientific persuasion. People think in terms of stories - thus the unreasonable power of the anecdote to drive decision-making, well-founded or not. But existing analytics largely fails to provide this kind of story; instead, numbers seemingly appear out of thin air, with little of the causal context that humans prefer when weighing their options."
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "### Same story; different ending.\n",
      "\n",
      "Interestingly, we can create *new datasets* by retelling the story.\n",
      "For example, if we reverse the above steps, we can simulate a possible realization of the dataset.\n",
      "\n",
      "1\\. Specify when the user's behaviour switches by sampling from $\\text{DiscreteUniform}(0, 80)$:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "tau = pm.rdiscrete_uniform(0, 80)\n",
      "print tau"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "37\n"
       ]
      }
     ],
     "prompt_number": 14
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "2\\. Draw $\\lambda_1$ and $\\lambda_2$ from an $\\text{Exp}(\\alpha)$ distribution:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "alpha = 1. / 20.\n",
      "lambda_1, lambda_2 = pm.rexponential(alpha, 2)\n",
      "print lambda_1, lambda_2"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "29.0394614963 13.5921161471\n"
       ]
      }
     ],
     "prompt_number": 15
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "3\\.  For days before $\\tau$, represent the user's received SMS count by sampling from $\\text{Poi}(\\lambda_1)$, and sample from  $\\text{Poi}(\\lambda_2)$ for days after $\\tau$. For example:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "data = np.r_[pm.rpoisson(lambda_1, tau), pm.rpoisson(lambda_2, 80 - tau)]"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 16
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "4\\. Plot the artificial dataset:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "plt.bar(np.arange(80), data, color=\"#348ABD\")\n",
      "plt.bar(tau - 1, data[tau - 1], color=\"r\", label=\"user behaviour changed\")\n",
      "plt.xlabel(\"Time (days)\")\n",
      "plt.ylabel(\"count of text-msgs received\")\n",
      "plt.title(\"Artificial dataset\")\n",
      "plt.xlim(0, 80)\n",
      "plt.legend();"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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wevVqzJ07F+fOndO+d8uWLYiIiMDly5fh4eGBd999V7use/fu+N///ofLly8jODgYU6dO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\niIjECBXvIiIiIiIx4l9tpesCEGN+eQAAAABJRU5ErkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0x10929fb90>"
       ]
      }
     ],
     "prompt_number": 17
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "It is okay that our fictional dataset does not look like our observed dataset: the probability is incredibly small it indeed would. PyMC's engine is designed to find good parameters, $\\lambda_i, \\tau$, that maximize this probability.  \n",
      "\n",
      "\n",
      "The ability to generate artificial dataset is an interesting side effect of our modeling, and we will see that this ability is a very important method of Bayesian inference. We produce a few more datasets below:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def plot_artificial_sms_dataset():\n",
      "    tau = pm.rdiscrete_uniform(0, 80)\n",
      "    alpha = 1. / 20.\n",
      "    lambda_1, lambda_2 = pm.rexponential(alpha, 2)\n",
      "    data = np.r_[pm.rpoisson(lambda_1, tau), pm.rpoisson(lambda_2, 80 - tau)]\n",
      "    plt.bar(np.arange(80), data, color=\"#348ABD\")\n",
      "    plt.bar(tau - 1, data[tau - 1], color=\"r\", label=\"user behaviour changed\")\n",
      "    plt.xlim(0, 80)\n",
      "\n",
      "figsize(12.5, 5)\n",
      "plt.title(\"More example of artificial datasets\")\n",
      "for i in range(4):\n",
      "    plt.subplot(4, 1, i)\n",
      "    plot_artificial_sms_dataset()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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nve13xNcEeZzZvcThjpQfffQR1q1bh/379yMiIgKHDh1ii1EiIiIioi70sncD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\n4v3m3FbxAAAAAElFTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0x109259c10>"
       ]
      }
     ],
     "prompt_number": 18
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Later we will see how we use this to make predictions and test the appropriateness of our models."
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "#####Example: Bayesian A/B testing\n",
      "\n",
      "A/B testing is a statistical design pattern for determining the difference of effectiveness between two different treatments. For example, a pharmaceutical company is interested in the effectiveness of drug A vs drug B. The company will test drug A on some fraction of their trials, and drug B on the other fraction (this fraction is often 1/2, but we will relax this assumption). After performing enough trials, the in-house statisticians sift through the data to determine which drug yielded better results. \n",
      "\n",
      "Similarly, front-end web developers are interested in which design of their website yields more sales or some other metric of interest. They will route some fraction of visitors to site A, and the other fraction to site B, and record if the visit yielded a sale or not. The data is recorded (in real-time), and analyzed afterwards. \n",
      "\n",
      "Often, the post-experiment analysis is done using something called a hypothesis test like *difference of means test* or *difference of proportions test*. This involves often misunderstood quantities like a \"Z-score\" and even more confusing \"p-values\" (please don't ask). If you have taken a statistics course, you have probably been taught this technique (though not necessarily *learned* this technique). And if you were like me, you may have felt uncomfortable with their derivation -- good: the Bayesian approach to this problem is much more natural. \n",
      "\n",
      "### A Simple Case\n",
      "\n",
      "As this is a hacker book, we'll continue with the web-dev example. For the moment, we will focus on the analysis of site A only. Assume that there is some true $0 \\lt p_A \\lt 1$ probability that users who, upon shown site A, eventually purchase from the site. This is the true effectiveness of site A. Currently, this quantity is unknown to us. \n",
      "\n",
      "Suppose site A was shown to $N$ people, and $n$ people purchased from the site. One might conclude hastily that $p_A = \\frac{n}{N}$. Unfortunately, the *observed frequency* $\\frac{n}{N}$ does not necessarily equal $p_A$ -- there is a difference between the *observed frequency* and the *true frequency* of an event. The true frequency can be interpreted as the probability of an event occurring. For example, the true frequency of rolling a 1 on a 6-sided die is $\\frac{1}{6}$. Knowing the true frequency of events like:\n",
      "\n",
      "- fraction of users who make purchases, \n",
      "- frequency of social attributes, \n",
      "- percent of internet users with cats etc. \n",
      "\n",
      "are common requests we ask of Nature. Unfortunately, often Nature hides the true frequency from us and we must *infer* it from observed data.\n",
      "\n",
      "The *observed frequency* is then the frequency we observe: say rolling the die 100 times you may observe 20 rolls of 1. The observed frequency, 0.2, differs from the true frequency, $\\frac{1}{6}$. We can use Bayesian statistics to infer probable values of the true frequency using an appropriate prior and observed data.\n",
      "\n",
      "\n",
      "With respect to our A/B example, we are interested in using what we know, $N$ (the total trials administered) and $n$ (the number of conversions), to estimate what $p_A$, the true frequency of buyers, might be. \n",
      "\n",
      "To setup a Bayesian model, we need to assign prior distrbutions to our unknown quantities. *A priori*, what do we think $p_A$ might be? For this example, we have no strong conviction about $p_A$, so for now, let's assume $p_A$ is uniform over [0,1]:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import pymc as pm\n",
      "\n",
      "# The parameters are the bounds of the Uniform.\n",
      "p = pm.Uniform('p', lower=0, upper=1)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 19
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Had we had stronger beliefs, we could have expressed them in the prior above.\n",
      "\n",
      "For this example, consider $p_A = 0.05$, and $N = 1500$ users shown site A, and we will simulate whether the user made a purchase or not. To simulate this from $N$ trials, we will use a *Bernoulli* distribution: if  $ X\\ \\sim \\text{Ber}(p)$, then $X$ is 1 with probability $p$ and 0 with probability $1 - p$. Of course, in practice we do not know $p_A$, but we will use it here to simulate the data."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# set constants\n",
      "p_true = 0.05  # remember, this is unknown.\n",
      "N = 1500\n",
      "\n",
      "# sample N Bernoulli random variables from Ber(0.05).\n",
      "# each random variable has a 0.05 chance of being a 1.\n",
      "# this is the data-generation step\n",
      "occurrences = pm.rbernoulli(p_true, N)\n",
      "\n",
