{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Chapter 2\n",
    "======\n",
    "`Original content created by Cam Davidson-Pilon`\n",
    "\n",
    "`Ported to Python 3 and PyMC3 by Max Margenot (@clean_utensils) and Thomas Wiecki (@twiecki) at Quantopian (@quantopian)`\n",
    "\n",
    "___\n",
    "\n",
    "This chapter introduces more PyMC3 syntax and variables 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 PyMC3\n",
    "\n",
    "### Model Context\n",
    "\n",
    "In PyMC3, we typically handle all the variables we want in our model within the context of the `Model` object."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Applied log-transform to poisson_param and added transformed poisson_param_log_ to model.\n"
     ]
    }
   ],
   "source": [
    "import pymc3 as pm\n",
    "\n",
    "with pm.Model() as model:\n",
    "    parameter = pm.Exponential(\"poisson_param\", 1.0)\n",
    "    data_generator = pm.Poisson(\"data_generator\", parameter)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This is an extra layer of convenience compared to PyMC. Any variables created within a given `Model`'s context will be automatically assigned to that model. If you try to define a variable outside of the context of a model, you will get an error.\n",
    "\n",
    "We can continue to work within the context of the same model by using `with` with the name of the model object that we have already created."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "with model:\n",
    "    data_plus_one = data_generator + 1"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can examine the same variables outside of the model context once they have been defined, but to define more variables that the model will recognize they have to be within the context."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array(0.693147177890573)"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "parameter.tag.test_value"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Each variable assigned to a model will be defined with its own name, the first string parameter (we will cover this further in the variables section). To create a different model object with the same name as one we have used previously, we need only run the first block of code again."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Applied log-transform to theta and added transformed theta_log_ to model.\n"
     ]
    }
   ],
   "source": [
    "with pm.Model() as model:\n",
    "    theta = pm.Exponential(\"theta\", 2.0)\n",
    "    data_generator = pm.Poisson(\"data_generator\", theta)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can also define an entirely separate model. Note that we are free to name our models whatever we like, so if we do not want to overwrite an old model we need only make another."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Applied interval-transform to P(A) and added transformed P(A)_interval_ to model.\n",
      "Applied interval-transform to P(B) and added transformed P(B)_interval_ to model.\n"
     ]
    }
   ],
   "source": [
    "with pm.Model() as ab_testing:\n",
    "    p_A = pm.Uniform(\"P(A)\", 0, 1)\n",
    "    p_B = pm.Uniform(\"P(B)\", 0, 1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "You probably noticed that PyMC3 will often give you notifications about transformations when you add variables to your model. These transformations are done internally by PyMC3 to modify the space that the variable is sampled in (when we get to actually sampling the model). This is an internal feature which helps with the convergence of our samples to the posterior distribution and serves to improve the results."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### PyMC3 Variables\n",
    "\n",
    "All PyMC3 variables have an initial value (i.e. test value). Using the same variables from before:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "parameter.tag.test_value = 0.693147177890573\n",
      "data_generator.tag.test_value = 0\n",
      "data_plus_one.tag.test_value = 1\n"
     ]
    }
   ],
   "source": [
    "print(\"parameter.tag.test_value =\", parameter.tag.test_value)\n",
    "print(\"data_generator.tag.test_value =\", data_generator.tag.test_value)\n",
    "print(\"data_plus_one.tag.test_value =\", data_plus_one.tag.test_value)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The `test_value` is used only for the model, as the starting point for sampling if no other start is specified. It will not change as a result of sampling. This initial state can be changed at variable creation by specifying a value for the `testval` parameter."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Applied log-transform to poisson_param and added transformed poisson_param_log_ to model.\n",
      "\n",
      "parameter.tag.test_value = 0.49999999904767284\n"
     ]
    }
   ],
   "source": [
    "with pm.Model() as model:\n",
    "    parameter = pm.Exponential(\"poisson_param\", 1.0, testval=0.5)\n",
    "\n",
    "print(\"\\nparameter.tag.test_value =\", parameter.tag.test_value)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This can be helpful if you are using a more unstable prior that may require a better starting point.\n",
    "\n",
    "PyMC3 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' parameters and components, 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' parameters and components were known. This might be confusing at first: a quick mental check is *if I knew all of variable `foo`'s component 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, or random, 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 [PyMC3 docs](https://docs.pymc.io/en/stable/api.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 `shape` 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 `tag.test_value` attribute return NumPy arrays.  \n",
    "\n",
    "The `shape` 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, shape=N)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Deterministic variables\n",
    "\n",
    "We can create a deterministic variable similarly to how we create a stochastic variable. We simply call up the `Deterministic` class in PyMC3 and pass in the function that we desire\n",
    "\n",
    "    deterministic_variable = pm.Deterministic(\"deterministic variable\", some_function_of_variables)\n",
    "\n",
    "For all purposes, we can treat the object `some_deterministic_var` as a variable and not a Python function. \n",
    "\n",
    "Calling `pymc3.Deterministic` is the most obvious way, but not the only way, to create deterministic variables. Elementary operations, like addition, exponentials etc. implicitly create deterministic variables. For example, the following returns a deterministic variable:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Applied log-transform to lambda_1 and added transformed lambda_1_log_ to model.\n",
      "Applied log-transform to lambda_2 and added transformed lambda_2_log_ to model.\n"
     ]
    }
   ],
   "source": [
    "with pm.Model() as model:\n",
    "    lambda_1 = pm.Exponential(\"lambda_1\", 1.0)\n",
    "    lambda_2 = pm.Exponential(\"lambda_2\", 1.0)\n",
    "    tau = pm.DiscreteUniform(\"tau\", lower=0, upper=10)\n",
    "\n",
    "new_deterministic_variable = lambda_1 + lambda_2"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "If we want a `deterministic` variable to actually be tracked by our sampling, however, we need to define it explicitly as a named `deterministic` variable with the constructor.\n",
    "\n",
    "The use of the `deterministic` variable was seen in the previous chapter's text-message example.  Recall the model for $\\lambda$ looked like: \n",
    "\n",
    "$$\n",
    "\\lambda = \n",
    "\\begin{cases}\\lambda_1  & \\text{if } t \\lt \\tau \\cr\n",
    "\\lambda_2 & \\text{if } t \\ge \\tau\n",
    "\\end{cases}\n",
    "$$\n",
    "\n",
    "And in PyMC3 code:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "\n",
    "n_data_points = 5  # in CH1 we had ~70 data points\n",
    "idx = np.arange(n_data_points)\n",
    "with model:\n",
    "    lambda_ = pm.math.switch(tau >= idx, lambda_1, lambda_2)"
   ]
  },
  {
   "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. We use the `switch` function here to change from $\\lambda_1$ to $\\lambda_2$ at the appropriate time. This function is directly from the `theano` package, which we will discuss in the next section.\n",
    "\n",
    "Inside a `deterministic` variable, the stochastic variables passed in behave like scalars or NumPy arrays (if multivariable). We can do whatever we want with them as long as the dimensions match up in our calculations.\n",
    "\n",
    "For example, running the following:\n",
    "\n",
    "    def subtract(x, y):\n",
    "        return x - y\n",
    "    \n",
    "    stochastic_1 = pm.Uniform(\"U_1\", 0, 1)\n",
    "    stochastic_2 = pm.Uniform(\"U_2\", 0, 1)\n",
    "    \n",
    "    det_1 = pm.Deterministic(\"Delta\", subtract(stochastic_1, stochastic_2))\n",
    "    \n",
    "Is perfectly valid PyMC3 code. Saying that our expressions behave like NumPy arrays is not exactly honest here, however. The main catch is that the expression that we are making *must* be compatible with `theano` tensors, which we will cover in the next section. Feel free to define whatever functions that you need in order to compose your model. However, if you need to do any array-like calculations that would require NumPy functions, make sure you use their equivalents in `theano`."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Theano\n",
    "\n",
    "The majority of the heavy lifting done by PyMC3 is taken care of with the `theano` package. The notation in `theano` is remarkably similar to NumPy. It also supports many of the familiar computational elements of NumPy. However, while NumPy directly executes computations, e.g. when you run `a + b`, `theano` instead builds up a \"compute graph\" that tracks that you want to perform the `+` operation on the elements `a` and `b`. Only when you `eval()` a `theano` expression does the computation take place (i.e. `theano` is lazy evaluated). Once the compute graph is built, we can perform all kinds of mathematical optimizations (e.g. simplifications), compute gradients via autodiff, compile the entire graph to C to run at machine speed, and also compile it to run on the GPU. PyMC3 is basically a collection of `theano` symbolic expressions for various probability distributions that are combined to one big compute graph making up the whole model log probability, and a collection of inference algorithms that use that graph to compute probabilities and gradients. For practical purposes, what this means is that in order to build certain models we sometimes have to use `theano`.\n",
    "\n",
    "Let's write some PyMC3 code that involves `theano` calculations."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Applied interval-transform to p and added transformed p_interval_ to model.\n"
     ]
    }
   ],
   "source": [
    "import theano.tensor as tt\n",
    "\n",