      "print occurrences  # Remember: Python treats True == 1, and False == 0\n",
      "print occurrences.sum()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "[False False False ..., False False  True]\n",
        "87\n"
       ]
      }
     ],
     "prompt_number": 20
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "The observed frequency is:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# Occurrences.mean is equal to n/N.\n",
      "print \"What is the observed frequency in Group A? %.4f\" % occurrences.mean()\n",
      "print \"Does this equal the true frequency? %s\" % (occurrences.mean() == p_true)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "What is the observed frequency in Group A? 0.0580\n",
        "Does this equal the true frequency? False\n"
       ]
      }
     ],
     "prompt_number": 21
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "We combine the observations into the PyMC `observed` variable, and run our inference algorithm:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# include the observations, which are Bernoulli\n",
      "obs = pm.Bernoulli(\"obs\", p, value=occurrences, observed=True)\n",
      "\n",
      "# To be explained in chapter 3\n",
      "mcmc = pm.MCMC([p, obs])\n",
      "mcmc.sample(18000, 1000)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " \r",
        "[****************100%******************]  18000 of 18000 complete"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n"
       ]
      }
     ],
     "prompt_number": 22
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "We plot the posterior distribution of the unknown $p_A$ below:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "figsize(12.5, 4)\n",
      "plt.title(\"Posterior distribution of $p_A$, the true effectiveness of site A\")\n",
      "plt.vlines(p_true, 0, 90, linestyle=\"--\", label=\"true $p_A$ (unknown)\")\n",
      "plt.hist(mcmc.trace(\"p\")[:], bins=25, histtype=\"stepfilled\", normed=True)\n",
      "plt.legend()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 23,
       "text": [
        "<matplotlib.legend.Legend at 0x109862250>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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Ntn3bSUlJ2Lt3L958800888wzDo+HbbbZZptttp25nZOTg9LSUgBAfn4+EhMT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\nU1kKuQ0w4wAAAABJRU5ErkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0x109615390>"
       ]
      }
     ],
     "prompt_number": 23
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Our posterior distribution puts most weight near the true value of $p_A$, but also some weights in the tails. This is a measure of how uncertain we should be, given our observations. Try changing the number of observations, `N`, and observe how the posterior distribution changes.\n",
      "\n",
      "### *A* and *B* Together\n",
      "\n",
      "A similar anaylsis can be done for site B's response data to determine the analogous $p_B$. But what we are really interested in is the *difference* between $p_A$ and $p_B$. Let's infer $p_A$, $p_B$, *and* $\\text{delta} = p_A - p_B$, all at once. We can do this using PyMC's deterministic variables. (We'll assume for this exercise that $p_B = 0.04$, so $\\text{delta} = 0.01$, $N_B = 750$ (signifcantly less than $N_A$) and we will simulate site B's data like we did for site A's data )"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import pymc as pm\n",
      "figsize(12, 4)\n",
      "\n",
      "# these two quantities are unknown to us.\n",
      "true_p_A = 0.05\n",
      "true_p_B = 0.04\n",
      "\n",
      "# notice the unequal sample sizes -- no problem in Bayesian analysis.\n",
      "N_A = 1500\n",
      "N_B = 750\n",
      "\n",
      "# generate some observations\n",
      "observations_A = pm.rbernoulli(true_p_A, N_A)\n",
      "observations_B = pm.rbernoulli(true_p_B, N_B)\n",
      "print \"Obs from Site A: \", observations_A[:30].astype(int), \"...\"\n",
      "print \"Obs from Site B: \", observations_B[:30].astype(int), \"...\""
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Obs from Site A:  [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0] ...\n",
        "Obs from Site B:  [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0] ...\n"
       ]
      }
     ],
     "prompt_number": 24
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "print observations_A.mean()\n",
      "print observations_B.mean()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "0.056\n",
        "0.0306666666667\n"
       ]
      }
     ],
     "prompt_number": 25
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# Set up the pymc model. Again assume Uniform priors for p_A and p_B.\n",
      "p_A = pm.Uniform(\"p_A\", 0, 1)\n",
      "p_B = pm.Uniform(\"p_B\", 0, 1)\n",
      "\n",
      "\n",
      "# Define the deterministic delta function. This is our unknown of interest.\n",
      "@pm.deterministic\n",
      "def delta(p_A=p_A, p_B=p_B):\n",
      "    return p_A - p_B\n",
      "\n",
      "# Set of observations, in this case we have two observation datasets.\n",
      "obs_A = pm.Bernoulli(\"obs_A\", p_A, value=observations_A, observed=True)\n",
      "obs_B = pm.Bernoulli(\"obs_B\", p_B, value=observations_B, observed=True)\n",
      "\n",
      "# To be explained in chapter 3.\n",
      "mcmc = pm.MCMC([p_A, p_B, delta, obs_A, obs_B])\n",
      "mcmc.sample(20000, 1000)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " \r",
        "[****************100%******************]  20000 of 20000 complete"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n"
       ]
      }
     ],
     "prompt_number": 26
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Below we plot the posterior distributions for the three unknowns: "
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "p_A_samples = mcmc.trace(\"p_A\")[:]\n",
      "p_B_samples = mcmc.trace(\"p_B\")[:]\n",
      "delta_samples = mcmc.trace(\"delta\")[:]"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 27
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "figsize(12.5, 10)\n",
      "\n",
      "# histogram of posteriors\n",
      "\n",
      "ax = plt.subplot(311)\n",
      "\n",
      "plt.xlim(0, .1)\n",
      "plt.hist(p_A_samples, histtype='stepfilled', bins=25, alpha=0.85,\n",
      "         label=\"posterior of $p_A$\", color=\"#A60628\", normed=True)\n",
      "plt.vlines(true_p_A, 0, 80, linestyle=\"--\", label=\"true $p_A$ (unknown)\")\n",
      "plt.legend(loc=\"upper right\")\n",
      "plt.title(\"Posterior distributions of $p_A$, $p_B$, and delta unknowns\")\n",
      "\n",
      "ax = plt.subplot(312)\n",
      "\n",
      "plt.xlim(0, .1)\n",
      "plt.hist(p_B_samples, histtype='stepfilled', bins=25, alpha=0.85,\n",
      "         label=\"posterior of $p_B$\", color=\"#467821\", normed=True)\n",
      "plt.vlines(true_p_B, 0, 80, linestyle=\"--\", label=\"true $p_B$ (unknown)\")\n",
      "plt.legend(loc=\"upper right\")\n",
      "\n",
      "ax = plt.subplot(313)\n",
      "plt.hist(delta_samples, histtype='stepfilled', bins=30, alpha=0.85,\n",
      "         label=\"posterior of delta\", color=\"#7A68A6\", normed=True)\n",
      "plt.vlines(true_p_A - true_p_B, 0, 60, linestyle=\"--\",\n",
      "           label=\"true delta (unknown)\")\n",
      "plt.vlines(0, 0, 60, color=\"black\", alpha=0.2)\n",
      "plt.legend(loc=\"upper right\");"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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xmCskt61bt8LFxQV79uxBdnY2XnvtNQDAgQMHEBUVhczMTBgaGjbbt3HaRkND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fddvPnmm3jmmWdw9OhRxMfH48SJE0bUStO4XC7eCVcgJSUFEgAiIzTP1KJZtHU0cwUPhZivNu5r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\nRK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0x109207450>"
       ]
      }
     ],
     "prompt_number": 29
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Notice that as a result of `N_B < N_A`, i.e. we have less data from site B, our posterior distribution of $p_B$ is fatter, implying we are less certain about the true value of $p_B$ than we are of $p_A$.  \n",
      "\n",
      "With respect to the posterior distribution of $\\text{delta}$, we can see that the majority of the distribution is above $\\text{delta}=0$, implying there site A's response is likely better than site B's response. The probability this inference is incorrect is easily computable:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# Count the number of samples less than 0, i.e. the area under the curve\n",
      "# before 0, represent the probability that site A is worse than site B.\n",
      "print \"Probability site A is WORSE than site B: %.3f\" % \\\n",
      "    (delta_samples < 0).mean()\n",
      "\n",
      "print \"Probability site A is BETTER than site B: %.3f\" % \\\n",
      "    (delta_samples > 0).mean()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Probability site A is WORSE than site B: 0.003\n",
        "Probability site A is BETTER than site B: 0.997\n"
       ]
      }
     ],
     "prompt_number": 30
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "If this probability is too high for comfortable decision-making, we can perform more trials on site B (as site B has less samples to begin with, each additional data point for site B contributes more inferential \"power\" than each additional data point for site A). \n",