    "with pm.Model() as theano_test:\n",
    "    p1 = pm.Uniform(\"p\", 0, 1)\n",
    "    p2 = 1 - p1\n",
    "    p = tt.stack([p1, p2])\n",
    "    \n",
    "    assignment = pm.Categorical(\"assignment\", p)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here we use `theano`'s `stack()` function in the same way we would use one of NumPy's stacking functions: to combine our two separate variables, `p1` and `p2`, into a vector with $2$ elements. The stochastic `categorical` variable does not understand what we mean if we pass a NumPy array of `p1` and `p2` to it because they are both `theano` variables. Stacking them like this combines them into one `theano` variable that we can use as the complementary pair of probabilities for our two categories.\n",
    "\n",
    "Throughout the course of this book we use several `theano` functions to help construct our models. If you have more interest in looking at `theano` itself, be sure to check out the [documentation](http://deeplearning.net/software/theano/library/).\n",
    "\n",
    "After these technical considerations, we can get back to defining our model!"
   ]
  },
  {
   "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",
   "execution_count": 11,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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S9589cSSTbwBAv8M+3znBPtSxyDfOoWbb4dLOffu1bU9b4o803+mrBeznG4ds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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fa0aad107f0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "%matplotlib inline\n",
    "from IPython.core.pylabtools import figsize\n",
    "import matplotlib.pyplot as plt\n",
    "import scipy.stats as stats\n",
    "figsize(12.5, 4)\n",
    "\n",
    "\n",
    "samples = lambda_1.random(size=20000)\n",
    "plt.hist(samples, bins=70, density=True, histtype=\"stepfilled\")\n",
    "plt.title(\"Prior distribution for $\\lambda_1$\")\n",
    "plt.xlim(0, 8);"
   ]
  },
  {
   "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",
    "PyMC3 stochastic variables have a keyword argument `observed`. The keyword `observed` has a very simple role: fix the variable's current value to be the given data, typically a NumPy `array` or pandas `DataFrame`. For example:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "value:  [10  5]\n"
     ]
    }
   ],
   "source": [
    "data = np.array([10, 5])\n",
    "with model:\n",
    "    fixed_variable = pm.Poisson(\"fxd\", 1, observed=data)\n",
    "print(\"value: \", fixed_variable.tag.test_value)"
   ]
  },
  {
   "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 PyMC3 variable `observations` to the observed dataset. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[10 25 15 20 35]\n"
     ]
    }
   ],
   "source": [
    "# We're using some fake data here\n",
    "data = np.array([10, 25, 15, 20, 35])\n",
    "with model:\n",
    "    obs = pm.Poisson(\"obs\", lambda_, observed=data)\n",
    "print(obs.tag.test_value)"
   ]
  },
  {
   "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 later 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",
    "PyMC3, 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",
   "execution_count": 14,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "59\n"
     ]
    }
   ],
   "source": [
    "tau = np.random.randint(0, 80)\n",
    "print(tau)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "2\\. Draw $\\lambda_1$ and $\\lambda_2$ from an $\\text{Exp}(\\alpha)$ distribution:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "49.7521280843 10.1226712418\n"
     ]
    }
   ],
   "source": [
    "alpha = 1./20.\n",
    "lambda_1, lambda_2 = np.random.exponential(scale=1/alpha, size=2)\n",
    "print(lambda_1, lambda_2)"
   ]
  },
  {
   "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",
   "execution_count": 16,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "data = np.r_[stats.poisson.rvs(mu=lambda_1, size=tau), stats.poisson.rvs(mu=lambda_2, size = 80 - tau)]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "4\\. Plot the artificial dataset:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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JJ9KhQwe+/OUvs+eee9Ztd9ddd/GNb3yDoUOH0qFDB77xjW/w8ssvs3TpUp5++mn2339/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\nQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fa09e0b9e80>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "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();"
   ]
  },
  {
   "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. PyMC3'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",
   "execution_count": 18,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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Y9xKdly2ZMD37+vrYvXs3EL286Oyzz6a7u5vxksjn28zuAHa5+5dKpi0DXnb3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\nzMwq8v9VOpInhJptAAAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fa09b5d2eb8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "def plot_artificial_sms_dataset():\n",
    "    tau = stats.randint.rvs(0, 80)\n",
    "    alpha = 1./20.\n",
    "    lambda_1, lambda_2 = stats.expon.rvs(scale=1/alpha, size=2)\n",
    "    data = np.r_[stats.poisson.rvs(mu=lambda_1, size=tau), stats.poisson.rvs(mu=lambda_2, size=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+1)\n",
    "    plot_artificial_sms_dataset()\n"
   ]
  },
  {
   "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 distributions 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",