      "\n",
      "Try playing with the parameters `true_p_A`, `true_p_B`, `N_A`, and `N_B`, to see what the posterior of $\\text{delta}$ looks like. Notice in all this, the difference in sample sizes between site A and site B was never mentioned: it naturally fits into Bayesian analysis.\n",
      "\n",
      "I hope the readers feel this style of A/B testing is more natural than hypothesis testing, which has probably confused more than helped practitioners. Later in this book, we will see two extensions of this model: the first to help dynamically adjust for bad sites, and the second will improve the speed of this computation by reducing the analysis to a single equation.   "
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "## An algorithm for human deceit\n",
      "\n",
      "Social data has an additional layer of interest as people are not always honest with responses, which adds a further complication into inference. For example, simply asking individuals \"Have you ever cheated on a test?\" will surely contain some rate of dishonesty. What you can say for certain is that the true rate is less than your observed rate (assuming individuals lie *only* about *not cheating*; I cannot imagine one who would admit \"Yes\" to cheating when in fact they hadn't cheated). \n",
      "\n",
      "To present an elegant solution to circumventing this dishonesty problem, and to demonstrate Bayesian modeling, we first need to introduce the binomial distribution.\n",
      "\n",
      "### The Binomial Distribution\n",
      "\n",
      "The binomial distribution is one of the most popular distributions, mostly because of its simplicity and usefulness. Unlike the other distributions we have encountered thus far in the book, the binomial distribution has 2 parameters: $N$, a positive integer representing $N$ trials or number of instances of potential events, and $p$, the probability of an event occurring in a single trial. Like the Poisson distribution, it is a discrete distribution, but unlike the Poisson distribution, it only weighs integers from $0$ to $N$. The mass distribution looks like:\n",
      "\n",
      "$$P( X = k ) =  {{N}\\choose{k}}  p^k(1-p)^{N-k}$$\n",
      "\n",
      "If $X$ is a binomial random variable with parameters $p$ and $N$, denoted $X \\sim \\text{Bin}(N,p)$, then $X$ is the number of events that occurred in the $N$ trials (obviously $0 \\le X \\le N$). The larger $p$ is (while still remaining between 0 and 1), the more events are likely to occur. The expected value of a binomial is equal to $Np$. Below we plot the mass probability distribution for varying parameters. \n"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "figsize(12.5, 4)\n",
      "\n",
      "import scipy.stats as stats\n",
      "binomial = stats.binom\n",
      "\n",
      "parameters = [(10, .4), (10, .9)]\n",
      "colors = [\"#348ABD\", \"#A60628\"]\n",
      "\n",
      "for i in range(2):\n",
      "    N, p = parameters[i]\n",
      "    _x = np.arange(N + 1)\n",
      "    plt.bar(_x - 0.5, binomial.pmf(_x, N, p), color=colors[i],\n",
      "            edgecolor=colors[i],\n",
      "            alpha=0.6,\n",
      "            label=\"$N$: %d, $p$: %.1f\" % (N, p),\n",
      "            linewidth=3)\n",
      "\n",
      "plt.legend(loc=\"upper left\")\n",
      "plt.xlim(0, 10.5)\n",
      "plt.xlabel(\"$k$\")\n",
      "plt.ylabel(\"$P(X = k)$\")\n",
      "plt.title(\"Probability mass distributions of binomial random variables\");"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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Fl5cXOnbsCCsrK5w7d07t3GUymUa/l6dPn8akSZPg5uYGa2trZdnYn3/+qbZeQ9d3VSdO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\ngg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0x1097c4750>"
       ]
      }
     ],
     "prompt_number": 32
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "The special case when $N = 1$ corresponds to the Bernoulli distribution. There is another connection between Bernoulli and Binomial random variables. If we have $X_1, X_2, ... , X_N$ Bernoulli random variables with the same $p$, then $Z = X_1 + X_2 + ... + X_N \\sim \\text{Binomial}(N, p )$.\n",
      "\n",
      "The expected value of a Bernoulli random variable is $p$. This can be seen by noting the more general Binomial random variable has expected value $Np$ and setting $N=1$."
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "##### Example: Cheating among students\n",
      "\n",
      "We will use the binomial distribution to determine the frequency of students cheating during an exam. If we let $N$ be the total number of students who took the exam, and assuming each student is interviewed post-exam (answering without consequence), we will receive integer $X$ \"Yes I did cheat\" answers. We then find the posterior distribution of $p$, given $N$, some specified prior on $p$, and observed data $X$. \n",
      "\n",
      "This is a completely absurd model. No student, even with a free-pass against punishment, would admit to cheating. What we need is a better *algorithm* to ask students if they had cheated. Ideally the algorithm should encourage individuals to be honest while preserving privacy. The following proposed algorithm is a solution I greatly admire for its ingenuity and effectiveness:\n",
      "\n",
      "> In the interview process for each student, the student flips a coin, hidden from the interviewer. The student agrees to answer honestly if the coin comes up heads. Otherwise, if the coin comes up tails, the student (secretly) flips the coin again, and answers \"Yes, I did cheat\" if the coin flip lands heads, and \"No, I did not cheat\", if the coin flip lands tails. This way, the interviewer does not know if a \"Yes\" was the result of a guilty plea, or a Heads on a second coin toss. Thus privacy is preserved and the researchers receive honest answers. \n",
      "\n",
      "I call this the Privacy Algorithm. One could of course argue that the interviewers are still receiving false data since some *Yes*'s are not confessions but instead randomness, but an alternative perspective is that the researchers are discarding approximately half of their original dataset since half of the responses will be noise. But they have gained a systematic data generation process that can be modeled. Furthermore, they do not have to incorporate (perhaps somewhat naively) the possibility of deceitful answers. We can use PyMC to dig through this noisy model, and find a posterior distribution for the true frequency of liars. "
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Suppose 100 students are being surveyed for cheating, and we wish to find $p$, the proportion of cheaters. There are a few ways we can model this in PyMC. I'll demonstrate the most explicit way, and later show a simplified version. Both versions arrive at the same inference. In our data-generation model, we sample $p$, the true proportion of cheaters, from a prior. Since we are quite ignorant about $p$, we will assign it a $\\text{Uniform}(0,1)$ prior."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import pymc as pm\n",
      "\n",
      "N = 100\n",
      "p = pm.Uniform(\"freq_cheating\", 0, 1)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 33
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Again, thinking of our data-generation model, we assign Bernoulli random variables to the 100 students: 1 implies they cheated and 0 implies they did not. "
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "true_answers = pm.Bernoulli(\"truths\", p, size=N)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 34
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "If we carry out the algorithm, the next step that occurs is the first coin-flip each student makes. This can be modeled again by sampling 100 Bernoulli random variables with $p=1/2$: denote a 1 as a *Heads* and 0 a *Tails*."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "first_coin_flips = pm.Bernoulli(\"first_flips\", 0.5, size=N)\n",
      "print first_coin_flips.value"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "[False  True  True  True  True False False  True False False False False\n",
        " False  True  True False  True  True False False  True  True False False\n",
        " False False False  True False False  True False  True  True  True  True\n",
        "  True False  True False  True  True  True  True  True False False False\n",
        "  True  True  True  True  True  True False  True False False False  True\n",
        "  True  True False False False False  True False  True False False  True\n",
        "  True False False False False  True  True False False  True False  True\n",
        " False False  True False False False  True  True  True  True  True False\n",
        " False False False False]\n"
       ]
      }
     ],
     "prompt_number": 35
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Although *not everyone* flips a second time, we can still model the possible realization of second coin-flips:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "second_coin_flips = pm.Bernoulli(\"second_flips\", 0.5, size=N)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 36