   "execution_count": 19,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Applied interval-transform to p and added transformed p_interval_ to model.\n"
     ]
    }
   ],
   "source": [
    "import pymc3 as pm\n",
    "\n",
    "# The parameters are the bounds of the Uniform.\n",
    "with pm.Model() as model:\n",
    "    p = pm.Uniform('p', lower=0, upper=1)"
   ]
  },
  {
   "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",
   "execution_count": 20,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[1 0 1 ..., 0 0 0]\n",
      "77\n"
     ]
    }
   ],
   "source": [
    "#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 = stats.bernoulli.rvs(p_true, size=N)\n",
    "\n",
    "print(occurrences) # Remember: Python treats True == 1, and False == 0\n",
    "print(np.sum(occurrences))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The observed frequency is:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "What is the observed frequency in Group A? 0.0513\n",
      "Does this equal the true frequency? False\n"
     ]
    }
   ],
   "source": [
    "# Occurrences.mean is equal to n/N.\n",
    "print(\"What is the observed frequency in Group A? %.4f\" % np.mean(occurrences))\n",
    "print(\"Does this equal the true frequency? %s\" % (np.mean(occurrences) == p_true))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We combine the observations into the PyMC3 `observed` variable, and run our inference algorithm:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      " [-------100%-------] 18000 of 18000 in 1.7 sec. | SPS: 10329.7 | ETA: 0.0"
     ]
    }
   ],
   "source": [
    "#include the observations, which are Bernoulli\n",
    "with model:\n",
    "    obs = pm.Bernoulli(\"obs\", p, observed=occurrences)\n",
    "    # To be explained in chapter 3\n",
    "    step = pm.Metropolis()\n",
    "    trace = pm.sample(18000, step=step)\n",
    "    burned_trace = trace[1000:]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We plot the posterior distribution of the unknown $p_A$ below:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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PP54JEyZwxx13lLTddXV1TJw4cb/bsrVx/Pjx3HrrrZx11lmMHj2az33uc+zatSu27qVL\nl3Lqqacye/bsnPu+/vrrXHTRRYwePZqJEyfy+OOPd9Rz7733Mnny5I5ybW0tU6ZM6SjX1NTwyiuv\n5GzboEGDOOWUU3jqqae6ebaKp5xxKYjyF8OieIpUNvXR3u3222/n6KOP5pe//CXNzc1cc801AMye\nPZsHHniAN998k/79+2e9uqO7M3nyZE4++WSWLFnCr3/9a376058yb968krX71Vdf5bjjjtvvtlxX\noHzkkUd46KGHaGxs5OWXX+bee+89YJvFixdz6aWXMn36dD796U9n3XfPnj1MnjyZVCrFG2+8wU03\n3cQXvvAFli9fDsDEiRN59tlngejDyu7du3nhhRcAWLlyJdu3b+fEE0/Mq23HH388L7/8coFnKTm6\nAqeIiIgEq6vfUbS2tua9fVfb5svd9ytfddVVHHnkkV3e31lDQwMbN27kuuuuA6C6uprPfvazzJ49\nm3POOWe/bZcsWcKLL77I0qVLOeOMM9iwYQMHHXQQl112WUHtbWtrY+jQoVkfQ6Z//Md/ZMSIEUCU\n+pE5uJ0/fz6/+MUv+NnPfsYZZ5yRc9+FCxeyfft2rr32WgDOOussLrjgAh566CGmTZvGsccey9Ch\nQ2lqauKNN97gz//8z3n55ZdZtmwZzz///H7HyNW2YcOG0dLSku/pSZxyxqUgyl8Mi+IpUtnUR8N0\n1FFH5b3tW2+9xdq1axkzZgxjxoxh9OjR3HzzzbzzzjsHbLtmzRpOOukkmpubufDCC7n00kv593//\n9/22cXemTp2a9Zjve9/72Lp1a95tBHj/+9/f8f9DDjmEbdu27Xf/rFmz+NjHPnbAQLyrfdeuXXvA\neTrmmGNYu3ZtR3nixIn84Q9/YMGCBUyaNIlJkyZRX1/PM888w5lnnpl327Zs2UJVVVVBjzdJyhkX\nEQlEa2srjz76aLmbIVJRWltbY/8K2b4YcekdmbcNHjyY7du3d5TXr1/f8f8PfOADfPCDH2TFihWs\nWLGCN998k1WrVnHfffcdUG8qlWLevHlccMEFALz00ksHzPS/9tprrFu3LmubP/zhD3ekg+TTxnzM\nmDGD1atX841vfCOv7Y888kjefvvt/W5bvXr1ft8onHHGGTzzzDM8++yznHnmmZx55pnMnz+fBQsW\nHJDzns3rr7/OSSedlPf2SctrMG5mXzWzl83sJTO7x8wOMrNDzWyOmS01syfMLPYjhXLGw6L8xbAo\nnuFRTMOiePZ+I0aM2O+Hj3Fqamp46KGH2LdvH3PnzmX+/Pkd95122mkMHTqUmTNnsmPHDvbu3cuS\nJUtYtGhRbF3z5s3rGIjef//9fOlLX+q4b8eOHRx55JEMHz6cnTt3dtme884774BvZbK1MR9Dhw7l\nV7/6FQsWLOBb3/pWzu1PO+00Bg8ezMyZM9mzZw/19fU88cQT++Wat8+Mtz+u008/nbq6OlpbWzn5\n5JPzatfOnTtZvHgxZ599dkGPJ0k5B+NmdhTwZWCCu59MlGd+GXA9MNfdxwFPATeUsqEiIiIivc1X\nvvIVfvjDHzJmzBhuvfXW2JnyG2+8kccee4zRo0cze/ZsPvGJT3Tc169fP+677z6ampo49dRTOf74\n4/nKV77Cli1bDqhn27ZtrF+/ngULFjBr1ixOPfVUPvnJT3bc39jYyPz589m5c2fWpfz+9m//lrlz\n5+43YM/Wxlw/7my/f/jw4cyePZu6ujq+973vZd134MCB3HvvvTz55JMcd9xxTJs2jZ/85Cf7/bB0\n7NixDBs2rCP1ZdiwYYwePZrTTz+9o95cbXvssceYNGkSI0eOzLpdKVmuhPz0YHwBMB7YAswGZgK3\nAn/m7i1mNgr4nbufkLn/jBkzvPNSM9K71dfXa6YmIIpneBTTsCieua1Zs6agHOyQPf7449TX1/Od\n73zngPtWrlzJqFGjOPjgg7nppps477zzOO2007qs67vf/S5HHHEEV111VSmbXHbnn38+M2fO5IQT\nDhjCdujqOdbQ0EAqlco+2s9DztVU3H2Nmc0AmoHtwBx3n2tmI929Jb3NOjMbUWxjRERERKRwy5cv\n57bbbuOYY46hra1tvx8kzp8/n5///Of86Ec/YvPmzbz22mvs2rUr62A839zu3m7OnDnlbkJeM+Pv\nAx4CLgXagF+lyz9y98M6bbfR3Q/P3H/q1Km+adMmqqurAaiqqqKmpqbjk357TpLKKqusssoqq6xy\noeUxY8ZoZlxKas2aNaxYsYKmpiba2toAaG5upra2luuuu67omfF8BuOXABe4++fT5c8CpwN/Dpzd\nKU1lnrt/KHP/uro6nzBhQrHtFBGRHNpXTSh29QeR3kRpKlJqpU5TyWc1lWbgdDM72KIs+BTwKvAo\ncGV6myuAR+J21jrjYWmfiZAwKJ4ilU19VCR8A3Jt4O7Pm9mDwCJgd/rfO4BhwANmNgVYBXymlA0V\nEREREQlNzsE4gLt/E/hmxs2twLm59tU642Fpz9WTMCieIpVNfVQkfLoCp4iIiIhImZR8MK6c8bAo\nfzEsiqdIZVMfza1///77XaZdJEnbt2+nf//+JT1GXmkqIiJS+VpbWzV4kz5nxIgRrF+/nk2bNpW7\nKTllrv8tla9///6MGFHaS+nkXNqwWFraUERERERC05NLG4qIiIiISAkoZ1wKoq/Aw6J4hkcxDYvi\nGRbFU+IoZ1xEpI96d/deduzel2idBw/sxyEDS/tjJxGRkChnXESkj1qx8V2+8cTyROv87gVjGHP4\n4ETrFBGpREnljGtmXEQkEIcddhgQraqSr43bdyfahtJO74iIhEc541IQ5buFRfEUqWzqo2FRPCWO\nVlMRERERESmTkg/Gx48fX+pDSA+aNGlSuZsgCVI8RSqb+mhYFE+Jo5lxEREREZEyUc64FET5bmFR\nPEUqm/poWBRPiaPVVEREAtHa2qo3exGRXkY541IQ5buFRfEMj2IaFsUzLIqnxMk5GDez481skZk1\npP9tM7NrzOxQM5tjZkvN7Akzq+qJBouIiIiIhCLnYNzdX3f3U919AnAasA14GLgemOvu44CngBvi\n9lfOeFj0FXhYFM/wKKZhUTzDonhKnELTVM4Flrv7W8DFwKz07bOATyXZMBERERGR0BU6GP8b4N70\n/0e6ewuAu68DRsTtoJzxsCjfLSyKZ3gU07AonmFRPCVO3qupmNlA4CLga+mbPGOTzDIADz74IHfe\neSfV1dUAVFVVUVNT0/GEbP/KRmWVVVZZ5eLKhx12GBCtqpLP9gufm8/m5c0MHxtNmmxeHqUVFlN+\n8bmNjL3w3Io4HyqrrLLKSZabmppoa2sDoLm5mdraWlKpFMUy99gx9IEbml0EfNHdP54uLwHOdvcW\nMxsFzHP3D2XuN2PGDJ8yZUrRDZXKUF9f3/HElN5P8QxL5mA8lxUb3+UfH34t0Tbc/lfjGHv44ETr\n7MvUR8OieIaloaGBVCplxdZTSJrKZcB9ncqPAlem/38F8EixjRERERER6UvyGoyb2WCiH2/O7nTz\n94HzzGwpkAJuittXOeNh0Sf6sCieIpVNfTQsiqfEGZDPRu6+HXh/xm2tRAN0ERERERHphpJfgVPr\njIel/QcNEgbFU6SyqY+GRfGUOHnNjIuISOVrbW3Vm72ISC9T8plx5YyHRfluYVE8w6OYhkXxDIvi\nKXFKPhgXEREREZF4yhmXgugr8LAonuFRTMOieIZF8ZQ4mhkXERERESmTkv+AUznjYVG+W1gUz97j\n3V17eXX9Nnbu3Zd1u37HnMT8VZvyqrPt3T1JNE1KSH00LIqnxNFqKiIivcAed25bsJrVbTu73Gbh\ntBQAtdPreqpZIiJSJOWMS0GU7xYWxVOksqmPhkXxlDjKGRcRERERKROtMy4FUb5bWBRPkcqmPhoW\nxVPiaGZcRERERKRMlDMuBVG+W1gUT5HKpj4aFsVT4mg1FRGRQNROr2Pzck2AiIj0JsoZl4Io3y0s\nimd4ho/Va25I1EfDonhKHOWMi4j0AlbuBuRpYH+9rYiIFCKvNBUzqwLuBE4C9gFTgNeB+4FjgZXA\nZ9y9LXPfxsZGJkyYkFR7pczq6+v1yT4gimfpLFm/jSXrtyVW3959zjvbdufcbvPyxrLOjv/HH5oZ\nfnD/xOo77JCBXPmRoxg+qG9mVaqPhkXxlDj5vrrdAvzW3S81swHAEODrwFx3n25mXwNuAK4vUTtF\nRHqVF1dv4e6GteVuRo97uSW5DyAARw47iCtrE61SRKSi5Pw+0cyGA2e5+10A7r4nPQN+MTArvdks\n4FNx+ytnPCz6RB8WxTM8yhkPi/poWBRPiZNPct9o4B0zu8vMGszsDjMbDIx09xYAd18HjChlQ0VE\nJLuF01IsnJYqdzNERKQA+aSpDAAmAFe7+0Izu5koHcUztsssA3DLLbcwZMgQqqurAaiqqqKmpqbj\n02H7mpsq947y7bffrvgFVFY8S1tuX2awfba61OVMPX38UpQHDh4IjAPKH89ylJuampg6dWrFtEdl\nxbMvl5uammhri34e2dzcTG1tLalU8RMg5h47hn5vA7ORwAJ3H5MuTyIajI8Fznb3FjMbBcxz9w9l\n7j9jxgyfMmVK0Q2VylBfrx+fhETxLJ1fNKzr8Zzx9lnx2ul1PXrcUjpy2EH86OJxDD94QLmbUhbq\no2FRPMPS0NBAKpUqerGrnGkq6VSUt8zs+PRNKeAV4FHgyvRtVwCPxO2vnPGw6EUkLIqnSGVTHw2L\n4ilx8p1quAa4x8wGAiuAvwf6Aw+Y2RRgFfCZ0jRRRERERCRMeV2dwd0Xu/tH3H28u3/a3dvcvdXd\nz3X3ce5+vrtvitu3sVGXZg5Jew6VhEHxFKls6qNhUTwlTt9MwhMRCVDt9LqOH0GKiEjvUPLrFitn\nPCzKdwuL4hkerTMeFvXRsCieEqfkg3EREREREYlX8sG4csbDony3sCie4VGaSljUR8OieEoczYyL\niIiIiJSJcsalIMp3C4viGR7ljIdFfTQsiqfE0cy4iEggFk5LdVyFU0REegfljEtBlO8WFsVTpLKp\nj4ZF8ZQ4mhkXERERESkT5YxLQZTvFhbFU6SyqY+GRfGUOJoZFxEREREpkwGlPkBjYyMTJkwo9WGk\nh9TX1+uTfUAUT6l07+7ZR8vWXby9eWdidQ4e2I9jDz0ksfpKSX00LIqnxCn5YFxERHpG7fS64C76\ns+ndPVz966WJ1jl5/EiurO0dg3ERCZ9yxqUg+kQfFsUzPFpnPCzqo2FRPCWOcsZFRERERMokr8G4\nma00s8VmtsjMnk/fdqiZzTGzpWb2hJlVxe2rdcbDojVSw6J4hie0NJW+Tn00LIqnxMl3ZnwfcLa7\nn+ruH03fdj0w193HAU8BN5SigSIiIiIiocp3MG4x214MzEr/fxbwqbgdlTMeFuW7hUXxDI9yxsOi\nPhoWxVPi5DsYd+BJM3vBzD6Xvm2ku7cAuPs6YEQpGigiIvlZOC3FwmmpcjdDREQKkO9gfKK7TwAu\nBK42s7OIBuidZZYB5YyHRvluYVE8RSqb+mhYFE+Jk9c64+6+Nv3vBjP7NfBRoMXMRrp7i5mNAtbH\n7fv000+zcOFCqqurAaiqqqKmpqbjq5r2J6bKvaPc1NRUUe1RWfGs5HL7jynbU0dKXc7U08fvLWXG\nXwCU//mRT7mpqami2qOy4tmXy01NTbS1tQHQ3NxMbW0tqVTx30aae+yE9nsbmA0G+rn7VjMbAswB\nvgmkgFZ3/76ZfQ041N2vz9y/rq7OdQVOEelrftGwjrsb1vboMdtTVGqn1/XocXub6KI/R5W7GSLS\nyzU0NJBKpazYegbksc1I4GEz8/T297j7HDNbCDxgZlOAVcBnim2MiIiIiEhfkjNn3N3fdPfx6WUN\na9z9pvTtre5+rruPc/fz3X1T3P7KGQ9L+9c2EgbFU6SyqY+GRfGUOPnMjIuISC9QO71OF/0REell\n8l1Npdu0znhY2n/IIGFQPMOjdcbDoj4aFsVT4mhmXET6vK0797B7b/Yfsxein8GeffsSq09ERMJV\n8sF4Y2MjWk0lHPX19fpkHxDFM/L6O9v5wdPNidbZtmNPovXla/PyRs2OB0R9NCyKp8TRzLiI9Hl7\n9jkbt++mQ5eHAAAU2ElEQVQudzNERKQPUs64FESf6MOieIZHs+JhUR8Ni+IpcUo+GBcRkZ6xcFqq\n48I/IiLSO5R8MK51xsOiNVLDoniKVDb10bAonhJHM+MiIiIiImWinHEpiPLdwqJ4ilQ29dGwKJ4S\nRzPjIiIiIiJlopxxKYjy3cKieIpUNvXRsCieEkfrjIuIBKJ2eh2bl2sCRESkN1HOuBRE+W5hUTzD\no3XGw6I+GhbFU+IoZ1xEREREpEyUMy4FUb5bWBTP8ChNJSzqo2FRPCVO3oNxM+tnZg1m9mi6fKiZ\nzTGzpWb2hJlVla6ZIiIiIiLhKWRm/Frg1U7l64G57j4OeAq4IW4n5YyHRfluYVE8w6Oc8bCoj4ZF\n8ZQ4eQ3Gzexo4ELgzk43XwzMSv9/FvCpZJsmIiKFWDgtxcJpqXI3Q0RECpDvzPjNwD8D3um2ke7e\nAuDu64ARcTsqZzwsyncLi+IpUtnUR8OieEqcnINxM/sE0OLujYBl2dSz3CciIiIiIhnyuejPROAi\nM7sQOAQYZmb/Dawzs5Hu3mJmo4D1cTsvW7aML37xi1RXVwNQVVVFTU1NR95U+6dElXtHuf22SmmP\nyopnEuWDjq0B3luJpD3vureVM5W7PZVaZvwFQOU8/3KV21VKe1RWPPtquampiba2NgCam5upra0l\nlSo+NdDc85/QNrM/A65z94vMbDqw0d2/b2ZfAw519+sz96mrq/MJEyYU3VARkVJ5/q02/uWJFeVu\nRtHa88Vrp9eVuSWVbfL4kVxZe1S5myEivVxDQwOpVCpb1kheilln/CbgPDNbCqTS5QMoZzwsmZ/s\npXdTPEUqm/poWBRPiTOgkI3d/Wng6fT/W4FzS9EoEREpXO30Ol30R0Sklyn5FTi1znhYOucaS++n\neIZH64yHRX00LIqnxCloZlxERKS3+58l7/Byy7ZE67x8wpGcfOTQROsUkb6h5IPxxsZG9APOcHRe\neUN6P8UzPJuXN2p2PIctO/fy0tqtidb57u69idbXTn00LIqnxCl5moqIiIiIiMRTzrgURJ/ow6J4\nhkez4mFRHw2L4ilxNDMuIhKIhdNSHWuNi4hI71DywbjWGQ+L1kgNi+IpUtnUR8OieEoczYyLSJ83\noF/RF1ATERHplpKvpqKc8bAo3y0svTGeq9t28LPn3k60zrVbdiVan0hSemMfla4pnhJH64yLSK+y\nz2FB8+ZyN0NERCQRyhmXgijfLSyKp0hlUx8Ni+IpcTQzLiISiNrpdWxergkQEZHeROuMS0GU7xYW\nxTM8Wmc8LOqjYVE8JY5WUxERERERKRPljEtBlO8WFsUzPEpTCYv6aFgUT4mjmXERERERkTLJORg3\ns0Fm9pyZLTKzJjP71/Tth5rZHDNbamZPmFlV3P7KGQ+L8t3ConiGRznjYVEfDYviKXFyDsbdfSdw\njrufCowH/sLMPgpcD8x193HAU8ANJW2piIhktXBaioXTUuVuhoiIFCCvNBV3357+7yCi5RAduBiY\nlb59FvCpuH2VMx4W5buFRfEUqWzqo2FRPCVOXuuMm1k/4EVgLHCbu79gZiPdvQXA3deZ2YgStlNE\nRKRiucOGrbsSrXPwQfpZl0hfkNdg3N33Aaea2XDgYTM7kWh2fL/N4vZdtmwZX/ziF6murgagqqqK\nmpqajryp9k+JKveOcvttldIelftePFu27gIOBd5bOaQ9T7qvlzOVuz19qfztujfZ9uZiAN53XHT/\npmWNRZU/O+IdRg4bRLtK6H8qF19uVyntUTn/clNTE21tbQA0NzdTW1tLKlV8aqC5x46hu97B7P8C\n24HPAWe7e4uZjQLmufuHMrevq6vzCRMmFN1QERGA5k07+NyDS8rdjIrUni9eO72uzC2RJPzsr0/g\n2EMPKXczRKQLDQ0NpFIpK7aefFZTOaJ9pRQzOwQ4D1gCPApcmd7sCuCRuP2VMx4W5buFRfEUqWzq\no2FRPCVOPmkqRwKz0nnj/YD73f23ZvYs8ICZTQFWAZ8pYTtFRCSH2ul1uuiPiEgvk3Mw7u5NwAF5\nJu7eCpyba3+tMx4WrZEaFsUzPFpnPCzqo2FRPCWOfqotIiIiIlImJR+MK2c8LMp3C4viGR6lqYRF\nfTQsiqfE0cy4iIiIiEiZlHwwrpzxsCjfLSyKZ3iUMx4W9dGwKJ4SRzPjIiKBWDgt1bHWuIiI9A7K\nGZeCKN8tLIqnSGVTHw2L4ilxNDMuIiIiIlImyhmXgijfLSyKp0hlUx8Ni+IpcTQzLiIiIiJSJsoZ\nl4Io3y0siqdIZVMfDYviKXEGlLsBIiKSjNrpdbroj4hIL6OccSmI8t3ConiGR+uMh0V9NCyKp8RR\nzriIiIiISJkoZ1wKony3sCie4VGaSljUR8OieEoczYyLiIiIiJSJcsalIMp3C4viGR7ljIdFfTQs\niqfEyTkYN7OjzewpM3vFzJrM7Jr07Yea2RwzW2pmT5hZVembKyIiXVk4LcXCaalyN0NERAqQz8z4\nHuCf3P1E4AzgajM7AbgemOvu44CngBvidlbOeFiU7xYWxVOksqmPhkXxlDg51xl393XAuvT/t5rZ\nEuBo4GLgz9KbzQJ+RzRAFxEBYNfefTSu2cKWnXsTq3PTu3sSq0tERKTcCrroj5l9EBgPPAuMdPcW\niAbsZjYibh/ljIdF+W5hKXU83Z1ZL67ljXfeLelxREKl19ywKJ4SJ+/BuJkNBR4Erk3PkHvGJpll\nAB588EHuvPNOqqurAaiqqqKmpqbjCdn+lY3KKqscXnn+M8/Q8tpqOOJDwHvL7rX/yFDlZMuZyt0e\nlYsrP/7U0wzq34/xHz0DgMbnFwB0u9y08FmOrhrEOX/2p0D5Xx9UVrm3lZuammhrawOgubmZ2tpa\nUqnif6dj7rFj6P03MhsA/AZ4zN1vSd+2BDjb3VvMbBQwz90/lLnvjBkzfMqUKUU3VCpDfX29PtkH\npNTx3LlnL//0mzc0M95D2n+8WTu9rswtkaRsXt6Y2Ao5Yw47hJs/+SccMrB/IvVJ4fQeGpaGhgZS\nqZQVW0++M+M/B15tH4inPQpcCXwfuAJ4pNjGiIhI99VOr9NFf0REepmcg3Ezmwj8HdBkZouI0lG+\nTjQIf8DMpgCrgM/E7a+c8bDoE31YFM/waJ3xsCieYdFrrsTJZzWVZ4CuvtM6N9nmiIiIiIj0HSW/\nAqfWGQ+L1kgNi+IZHqWphEXxDItecyVOyQfjIiIiIiISr+SDceWMh0X5bmFRPMOjHOOwKJ5h0Wuu\nxNHMuIhIIBZOS3UsbygiIr2DcsalIMp3C4viKVLZlDMeFr3mShzNjIuIiIiIlIlyxqUgyncLi+Ip\nUtmUMx4WveZKHM2Mi4iIiIiUiXLGpSDKdwuL4ilS2ZQzHha95kqcnFfgFBGR3qF2ep0GbyIivYxy\nxqUgyncLi+IZHuUYh0XxDItecyWOcsZFRERERMpEOeNSEOW7hUXxDI/SVMKSZDx3793Htl17Wbtl\nZ2J/G7btSqx9fYFecyWOcsZFpMOGrbvYvc8Tq29AP2PXnuTqE5Hue6ttJ5PveyXROq/62Af465oR\nidYp0teUfDCunPGwKN8tLJnxnL+qjdsWrC5TayQJyjEOi+IZFr2HShzljIuIBGLhtBQLp6XK3QwR\nESlAzsG4mf2nmbWY2UudbjvUzOaY2VIze8LMqrraXznjYVG+W1gUT5HKpt8AhEWvuRInn5nxu4AL\nMm67Hpjr7uOAp4Abkm6YiIiIiEjocg7G3b0e+GPGzRcDs9L/nwV8qqv9lTMeFuW7hUXxFKlsyhkP\ni15zJU53c8ZHuHsLgLuvA/RTahERERGRAiW1mkqXa5fdcsstDBkyhOrqagCqqqqoqanp+HTYnj+l\ncu8o33777YpfQOXMeL626Dk2L9/QMRvXnq+qcu8oZyp3e1Quvrx9zTJGnXVJxbQns7z0oNVQ80mg\n/K9nvaHc1NTE1KlTK6Y9Khcev7a2NgCam5upra0llSr+R/PmnnsNYDM7Fvgfdz85XV4CnO3uLWY2\nCpjn7h+K23fGjBk+ZcqUohsqlaG+vl5fswUkM56PvLJBSxv2cpuXNyq1ISCVHk+tM14YvYeGpaGh\ngVQqZcXWk2+aiqX/2j0KXJn+/xXAI13tqJzxsOhFJCyKZ3gqeeAmhVM8w6LXXImTz9KG9wLzgePN\nrNnM/h64CTjPzJYCqXRZREREREQKkM9qKpPd/Sh3H+Tu1e5+l7v/0d3Pdfdx7n6+u2/qan+tMx4W\nrZEaFsUzPFqXOiyKZ1j0mitxdAVOEREREZEySWo1lS4pZzwsyncLi+IZHuUYh6XS4/nE0o1s27U3\n0TonfbCKMYcPTrTOSqHXXIlT8sG4iJTGxu27eXd3cm+CBrTt2JNYfdLzFk6LltiqnV5X5pZIX7Fy\n0w5WLlqXaJ0njhySaH0ila7kg/HGxkYmTJhQ6sNID9GyTJWj+Y87+Npjy4qqo9KXTRPp69RHw6L3\nUImjnHERERERkTIp+WBcOeNh0Sf6sGjGTaSyqY+GRe+hEkcz4yIiIiIiZVLywbjWGQ+L1kgNi9Yw\nFqlsfbGP9u9X9NXFK5beQyWOVlMREQlE7fS6Pjl4k7Dcs2gd9Su7vJZgt1xSM4JRwwYlWqdIUrTO\nuBRE+W5hUT5qeBTTsPTFeC5eu5XFa7cmWuenTxqRaH3dpfdQiaOccRERERGRMlHOuBRE+W5hUUpD\neBTTsCieYdF7qMTRzLhILxXyj5xERET6CuWMS0GU79Y9LVt38cvGZC8Z/VbbzqLr6Iv5qKFTTMOi\neCZjYH9jn3uidRpgVtikiN5DJY5WUxHpAfv2Of/72sZyN0MCt3BaCohWVRGR93zzyTcZNCC5bxNH\nH3YIU08/mv76glISUNRg3Mw+DvwHUbrLf7r79zO3aWxsZMKECcUcRipIfX29PtkHZPPyRs28iVQw\n9dFkvP7O9kTr29fNSXa9h0qcbueMm1k/4FbgAuBE4DIzOyFzu2XLlnW/dVJxmpqayt2EXqlS07u3\nr1H/FKlk6qNh0XtoWJJapKSYmfGPAm+4+yoAM/slcDHwWueNtm3bVsQhpNK0tbWVuwk94nfLW1m/\ndVdi9W3dtS+xupK09131T5FKpj5amd7evJOnlrcWvN+iN9fx5BvxKYvjjhhM9aGHFNs06UGLFy9O\npJ5iBuMfAN7qVF5NNEAX6fV+89pGXkr4ohMiIhKGTe/u4QdPNxe839sr21jZxX7XnVWd+GB8x+69\n7O5uTk0XDh7Qj4H9tRhfkkr+A85165JdQUJ6ztadezh4wP4dbtWqVezZ2/1Z3gEl6MCe9C/kzbjs\nlJGcUV2VaL2V6Od1m5nysQ+UuxmSkIXpf69STIOhPhqWbPH88Mgh7N3nJPmOZmYsXrMlsfr6GYx7\n/2AOH3JQYnVKcYPxt4HqTuWj07ftZ+zYsVx77bUd5VNOOUXLHfZiH/nIR3hpcfgXoTBgdLkb0QP+\n+rxJjN69utzNkITMnTuXxsZGxTQg6qNhyRbPDStgQwmOOTjh+la1wqqE6+wtGhsb90tNGTJkSCL1\nWndnFc2sP7AUSAFrgeeBy9x9SSItExEREREJXLdnxt19r5l9CZjDe0sbaiAuIiIiIpKnbs+Mi4iI\niIhIcYpZZ/zjZvaamb1uZl/rYpuZZvaGmTWa2fj0bUeb2VNm9oqZNZnZNd1tgySriJgOMrPnzGxR\nOqb/2rMtlzjdjWen+/qZWYOZPdozLZZsuhHPUzvdvtLMFqf76PM912rpSjH908yqzOxXZrYk/V76\nsZ5ruXSliPfQ49N9syH9b5vGRuVXZB/9qpm9bGYvmdk9Zpb9F6/uXvAf0SB+GXAsMBBoBE7I2OYv\ngP9N//9jwLPp/48Cxqf/P5Qo7/yE7rRDf8n9FRPTdHlw+t/+wLPAR8v9mPryX7HxTN/2VeAXwKPl\nfjx9/S+B/rkCOLTcj0N/icXzv4C/T/9/ADC83I+pr/8l8ZrbqZ41wDHlfkx9+a/Ice5R6dfcg9Ll\n+4HLsx2vuzPjHRf8cffdQPsFfzq7GLgbwN2fA6rMbKS7r3P3xvTtW4ElRGuWS3l1O6bpcvu1hgcR\nvTko/6m8ioqnmR0NXAjc2XNNliyKiifRAkFaGLhydDueZjYcOMvd70rft8fdN/dg2yVesX203bnA\ncnd/CymnYuPZHxhiZgOIFrRZk+1g3X1xjrvgT+aAOnObtzO3MbMPAuOB57rZDklOUTFNpzQsAtYB\nT7r7CyVsq+RWbB+9Gfhn9KGqUhQbTweeNLMXzOzzJWul5KuYeI4G3jGzu9JpDXeYmS7bWH6JjIuA\nvwHuS7x1Uqhux9Pd1wAzgOb0bZvcfW62g5VtpsTMhgIPAtemZ8ilF3P3fe5+KtF68x8zsw+Xu03S\nPWb2CaAl/Q2Wpf+kd5vo7hOIvu242swmlbtB0m0DgAnAbemYbgeuL2+TJAlmNhC4CPhVudsi3Wdm\n7yOaNT+WKGVlqJlNzrZPdwfj+Vzw523gmLht0tP2DwL/7e6PdLMNkqyiYtou/XXpPODjJWij5K+Y\neE4ELjKzFUQzNOeY2d0lbKvkVlT/dPe16X83AA8TfQUr5VNMPFcDb7l7+wVXHyQanEt5JfEe+hfA\ni+l+KuVVTDzPBVa4e6u77wVmA2dmO1h3B+MvAMeZ2bHpX4j+LZC54sKjwOUAZnY60TR9S/q+nwOv\nuvst3Ty+JK/bMTWzI8ysKn37IcB5wGs913SJ0e14uvvX3b3a3cek93vK3S/vycbLAYrpn4PT30Ri\nZkOA84GXe67pEqOY/tkCvGVmx6e3SwGv9lC7pWvFjosALkMpKpWimHg2A6eb2cFmZkR9NOt1eLp1\n0R/v4oI/ZnZVdLff4e6/NbMLzWwZsA24Mt3gicDfAU3pHGMHvu7uj3enLZKMbsb079O7HwnMMrN+\n6X3vd/ffluNxSKTIeEqFKTKeI4GHzcyJXvPvcfc55XgcEkmgf14D3JNOa1iB+m7ZFRtTMxtMNKP6\nhXK0X/ZXTDzd/XkzexBYBOxO/3tHtuPpoj8iIiIiImWipa5ERERERMpEg3ERERERkTLRYFxERERE\npEw0GBcRERERKRMNxkVEREREykSDcRERERGRMtFgXERERESkTDQYFxEREREpk/8PNKPems59D/IA\nAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fa09b13b8d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "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(burned_trace[\"p\"], bins=25, histtype=\"stepfilled\", density=True)\n",
    "plt.legend();"
   ]
  },
  {
   "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 analysis 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 PyMC3's deterministic variables. (We'll assume for this exercise that $p_B = 0.04$, so $\\text{delta} = 0.01$, $N_B = 750$ (significantly less than $N_A$) and we will simulate site B's data like we did for site A's data )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "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 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0] ...\n"
     ]
    }
   ],
   "source": [
    "import pymc3 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 = stats.bernoulli.rvs(true_p_A, size=N_A)\n",