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Using these variables, we can return a possible realization of the *observed proportion* of \"Yes\" responses. We do this using a PyMC `deterministic` variable:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "@pm.deterministic\n",
      "def observed_proportion(t_a=true_answers,\n",
      "                        fc=first_coin_flips,\n",
      "                        sc=second_coin_flips):\n",
      "\n",
      "    observed = fc * t_a + (1 - fc) * sc\n",
      "    return observed.sum() / float(N)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 37
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "The line `fc*t_a + (1-fc)*sc` contains the heart of the Privacy algorithm. Elements in this array are 1 *if and only if* i) the first toss is heads and the student cheated or ii) the first toss is tails, and the second is heads, and are 0 else. Finally, the last line sums this vector and divides by `float(N)`, produces a proportion. "
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "observed_proportion.value"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 38,
       "text": [
        "0.42999999999999999"
       ]
      }
     ],
     "prompt_number": 38
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Next we need a dataset. After performing our coin-flipped interviews the researchers received 35 \"Yes\" responses. To put this into a relative perspective, if there truly were no cheaters, we should expect to see on average 1/4 of all responses being a \"Yes\" (half chance of having first coin land Tails, and another half chance of having second coin land Heads), so about 25 responses in a cheat-free world. On the other hand, if *all students cheated*, we should expect to see approximately 3/4 of all responses be \"Yes\". \n",
      "\n",
      "The researchers observe a Binomial random variable, with `N = 100` and `p = observed_proportion` with `value = 35`:  "
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "X = 35\n",
      "\n",
      "observations = pm.Binomial(\"obs\", N, observed_proportion, observed=True,\n",
      "                           value=X)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 39
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Below we add all the variables of interest to a `Model` container and run our black-box algorithm over the model. "
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "model = pm.Model([p, true_answers, first_coin_flips,\n",
      "                  second_coin_flips, observed_proportion, observations])\n",
      "\n",
      "# To be explained in Chapter 3!\n",
      "mcmc = pm.MCMC(model)\n",
      "mcmc.sample(40000, 15000)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " \r",
        "[****************100%******************]  40000 of 40000 complete"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n"
       ]
      }
     ],
     "prompt_number": 40
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "figsize(12.5, 3)\n",
      "p_trace = mcmc.trace(\"freq_cheating\")[:]\n",
      "plt.hist(p_trace, histtype=\"stepfilled\", normed=True, alpha=0.85, bins=30,\n",
      "         label=\"posterior distribution\", color=\"#348ABD\")\n",
      "plt.vlines([.05, .35], [0, 0], [5, 5], alpha=0.3)\n",
      "plt.xlim(0, 1)\n",
      "plt.legend();"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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i7DVMcYYJdpAXmCIrcAINNgAAABBENNidSKPXp5KqetsfDc2+oNXAdbBhimvVwg7yAlNk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\n",
       "text": [
        "<matplotlib.figure.Figure at 0x10971e0d0>"
       ]
      }
     ],
     "prompt_number": 42
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "With regards to the above plot, we are still pretty uncertain about what the true frequency of cheaters might be, but we have narrowed it down to a range between 0.05 to 0.35 (marked by the solid lines). This is pretty good, as *a priori* we had no idea how many students might have cheated (hence the uniform distribution for our prior). On the other hand, it is also pretty bad since there is a .3 length window the true value most likely lives in. Have we even gained anything, or are we still too uncertain about the true frequency? \n",
      "\n",
      "I would argue, yes, we have discovered something. It is implausible, according to our posterior, that there are *no cheaters*, i.e. the posterior assigns low probability to $p=0$. Since we started with a uniform prior, treating all values of $p$ as equally plausible, but the data ruled out $p=0$ as a possibility, we can be confident that there were cheaters. \n",
      "\n",
      "This kind of algorithm can be used to gather private information from users and be *reasonably* confident that the data, though noisy, is truthful. \n",
      "\n"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "### Alternative PyMC Model\n",
      "\n",
      "Given a value for $p$ (which from our god-like position we know), we can find the probability the student will answer yes: \n",
      "\n",
      "\\begin{align}\n",
      "P(\\text{\"Yes\"}) = & P( \\text{Heads on first coin} )P( \\text{cheater} ) + P( \\text{Tails on first coin} )P( \\text{Heads on second coin} ) \\\\\\\\\n",
      "& = \\frac{1}{2}p + \\frac{1}{2}\\frac{1}{2}\\\\\\\\\n",
      "& = \\frac{p}{2} + \\frac{1}{4}\n",
      "\\end{align}\n",
      "\n",
      "Thus, knowing $p$ we know the probability a student will respond \"Yes\". In PyMC, we can create a deterministic function to evaluate the probability of responding \"Yes\", given $p$:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "p = pm.Uniform(\"freq_cheating\", 0, 1)\n",
      "\n",
      "\n",
      "@pm.deterministic\n",
      "def p_skewed(p=p):\n",
      "    return 0.5 * p + 0.25"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 43
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "I could have typed `p_skewed  = 0.5*p + 0.25` instead for a one-liner, as the elementary operations of addition and scalar multiplication will implicitly create a `deterministic` variable, but I wanted to make the deterministic boilerplate explicit for clarity's sake. \n",
      "\n",
      "If we know the probability of respondents saying \"Yes\", which is `p_skewed`, and we have $N=100$ students, the number of \"Yes\" responses is a binomial random variable with parameters `N` and `p_skewed`.\n",
      "\n",
      "This is where we include our observed 35 \"Yes\" responses. In the declaration of the `pm.Binomial`, we include `value = 35` and `observed = True`."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "yes_responses = pm.Binomial(\"number_cheaters\", 100, p_skewed,\n",
      "                            value=35, observed=True)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 44
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Below we add all the variables of interest to a `Model` container and run our black-box algorithm over the model. "
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "model = pm.Model([yes_responses, p_skewed, p])\n",
      "\n",
      "# To Be Explained in Chapter 3!\n",
      "mcmc = pm.MCMC(model)\n",
      "mcmc.sample(25000, 2500)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " \r",
        "[****************100%******************]  25000 of 25000 complete"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n"
       ]
      }
     ],
     "prompt_number": 45
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "figsize(12.5, 3)\n",
      "p_trace = mcmc.trace(\"freq_cheating\")[:]\n",
      "plt.hist(p_trace, histtype=\"stepfilled\", normed=True, alpha=0.85, bins=30,\n",
      "         label=\"posterior distribution\", color=\"#348ABD\")\n",
      "plt.vlines([.05, .35], [0, 0], [5, 5], alpha=0.2)\n",
      "plt.xlim(0, 1)\n",
      "plt.legend();"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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9dQerQ7QxycuGDRs0fvx4jR07VpdccomzBSJqBMtKVVWVrrjiCuXm5mrs2LF6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\nAACAjWiwAQAAABv9f9uiTdBTAeqOAAAAAElFTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0x109766f50>"
       ]
      }
     ],
     "prompt_number": 47
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "### More PyMC Tricks\n",
      "\n",
      "#### Protip: *Lighter* deterministic variables with `Lambda` class\n",
      "\n",
      "Sometimes writing a deterministic function using the `@pm.deterministic` decorator can seem like a chore, especially for a small function. I have already mentioned that elementary math operations *can* produce deterministic variables implicitly, but what about operations like indexing or slicing? Built-in `Lambda` functions can handle this with the elegance and simplicity required. For example,  \n",
      "\n",
      "    beta = pm.Normal(\"coefficients\", 0, size=(N, 1))\n",
      "    x = np.random.randn((N, 1))\n",
      "    linear_combination = pm.Lambda(lambda x=x, beta=beta: np.dot(x.T, beta))\n",
      "\n",
      "\n",
      "#### Protip: Arrays of PyMC variables\n",
      "There is no reason why we cannot store multiple heterogeneous PyMC variables in a Numpy array. Just remember to set the `dtype` of the array to `object` upon initialization. For example:\n",
      "\n",
      "\n"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "N = 10\n",
      "x = np.empty(N, dtype=object)\n",
      "for i in range(0, N):\n",
      "    x[i] = pm.Exponential('x_%i' % i, (i + 1) ** 2)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 48
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "The remainder of this chapter examines some practical examples of PyMC and PyMC modeling:"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "\n",
      "##### Example: Challenger Space Shuttle Disaster <span id=\"challenger\"/>\n",
      "\n",
      "On January 28, 1986, the twenty-fifth flight of the U.S. space shuttle program ended in disaster when one of the rocket boosters of the Shuttle Challenger exploded shortly after lift-off, killing all seven crew members. The presidential commission on the accident concluded that it was caused by the failure of an O-ring in a field joint on the rocket booster, and that this failure was due to a faulty design that made the O-ring unacceptably sensitive to a number of factors including outside temperature. Of the previous 24 flights, data were available on failures of O-rings on 23, (one was lost at sea), and these data were discussed on the evening preceding the Challenger launch, but unfortunately only the data corresponding to the 7 flights on which there was a damage incident were considered important and these were thought to show no obvious trend. The data are shown below (see [1]):\n",
      "\n",
      "\n",
      "\n"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "figsize(12.5, 3.5)\n",
      "np.set_printoptions(precision=3, suppress=True)\n",
      "challenger_data = np.genfromtxt(\"data/challenger_data.csv\", skip_header=1,\n",
      "                                usecols=[1, 2], missing_values=\"NA\",\n",
      "                                delimiter=\",\")\n",
      "# drop the NA values\n",
      "challenger_data = challenger_data[~np.isnan(challenger_data[:, 1])]\n",
      "\n",
      "# plot it, as a function of tempature (the first column)\n",
      "print \"Temp (F), O-Ring failure?\"\n",
      "print challenger_data\n",
      "\n",
      "plt.scatter(challenger_data[:, 0], challenger_data[:, 1], s=75, color=\"k\",\n",
      "            alpha=0.5)\n",
      "plt.yticks([0, 1])\n",
      "plt.ylabel(\"Damage Incident?\")\n",
      "plt.xlabel(\"Outside temperature (Fahrenheit)\")\n",
      "plt.title(\"Defects of the Space Shuttle O-Rings vs temperature\")"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Temp (F), O-Ring failure?\n",
        "[[ 66.   0.]\n",
        " [ 70.   1.]\n",
        " [ 69.   0.]\n",
        " [ 68.   0.]\n",
        " [ 67.   0.]\n",
        " [ 72.   0.]\n",
        " [ 73.   0.]\n",
        " [ 70.   0.]\n",
        " [ 57.   1.]\n",
        " [ 63.   1.]\n",
        " [ 70.   1.]\n",
        " [ 78.   0.]\n",
        " [ 67.   0.]\n",
        " [ 53.   1.]\n",
        " [ 67.   0.]\n",
        " [ 75.   0.]\n",
        " [ 70.   0.]\n",
        " [ 81.   0.]\n",
        " [ 76.   0.]\n",
        " [ 79.   0.]\n",
        " [ 75.   1.]\n",
        " [ 76.   0.]\n",
        " [ 58.   1.]]\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 49,
       "text": [
        "<matplotlib.text.Text at 0x109766650>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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z8zNrvOLiYly+fPm+43l4eMhi/evzbU9PTwCoML9qtVo28fK2ZW+XlJQA+Lso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\nhBBCHAgt0AkhhBBCCHEg/wDZEx1pK2CtCgAAAABJRU5ErkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0x109785fd0>"
       ]
      }
     ],
     "prompt_number": 49
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "It looks clear that *the probability* of damage incidents occurring increases as the outside temperature decreases. We are interested in modeling the probability here because it does not look like there is a strict cutoff point between temperature and a damage incident occurring. The best we can do is ask \"At temperature $t$, what is the probability of a damage incident?\". The goal of this example is to answer that question.\n",
      "\n",
      "We need a function of temperature, call it $p(t)$, that is bounded between 0 and 1 (so as to model a probability) and changes from 1 to 0 as we increase temperature. There are actually many such functions, but the most popular choice is the *logistic function.*\n",
      "\n",
      "$$p(t) = \\frac{1}{ 1 + e^{ \\;\\beta t } } $$\n",
      "\n",
      "In this model, $\\beta$ is the variable we are uncertain about. Below is the function plotted for $\\beta = 1, 3, -5$."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "figsize(12, 3)\n",
      "\n",
      "\n",
      "def logistic(x, beta):\n",
      "    return 1.0 / (1.0 + np.exp(beta * x))\n",
      "\n",
      "x = np.linspace(-4, 4, 100)\n",
      "plt.plot(x, logistic(x, 1), label=r\"$\\beta = 1$\")\n",
      "plt.plot(x, logistic(x, 3), label=r\"$\\beta = 3$\")\n",
      "plt.plot(x, logistic(x, -5), label=r\"$\\beta = -5$\")\n",
      "plt.legend();"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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P9afNZCG7qIFv8uvYVdbMusIG1hU2EOCh5tLEQKYmBzM06MxF4UDIpy40iHGr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\n0bZ3QaOgURRQNNFjld5jFQ1oNNFWUdBoeo/RnLH/zHV61zW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       "text": [
        "<matplotlib.figure.Figure at 0x1097f02d0>"
       ]
      }
     ],
     "prompt_number": 54
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "But something is missing. In the plot of the logistic function, the probability changes only near zero, but in our data above the probability changes around 65 to 70. We need to add a *bias* term to our logistic function:\n",
      "\n",
      "$$p(t) = \\frac{1}{ 1 + e^{ \\;\\beta t + \\alpha } } $$\n",
      "\n",
      "Some plots are below, with differing $\\alpha$."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def logistic(x, beta, alpha=0):\n",
      "    return 1.0 / (1.0 + np.exp(np.dot(beta, x) + alpha))\n",
      "\n",
      "x = np.linspace(-4, 4, 100)\n",
      "\n",
      "plt.plot(x, logistic(x, 1), label=r\"$\\beta = 1$\", ls=\"--\", lw=1)\n",
      "plt.plot(x, logistic(x, 3), label=r\"$\\beta = 3$\", ls=\"--\", lw=1)\n",
      "plt.plot(x, logistic(x, -5), label=r\"$\\beta = -5$\", ls=\"--\", lw=1)\n",
      "\n",
      "plt.plot(x, logistic(x, 1, 1), label=r\"$\\beta = 1, \\alpha = 1$\",\n",
      "         color=\"#348ABD\")\n",
      "plt.plot(x, logistic(x, 3, -2), label=r\"$\\beta = 3, \\alpha = -2$\",\n",
      "         color=\"#A60628\")\n",
      "plt.plot(x, logistic(x, -5, 7), label=r\"$\\beta = -5, \\alpha = 7$\",\n",
      "         color=\"#7A68A6\")\n",
      "\n",
      "plt.legend(loc=\"lower left\");"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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vTWfk+FhiBga6KVrBlUxNVtZ/nwnAhVcMFTPCCcI5nLUcYunSpaxdu5YPPvgA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\nXWniubW5PNLFZFhoX3WTjXe2FVHZZG3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HxYfqOX9WMpkXik4eQfCWM54sY9KkSRQUFFBS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       "text": [
        "<matplotlib.figure.Figure at 0x10aa12250>"
       ]
      }
     ],
     "prompt_number": 55
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Adding a constant term $\\alpha$ amounts to shifting the curve left or right (hence why it is called a *bias*).\n",
      "\n",
      "Let's start modeling this in PyMC. The $\\beta, \\alpha$ parameters have no reason to be positive, bounded or relatively large, so they are best modeled by a *Normal random variable*, introduced next."
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "### Normal distributions\n",
      "\n",
      "A Normal random variable, denoted $X \\sim N(\\mu, 1/\\tau)$, has a distribution with two parameters: the mean, $\\mu$, and the *precision*, $\\tau$. Those familiar with the Normal distribution already have probably seen $\\sigma^2$ instead of $\\tau^{-1}$. They are in fact reciprocals of each other. The change was motivated by simpler mathematical analysis and is an artifact of older Bayesian methods. Just remember: the smaller $\\tau$, the larger the spread of the distribution (i.e. we are more uncertain); the larger $\\tau$, the tighter the distribution (i.e. we are more certain). Regardless, $\\tau$ is always positive. \n",
      "\n",
      "The probability density function of a $N( \\mu, 1/\\tau)$ random variable is:\n",
      "\n",
      "$$ f(x | \\mu, \\tau) = \\sqrt{\\frac{\\tau}{2\\pi}} \\exp\\left( -\\frac{\\tau}{2} (x-\\mu)^2 \\right) $$\n",
      "\n",
      "We plot some different density functions below. "
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import scipy.stats as stats\n",
      "\n",
      "nor = stats.norm\n",
      "x = np.linspace(-8, 7, 150)\n",
      "mu = (-2, 0, 3)\n",
      "tau = (.7, 1, 2.8)\n",
      "colors = [\"#348ABD\", \"#A60628\", \"#7A68A6\"]\n",
      "parameters = zip(mu, tau, colors)\n",
      "\n",
      "for _mu, _tau, _color in parameters:\n",
      "    plt.plot(x, nor.pdf(x, _mu, scale=1. / _tau),\n",
      "             label=\"$\\mu = %d,\\;\\\\tau = %.1f$\" % (_mu, _tau), color=_color)\n",
      "    plt.fill_between(x, nor.pdf(x, _mu, scale=1. / _tau), color=_color,\n",
      "                     alpha=.33)\n",
      "\n",
      "plt.legend(loc=\"upper right\")\n",