    "observations_B = stats.bernoulli.rvs(true_p_B, size=N_B)\n",
    "print(\"Obs from Site A: \", observations_A[:30], \"...\")\n",
    "print(\"Obs from Site B: \", observations_B[:30], \"...\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.042\n",
      "0.0346666666667\n"
     ]
    }
   ],
   "source": [
    "print(np.mean(observations_A))\n",
    "print(np.mean(observations_B))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Applied interval-transform to p_A and added transformed p_A_interval_ to model.\n",
      "Applied interval-transform to p_B and added transformed p_B_interval_ to model.\n",
      " [-------100%-------] 20000 of 20000 in 3.2 sec. | SPS: 6201.6 | ETA: 0.0"
     ]
    }
   ],
   "source": [
    "# Set up the pymc3 model. Again assume Uniform priors for p_A and p_B.\n",
    "with pm.Model() as model:\n",
    "    p_A = pm.Uniform(\"p_A\", 0, 1)\n",
    "    p_B = pm.Uniform(\"p_B\", 0, 1)\n",
    "    \n",
    "    # Define the deterministic delta function. This is our unknown of interest.\n",
    "    delta = pm.Deterministic(\"delta\", p_A - p_B)\n",
    "\n",
    "    \n",
    "    # Set of observations, in this case we have two observation datasets.\n",
    "    obs_A = pm.Bernoulli(\"obs_A\", p_A, observed=observations_A)\n",
    "    obs_B = pm.Bernoulli(\"obs_B\", p_B, observed=observations_B)\n",
    "\n",
    "    # To be explained in chapter 3.\n",
    "    step = pm.Metropolis()\n",
    "    trace = pm.sample(20000, step=step)\n",
    "    burned_trace=trace[1000:]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Below we plot the posterior distributions for the three unknowns: "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "p_A_samples = burned_trace[\"p_A\"]\n",
    "p_B_samples = burned_trace[\"p_B\"]\n",
    "delta_samples = burned_trace[\"delta\"]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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C2rVruf/++8PWHzBgAG3btmXWrFkcO3aMzMxMli5dWiXXvHxmvPx9XXjhhaxc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FAAAN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\nERERkUI0GBcRERERKUSDcRERERGRQv4FzpBgPKO6HzUAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fa098200978>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "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\", density=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\", density=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\", density=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\");"
   ]
  },
  {
   "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",
   "execution_count": 29,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Probability site A is WORSE than site B: 0.208\n",
      "Probability site A is BETTER than site B: 0.792\n"
     ]
    }
   ],
   "source": [
    "# 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",
    "    np.mean(delta_samples < 0))\n",
    "\n",
    "print(\"Probability site A is BETTER than site B: %.3f\" % \\\n",
    "    np.mean(delta_samples > 0))"
   ]
  },
  {
   "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",
   "execution_count": 30,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
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TMXR8fA99l+hL/c/iY/6BZnaKReWGBwKY2V1m9tF4vUcRXSmrCUr6RPKiJF+kYzudCfJo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\npMwoyRcRERERKTNK8kVEREREysz/Bz7ixUPJmoxIAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fa097fdb470>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "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\");"
   ]
  },
  {
   "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 PyMC3 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 PyMC3. 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",
   "execution_count": 31,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Applied interval-transform to freq_cheating and added transformed freq_cheating_interval_ to model.\n"
     ]
    }
   ],
   "source": [
    "import pymc3 as pm\n",
    "\n",
    "N = 100\n",
    "with pm.Model() as model:\n",
    "    p = pm.Uniform(\"freq_cheating\", 0, 1)"
   ]
  },
  {
   "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",
   "execution_count": 32,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "with model:\n",
    "    true_answers = pm.Bernoulli(\"truths\", p, shape=N, testval=np.random.binomial(1, 0.5, N))"
   ]
  },
  {
   "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",
   "execution_count": 33,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0 0 1 0 1 1 0 1 0 1 1 1 0 0 0 1 1 1 0 0 0 0 0 1 0 1 0 1 1 1 0 0 0 1 0 1 1\n",
      " 1 1 0 1 0 0 1 1 1 1 0 0 0 0 0 0 1 1 0 0 1 1 0 1 0 0 1 0 1 1 0 0 0 0 0 1 1\n",
      " 1 0 1 0 1 1 1 0 1 0 0 0 1 0 0 0 0 1 0 1 0 1 0 0 1 0]\n"
     ]
    }
   ],
   "source": [
    "with model:\n",
    "    first_coin_flips = pm.Bernoulli(\"first_flips\", 0.5, shape=N, testval=np.random.binomial(1, 0.5, N))\n",
    "print(first_coin_flips.tag.test_value)"
   ]
  },
  {
   "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",
   "execution_count": 34,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "with model:\n",
    "    second_coin_flips = pm.Bernoulli(\"second_flips\", 0.5, shape=N, testval=np.random.binomial(1, 0.5, N))"
   ]
  },
  {
   "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 PyMC3 `deterministic` variable:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "import theano.tensor as tt\n",
    "with model:\n",
    "    val = first_coin_flips*true_answers + (1 - first_coin_flips)*second_coin_flips\n",