      "plt.xlabel(\"$x$\")\n",
      "plt.ylabel(\"density function at $x$\")\n",
      "plt.title(\"Probability distribution of three different Normal random \\\n",
      "variables\");"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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MV0MfAgCcO7cBJ+EAAC1amaJLT1sAwMN76VqLjzRd0dHR8Pf3BwC0atUKzs7O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\nnr3//jx7H/8VxrVz2Tl6NqBw0SV5klifwoQpGTQd6KS5qZs3f7eRBXd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Axx9/DMDq1asp\nLCwMc0SRa/78+axevRqAffv24fP5JLE+R1OmTKG5uZmamhpqamrIyclh8+bNklifh7KyMn72s5+x\nbNky7HZ7uMOJOGezgJc4e4ZhcN999zFp0iQeeuihcIcT8Z544gnq6+upqalh6dKlXHPNNZJYn6OM\njAxyc3PZt28fACtXrmTy5MlhjipyTZw4kfLycjweD4ZhsHLlSiZNmnTK/SOm5/p0fvOb3/Cd73wH\nr9eLw+HgN7/5TbhDilj33nsv9957L8XFxVitVjmwhZD8JH/+vve97+Hz+Zg7dy4Al1xyCb/+9a/D\nHFXkONUCXuLcfPLJJ7z66qtMnTqVkpISIDhd15e+9KUwRxYd5Jh5fp577jnuvPNOfD4f48aNk8X4\nzsO0adO46667mDlzJqqqctFFF/Gtb33rlPvLIjJCCCGEEEKESFSUhQghhBBCCDEcSHIthBBCCCFE\niEhyLYQQQgghRIhIci2EEEIIIUSISHIthBBCCCFEiEhyLYQQQgghRIhIci2EEEIIIUSISHIthBBC\nCCFEiEhyLYQQQgghRIhIci2EEEIIIUSISHIthBBCCCFEiJjDHYAQQogLZ/ny5ZhMJtauXUtxcTFl\nZWX88Ic/ZOLEieEOTQghooJiGIYR7iCEEEIMvbq6Onw+HwUFBcyYMYNVq1axbt06rrnmGmJiYsId\nnhBCRAXpuRZCiBFi9OjRADQ3NxMXF0diYiI33XRTmKMSQojoIjXXQggxQuzZs4etW7eyYsUK5syZ\nA8A777wT5qiEECK6SM+1EEKMEB988AE9PT1kZmbS19fH22+/TXZ2drjDEkKIqCI110IIIYQQQoSI\nlIUIIYQQQggRIpJcCyGEEEIIESKSXAshhBBCCBEiklwLIYQQQggRIpJcCyGEEEIIESKSXAshhBBC\nCBEiklwLIYQQQggRIpJcCyGEEEIIESL/H6BDeleYhO5KAAAAAElFTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0x10a952d50>"
       ]
      }
     ],
     "prompt_number": 57
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "A Normal random variable can be take on any real number, but the variable is very likely to be relatively close to $\\mu$. In fact, the expected value of a Normal is equal to its $\\mu$ parameter:\n",
      "\n",
      "$$ E[ X | \\mu, \\tau] = \\mu$$\n",
      "\n",
      "and its variance is equal to the inverse of $\\tau$:\n",
      "\n",
      "$$Var( X | \\mu, \\tau ) = \\frac{1}{\\tau}$$\n",
      "\n",
      "\n",
      "\n",
      "Below we continue our modeling of the Challenger space craft:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import pymc as pm\n",
      "\n",
      "temperature = challenger_data[:, 0]\n",
      "D = challenger_data[:, 1]  # defect or not?\n",
      "\n",
      "# notice the`value` here. We explain why below.\n",
      "beta = pm.Normal(\"beta\", 0, 0.001, value=0)\n",
      "alpha = pm.Normal(\"alpha\", 0, 0.001, value=0)\n",
      "\n",
      "\n",
      "@pm.deterministic\n",
      "def p(t=temperature, alpha=alpha, beta=beta):\n",
      "    return 1.0 / (1. + np.exp(beta * t + alpha))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 58
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "We have our probabilities, but how do we connect them to our observed data? A *Bernoulli* random variable with parameter $p$, denoted $\\text{Ber}(p)$, is a random variable that takes value 1 with probability $p$, and 0 else. Thus, our model can look like:\n",
      "\n",
      "$$ \\text{Defect Incident, $D_i$} \\sim \\text{Ber}( \\;p(t_i)\\; ), \\;\\; i=1..N$$\n",
      "\n",
      "where $p(t)$ is our logistic function and $t_i$ are the temperatures we have observations about. Notice in the above code we had to set the values of `beta` and `alpha` to 0. The reason for this is that if `beta` and `alpha` are very large, they make `p` equal to 1 or 0. Unfortunately, `pm.Bernoulli` does not like probabilities of exactly 0 or 1, though they are mathematically well-defined probabilities. So by setting the coefficient values to `0`, we set the variable `p` to be a reasonable starting value. This has no effect on our results, nor does it mean we are including any additional information in our prior. It is simply a computational caveat in PyMC. "
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "p.value"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 59,
       "text": [
        "array([ 0.5,  0.5,  0.5,  0.5,  0.5,  0.5,  0.5,  0.5,  0.5,  0.5,  0.5,\n",
        "        0.5,  0.5,  0.5,  0.5,  0.5,  0.5,  0.5,  0.5,  0.5,  0.5,  0.5,\n",
        "        0.5])"
       ]
      }
     ],
     "prompt_number": 59
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# connect the probabilities in `p` with our observations through a\n",
      "# Bernoulli random variable.\n",
      "observed = pm.Bernoulli(\"bernoulli_obs\", p, value=D, observed=True)\n",
      "\n",
      "model = pm.Model([observed, beta, alpha])\n",
      "\n",
      "# Mysterious code to be explained in Chapter 3\n",
      "map_ = pm.MAP(model)\n",
      "map_.fit()\n",
      "mcmc = pm.MCMC(model)\n",
      "mcmc.sample(120000, 100000, 2)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " \r",
        "[****************100%******************]  120000 of 120000 complete"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n"
       ]
      }
     ],
     "prompt_number": 60
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "We have trained our model on the observed data, now we can sample values from the posterior. Let's look at the posterior distributions for $\\alpha$ and $\\beta$:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "alpha_samples = mcmc.trace('alpha')[:, None]  # best to make them 1d\n",
      "beta_samples = mcmc.trace('beta')[:, None]\n",
      "\n",
      "figsize(12.5, 6)\n",
      "\n",
      "# histogram of the samples:\n",
      "plt.subplot(211)\n",
      "plt.title(r\"Posterior distributions of the variables $\\alpha, \\beta$\")\n",
      "plt.hist(beta_samples, histtype='stepfilled', bins=35, alpha=0.85,\n",
      "         label=r\"posterior of $\\beta$\", color=\"#7A68A6\", normed=True)\n",
      "plt.legend()\n",
      "\n",
      "plt.subplot(212)\n",
      "plt.hist(alpha_samples, histtype='stepfilled', bins=35, alpha=0.85,\n",
      "         label=r\"posterior of $\\alpha$\", color=\"#A60628\", normed=True)\n",
      "plt.legend();"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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h4SgoKMDChQsRFBSk935JSQm8vb11bS8vLxQXF7NA70IcVyaO0sdJ195swDdf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\noUAHAAAAHOT/AQEyFwHtzX9zAAAAAElFTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0x10aaeea50>"
       ]
      }
     ],
     "prompt_number": 61
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "All samples of $\\beta$ are greater than 0. If instead the posterior was centered around 0, we may suspect that $\\beta = 0$, implying that temperature has no effect on the probability of defect. \n",
      "\n",
      "Similarly, all $\\alpha$ posterior values are negative and far away from 0, implying that it is correct to believe that $\\alpha$ is significantly less than 0. \n",
      "\n",
      "Regarding the spread of the data, we are very uncertain about what the true parameters might be (though considering the low sample size and the large overlap of defects-to-nondefects this behaviour is perhaps expected).  \n",
      "\n",
      "Next, let's look at the *expected probability* for a specific value of the temperature. That is, we average over all samples from the posterior to get a likely value for $p(t_i)$."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "t = np.linspace(temperature.min() - 5, temperature.max() + 5, 50)[:, None]\n",
      "p_t = logistic(t.T, beta_samples, alpha_samples)\n",
      "\n",
      "mean_prob_t = p_t.mean(axis=0)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 62
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "figsize(12.5, 4)\n",
      "\n",
      "plt.plot(t, mean_prob_t, lw=3, label=\"average posterior \\nprobability \\\n",
      "of defect\")\n",
      "plt.plot(t, p_t[0, :], ls=\"--\", label=\"realization from posterior\")\n",
      "plt.plot(t, p_t[-2, :], ls=\"--\", label=\"realization from posterior\")\n",
      "plt.scatter(temperature, D, color=\"k\", s=50, alpha=0.5)\n",
      "plt.title(\"Posterior expected value of probability of defect; \\\n",
      "plus realizations\")\n",
      "plt.legend(loc=\"lower left\")\n",
      "plt.ylim(-0.1, 1.1)\n",
      "plt.xlim(t.min(), t.max())\n",
      "plt.ylabel(\"probability\")\n",
      "plt.xlabel(\"temperature\");"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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IIW2MatgJIYQQQgjpoARL2OfOnQsvLy9ER0c32eb5559HWFgYevfujTNnzgjV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\n27YkJSWxbds2Wb7ry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       "text": [
        "<matplotlib.figure.Figure at 0x10aae4d90>"
       ]
      }
     ],
     "prompt_number": 64
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Above we also plotted two possible realizations of what the actual underlying system might be. Both are equally likely as any other draw. The blue line is what occurs when we average all the 20000 possible dotted lines together.\n",
      "\n",
      "\n",
      "An interesting question to ask is for what temperatures are we most uncertain about the defect-probability? Below we plot the expected value line **and** the associated 95% intervals for each temperature. "
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from scipy.stats.mstats import mquantiles\n",
      "\n",
      "# vectorized bottom and top 2.5% quantiles for \"confidence interval\"\n",
      "qs = mquantiles(p_t, [0.025, 0.975], axis=0)\n",
      "plt.fill_between(t[:, 0], *qs, alpha=0.7,\n",
      "                 color=\"#7A68A6\")\n",
      "\n",
      "plt.plot(t[:, 0], qs[0], label=\"95% CI\", color=\"#7A68A6\", alpha=0.7)\n",
      "\n",
      "plt.plot(t, mean_prob_t, lw=1, ls=\"--\", color=\"k\",\n",
      "         label=\"average posterior \\nprobability of defect\")\n",
      "\n",
      "plt.xlim(t.min(), t.max())\n",
      "plt.ylim(-0.02, 1.02)\n",
      "plt.legend(loc=\"lower left\")\n",
      "plt.scatter(temperature, D, color=\"k\", s=50, alpha=0.5)\n",
      "plt.xlabel(\"temp, $t$\")\n",
      "\n",
      "plt.ylabel(\"probability estimate\")\n",
      "plt.title(\"Posterior probability estimates given temp. $t$\");"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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5DbEJdJdfQgghfUclMYR0w+6woaziDIrOHkFURCwmXDHb1yERP3fxtJozJB5D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       "text": [
        "<matplotlib.figure.Figure at 0x10b08f110>"
       ]
      }
     ],
     "prompt_number": 66
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "The *95% credible interval*, or 95% CI, painted in purple, represents the interval, for each temperature, that contains 95% of the distribution. For example, at 65 degrees, we can be 95% sure that the probability of defect lies between 0.25 and 0.75.\n",
      "\n",
      "More generally, we can see that as the temperature nears 60 degrees, the CI's spread out over [0,1] quickly. As we pass 70 degrees, the CI's tighten again. This can give us insight about how to proceed next: we should probably test more O-rings around 60-65 temperature to get a better estimate of probabilities in that range. Similarly, when reporting to scientists your estimates, you should be very cautious about simply telling them the expected probability, as we can see this does not reflect how *wide* the posterior distribution is."
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "### What about the day of the Challenger disaster?\n",
      "\n",
      "On the day of the Challenger disaster, the outside temperature was 31 degrees Fahrenheit. What is the posterior distribution of a defect occurring,  given this temperature? The distribution is plotted below. It looks almost guaranteed that the Challenger was going to be subject to defective O-rings."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "figsize(12.5, 2.5)\n",
      "\n",
      "prob_31 = logistic(31, beta_samples, alpha_samples)\n",
      "\n",
      "plt.xlim(0.995, 1)\n",
      "plt.hist(prob_31, bins=1000, normed=True, histtype='stepfilled')\n",
      "plt.title(\"Posterior distribution of probability of defect, given $t = 31$\")\n",
      "plt.xlabel(\"probability of defect occurring in O-ring\");"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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4Mlmch0hyMF9IKuYKycF8IWNhEU9EREREZGJYxJPJ4jxEkoP5QlIxV0gO5gsZ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\nAABJRU5ErkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0x10b495690>"
       ]
      }
     ],
     "prompt_number": 68
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "### Is our model appropriate?\n",
      "\n",
      "The skeptical reader will say \"You deliberately chose the logistic function for $p(t)$ and the specific priors. Perhaps other functions or priors will give different results. How do I know I have chosen a good model?\" This is absolutely true. To consider an extreme situation, what if I had chosen the function $p(t) = 1,\\; \\forall t$, which guarantees a defect always occurring: I would have again predicted disaster on January 28th. Yet this is clearly a poorly chosen model. On the other hand, if I did choose the logistic function for $p(t)$, but specified all my priors to be very tight around 0, likely we would have very different posterior distributions. How do we know our model is an expression of the data? This encourages us to measure the model's **goodness of fit**.\n",
      "\n",
      "We can think: *how can we test whether our model is a bad fit?* An idea is to compare observed data (which if we recall is a *fixed* stochastic variable) with artificial dataset which we can simulate. The rationale is that if the simulated dataset does not appear similar, statistically, to the observed dataset, then likely our model is not accurately represented the observed data. \n",
      "\n",
      "Previously in this Chapter, we simulated artificial dataset for the SMS example. To do this, we sampled values from the priors. We saw how varied the resulting datasets looked like, and rarely did they mimic our observed dataset. In the current example,  we should sample from the *posterior* distributions to create *very plausible datasets*. Luckily, our Bayesian framework makes this very easy. We only need to create a new `Stochastic` variable, that is exactly the same as our variable that stored the observations, but minus the observations themselves. If you recall, our `Stochastic` variable that stored our observed data was:\n",
      "\n",
      "    observed = pm.Bernoulli( \"bernoulli_obs\", p, value=D, observed=True)\n",
      "\n",
      "Hence we create:\n",
      "    \n",
      "    simulated_data = pm.Bernoulli(\"simulation_data\", p)\n",
      "\n",
      "Let's simulate 10 000:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "simulated = pm.Bernoulli(\"bernoulli_sim\", p)\n",
      "N = 10000\n",
      "\n",
      "mcmc = pm.MCMC([simulated, alpha, beta, observed])\n",
      "mcmc.sample(N)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " \r",
        "[****************100%******************]  10000 of 10000 complete"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n"
       ]
      }
     ],
     "prompt_number": 69
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "figsize(12.5, 5)\n",
      "\n",
      "simulations = mcmc.trace(\"bernoulli_sim\")[:]\n",
      "print simulations.shape\n",
      "\n",
      "plt.title(\"Simulated dataset using posterior parameters\")\n",
      "figsize(12.5, 6)\n",
      "for i in range(4):\n",
      "    ax = plt.subplot(4, 1, i + 1)\n",
      "    plt.scatter(temperature, simulations[1000 * i, :], color=\"k\",\n",
      "                s=50, alpha=0.6)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "(10000, 23)\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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LHMdh7NixiIiIwM6dOwGYv6gRsRxTeQDAli1bEBYWhkWLFtHXYW3g/v37cHd3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\nrkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0x10adccc50>"
       ]
      }
     ],
     "prompt_number": 71
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Note that the above plots are different (if you can think of a cleaner way to present this, please send a pull request and answer [here](http://stats.stackexchange.com/questions/53078/how-to-visualize-bayesian-goodness-of-fit-for-logistic-regression)!).\n",
      "\n",
      "We wish to assess how good our model is. \"Good\" is a subjective term of course, so results must be relative to other models. \n",
      "\n",
      "We will be doing this graphically as well, which may seem like an even less objective method. The alternative is to use *Bayesian p-values*. These are still subjective, as the proper cutoff between good and bad is arbitrary. Gelman emphasises that the graphical tests are more illuminating [7] than p-value tests. We agree.\n",
      "\n",
      "The following graphical test is a novel data-viz approach to logistic regression. The plots are called *separation plots*[8]. For a suite of models we wish to compare, each model is plotted on an individual separation plot. I leave most of the technical details about separation plots to the very accessible [original paper](http://mdwardlab.com/sites/default/files/GreenhillWardSacks.pdf), but I'll summarize their use here.\n",
      "\n",
      "For each model, we calculate the proportion of times the posterior simulation proposed a value of 1 for a particular temperature, i.e. compute $P( \\;\\text{Defect} = 1 | t, \\alpha, \\beta )$ by averaging. This gives us the posterior probability of a defect at each data point in our dataset. For example, for the model we used above:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "posterior_probability = simulations.mean(axis=0)\n",
      "print \"posterior prob of defect | realized defect \"\n",
      "for i in range(len(D)):\n",
      "    print \"%.2f                     |   %d\" % (posterior_probability[i], D[i])"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "posterior prob of defect | realized defect \n",
        "0.47                     |   0\n",
        "0.20                     |   1\n",
        "0.25                     |   0\n",
        "0.32                     |   0\n",
        "0.39                     |   0\n",
        "0.11                     |   0\n",
        "0.08                     |   0\n",
        "0.19                     |   0\n",
        "0.94                     |   1\n",
        "0.71                     |   1\n",
        "0.20                     |   1\n",
        "0.02                     |   0\n",
        "0.39                     |   0\n",
        "0.98                     |   1\n",
        "0.40                     |   0\n",
        "0.05                     |   0\n",
        "0.20                     |   0\n",
        "0.01                     |   0\n",
        "0.03                     |   0\n",
        "0.01                     |   0\n",
        "0.05                     |   1\n",
        "0.04                     |   0\n",
        "0.92                     |   1\n"
       ]
      }
     ],
     "prompt_number": 72
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Next we sort each column by the posterior probabilities:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "ix = np.argsort(posterior_probability)\n",
      "print \"probb | defect \"\n",
      "for i in range(len(D)):\n",
      "    print \"%.2f  |   %d\" % (posterior_probability[ix[i]], D[ix[i]])"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "probb | defect \n",
        "0.01  |   0\n",
        "0.01  |   0\n",
        "0.02  |   0\n",
        "0.03  |   0\n",
        "0.04  |   0\n",
        "0.05  |   0\n",
        "0.05  |   1\n",
        "0.08  |   0\n",
        "0.11  |   0\n",
        "0.19  |   0\n",
        "0.20  |   0\n",
        "0.20  |   1\n",
        "0.20  |   1\n",
        "0.25  |   0\n",
        "0.32  |   0\n",
        "0.39  |   0\n",
        "0.39  |   0\n",
        "0.40  |   0\n",
        "0.47  |   0\n",
        "0.71  |   1\n",
        "0.92  |   1\n",
        "0.94  |   1\n",
        "0.98  |   1\n"
       ]
      }
     ],
     "prompt_number": 73
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "We can present the above data better in a figure: I've wrapped this up into a `separation_plot` function."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from separation_plot import separation_plot\n",
      "\n",
      "\n",
      "figsize(11., 1.5)\n",
      "separation_plot(posterior_probability, D)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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       "text": [
        "<matplotlib.figure.Figure at 0x10ab87e90>"
       ]
      }
     ],
     "prompt_number": 74
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "The snaking-line is the sorted probabilities, blue bars denote defects, and empty space (or grey bars for the optimistic readers) denote non-defects.  As the probability rises, we see more and more defects occur. On the right hand side, the plot suggests that as the posterior probability is large (line close to 1), then more defects are realized. This is good behaviour. Ideally, all the blue bars *should* be close to the right-hand side, and deviations from this reflect missed predictions. \n",
      "\n",
      "The black vertical line is the expected number of defects we should observe, given this model. This allows the user to see how the total number of events predicted by the model compares to the actual number of events in the data.\n",
      "\n",
      "It is much more informative to compare this to separation plots for other models. Below we compare our model (top) versus three others:\n",
      "\n",
      "1. the perfect model, which predicts the posterior probability to be equal 1 if a defect did occur.\n",
      "2. a completely random model, which predicts random probabilities regardless of temperature.\n",
      "3. a constant model:  where $P(D = 1 \\; | \\; t) = c, \\;\\; \\forall t$. The best choice for $c$ is the observed frequency of defects, in this case 7/23.  \n"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "figsize(11., 1.25)\n",
      "\n",
      "# Our temperature-dependent model\n",
      "separation_plot(posterior_probability, D)\n",
      "plt.title(\"Temperature-dependent model\")\n",
      "\n",
      "# Perfect model\n",
      "# i.e. the probability of defect is equal to if a defect occurred or not.\n",
      "p = D\n",
      "separation_plot(p, D)\n",
      "plt.title(\"Perfect model\")\n",
      "\n",
      "# random predictions\n",
      "p = np.random.rand(23)\n",
      "separation_plot(p, D)\n",
      "plt.title(\"Random model\")\n",
      "\n",
      "# constant model\n",
      "constant_prob = 7. / 23 * np.ones(23)\n",
      "separation_plot(constant_prob, D)\n",
      "plt.title(\"Constant-prediction model\")"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 75,
       "text": [
        "<matplotlib.text.Text at 0x10c392b90>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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       "text": [
        "<matplotlib.figure.Figure at 0x10c11f2d0>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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       "text": [
        "<matplotlib.figure.Figure at 0x109861250>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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       "text": [
        "<matplotlib.figure.Figure at 0x109434bd0>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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       "text": [
        "<matplotlib.figure.Figure at 0x10c37a650>"
       ]
      }
     ],
     "prompt_number": 75
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "In the random model, we can see that as the probability increases there is no clustering of defects to the right-hand side. Similarly for the constant model.\n",
      "\n",
      "The perfect model, the probability line is not well shown, as it is stuck to the bottom and top of the figure. Of course the perfect model is only for demonstration, and we cannot infer any scientific inference from it."
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "##### Exercises\n",
      "\n",
      "1\\. Try putting in extreme values for our observations in the cheating example. What happens if we observe 25 affirmative responses? 10? 50? "
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "2\\. Try plotting $\\alpha$ samples versus $\\beta$ samples.  Why might the resulting plot look like this?"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# type your code here.\n",
      "figsize(12.5, 4)\n",
      "\n",
      "plt.scatter(alpha_samples, beta_samples, alpha=0.1)\n",
      "plt.title(\"Why does the plot look like this?\")\n",
      "plt.xlabel(r\"$\\alpha$\")\n",
      "plt.ylabel(r\"$\\beta$\")"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 76,
       "text": [
        "<matplotlib.text.Text at 0x10c358750>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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SSnkUFUFVlSGTkbrv0ahHNmvw+SAY9MhkLF1dBmN8hMMetbWWSy+Vkf5duyTQ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\n",
       "text": [
        "<matplotlib.figure.Figure at 0x10b092250>"
       ]
      }
     ],
     "prompt_number": 76
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "### References\n",
      "\n",
      "-  [1] Dalal, Fowlkes and Hoadley (1989),JASA, 84, 945-957.\n",
      "-  [2] German Rodriguez. Datasets. In WWS509. Retrieved 30/01/2013, from <http://data.princeton.edu/wws509/datasets/#smoking>.\n",
      "-  [3] McLeish, Don, and Cyntha Struthers. STATISTICS 450/850 Estimation and Hypothesis Testing. Winter 2012. Waterloo, Ontario: 2012. Print.\n",
      "-  [4] Fonnesbeck, Christopher. \"Building Models.\" PyMC-Devs. N.p., n.d. Web. 26 Feb 2013. <http://pymc-devs.github.com/pymc/modelbuilding.html>.\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>.\n",
      "- [6] S.P. Brooks, E.A. Catchpole, and B.J.T. Morgan. Bayesian animal survival estimation. Statistical Science, 15: 357\u2013376, 2000\n",
      "- [7] Gelman, Andrew. \"Philosophy and the practice of Bayesian statistics.\" British Journal of Mathematical and Statistical Psychology. (2012): n. page. Web. 2 Apr. 2013.\n",
      "- [8] Greenhill, Brian, Michael D. Ward, and Audrey Sacks. \"The Separation Plot: A New Visual Method for Evaluating the Fit of Binary Models.\" American Journal of Political Science. 55.No.4 (2011): n. page. Web. 2 Apr. 2013."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from IPython.core.display import HTML\n",
      "\n",
      "\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",
        "    @font-face {\n",
        "        font-family: \"Computer Modern\";\n",
        "        font-weight: bold;\n",
        "        src: url('http://9dbb143991406a7c655e-aa5fcb0a5a4ec34cff238a2d56ca4144.r56.cf5.rackcdn.com/cmunsx.otf');\n",
        "    }\n",
        "    @font-face {\n",
        "        font-family: \"Computer Modern\";\n",
        "        font-style: oblique;\n",
        "        src: url('http://9dbb143991406a7c655e-aa5fcb0a5a4ec34cff238a2d56ca4144.r56.cf5.rackcdn.com/cmunsi.otf');\n",
        "    }\n",
        "    @font-face {\n",
        "        font-family: \"Computer Modern\";\n",
        "        font-weight: bold;\n",
        "        font-style: oblique;\n",
        "        src: url('http://9dbb143991406a7c655e-aa5fcb0a5a4ec34cff238a2d56ca4144.r56.cf5.rackcdn.com/cmunso.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",
        "<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>\n"
       ],
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 1,
       "text": [
        "<IPython.core.display.HTML at 0x10cc9f550>"
       ]
      }
     ],
     "prompt_number": 1
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 105
    }
   ],
   "metadata": {}
  }
 ]
}