    "    observed_proportion = pm.Deterministic(\"observed_proportion\", tt.sum(val)/float(N))"
   ]
  },
  {
   "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",
   "execution_count": 36,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array(0.5600000023841858)"
      ]
     },
     "execution_count": 36,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "observed_proportion.tag.test_value"
   ]
  },
  {
   "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 expected 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",
   "execution_count": 37,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "X = 35\n",
    "\n",
    "with model:\n",
    "    observations = pm.Binomial(\"obs\", N, observed_proportion, observed=X)"
   ]
  },
  {
   "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",
   "execution_count": 38,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Assigned BinaryGibbsMetropolis to truths\n",
      "Assigned BinaryGibbsMetropolis to first_flips\n",
      "Assigned BinaryGibbsMetropolis to second_flips\n",
      " [-------100%-------] 40000 of 40000 in 1891.9 sec. | SPS: 21.1 | ETA: -0.0"
     ]
    }
   ],
   "source": [
    "# To be explained in Chapter 3!\n",
    "with model:\n",
    "    step = pm.Metropolis(vars=[p])\n",
    "    trace = pm.sample(40000, step=step)\n",
    "    burned_trace = trace[15000:]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
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xx+jOmXkanJHpa74kbd/frLc3fOl7/pnjcn3PRe/KysrYeYITsgIvyAvCEHOhba1tNsac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\nTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fa095334358>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "figsize(12.5, 3)\n",
    "p_trace = burned_trace[\"freq_cheating\"][15000:]\n",
    "plt.hist(p_trace, histtype=\"stepfilled\", density=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();"
   ]
  },
  {
   "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 an 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 PyMC3 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 PyMC3, we can create a deterministic function to evaluate the probability of responding \"Yes\", given $p$:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Applied interval-transform to freq_cheating and added transformed freq_cheating_interval_ to model.\n"
     ]
    }
   ],
   "source": [
    "with pm.Model() as model:\n",
    "    p = pm.Uniform(\"freq_cheating\", 0, 1)\n",
    "    p_skewed = pm.Deterministic(\"p_skewed\", 0.5*p + 0.25)"
   ]
  },
  {
   "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",
   "execution_count": 41,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "with model:\n",
    "    yes_responses = pm.Binomial(\"number_cheaters\", 100, p_skewed, observed=35)"
   ]
  },
  {
   "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",
   "execution_count": 42,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      " [-------100%-------] 25000 of 25000 in 2.1 sec. | SPS: 12171.2 | ETA: 0.0"
     ]
    }
   ],
   "source": [
    "with model:\n",
    "    # To Be Explained in Chapter 3!\n",
    "    step = pm.Metropolis()\n",
    "    trace = pm.sample(25000, step=step)\n",
    "    burned_trace = trace[2500:]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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6Z+fc6XvbN0lyXb0hEgAAAEA7n9fwXpU03cyOMrNDJP13Sb+PdlgAAABA75Y2\nOuKcazWzb0n6sz7e3m9V5CMDAAAAerG00REAAAAA4YLe/m1mp5vZajN7x8y+280x95nZu2aWNLN4\n3w2JvJKuXszsIjN7Y+9HwsyKczFO5J7P75a9x802s2YzOz/O8SG/eP4t+oKZrTCzt8zshbjHiPzg\n8XfoMDP7/d45S4WZfT0Hw0QeMLOHzKzGzN7s4ZjgOa73RNvnxjVmdoakac65oyVdKekB3/Ojb/G8\n0dH7kuY552ZKul3Sz+IdJfKB702x9h53p6Q/xTtC5BPPv0WFkv6vpC875z4t6R9jHyhyzvN3y7WS\nVjrnZkk6RdLdZsam8v3Tw2qvlS5lOscNWdFO3bjGOdcsqePGNfs6R9KjkuScWy6p0MzGBlwDfUfa\nenHO/d0513Frrr+rfc929D8+v1skaaGkpZI+jHNwyDs+9XKRpCeccxslyTkXdrcg9BU+teIkjdj7\n+QhJW51z4RvYo9dzziUkbe/hkIzmuCET7a5uXNN5YtT5mI1dHIP+wade9nW5pKcjHRHyVdpaMbMj\nJZ3rnPuJgu97iD7G53fLMZJGmtkLZvaqmX0tttEhn/jUyo8kfcrMNkl6Q9J1MY0NvU9Gc1xeHkHO\nmdkpki6VNCfXY0HeukfSvvlKJtvoyUBJJZJOlTRM0stm9rJzrjK3w0Ie+pKkFc65U81smqRnzew4\n51x9rgeGviFkor1RUtE+7Yl7v9b5mElpjkH/4FMvMrPjJD0o6XTnXE8v2aDv8qmVUkm/MTOT9AlJ\nZ5hZs3OOPf37H5962SBpi3Nut6TdZvaipJmSmGj3Lz61cqmk/yNJzrn3zGytpE9Kei2WEaI3yWiO\nGxId8blxze8lXSyl7ii5wzlXE3AN9B1p68XMiiQ9Ielrzrn3cjBG5Ie0teKcm7r3Y4rac9rXMMnu\nt3z+Fv1O0hwzKzCzQyWdKIn7P/Q/PrWyTtIXJWlv3vYYtb9RH/2TqftXTDOa43qvaHd34xozu7L9\nYfegc+6PZnammVVKalD7/xTRD/nUi6TbJI2U9OO9K5XNzrkTcjdq5IJnrezXJfZBIm94/i1abWZ/\nkvSmpFZJDzrn3s7hsJEDnr9bbpf0i322dLvRObctR0NGDpnZEklfkDTKzKokfV/SITrIOS43rAEA\nAAAiEHTDGgAAAAB+mGgDAAAAEWCiDQAAAESAiTYAAAAQASbaAAAAQASYaAMAAAARYKINAAAAROD/\nA5N7v12eSL54AAAAAElEQVQ1rwYeAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fa09b593c18>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "figsize(12.5, 3)\n",
    "p_trace = burned_trace[\"freq_cheating\"]\n",
    "plt.hist(p_trace, histtype=\"stepfilled\", density=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();"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### More PyMC3 Tricks\n",
    "\n",
    "#### Protip: Arrays of PyMC3 variables\n",
    "There is no reason why we cannot store multiple heterogeneous PyMC3 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",
   "execution_count": 44,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Applied log-transform to x_0 and added transformed x_0_log_ to model.\n",
      "Applied log-transform to x_1 and added transformed x_1_log_ to model.\n",
      "Applied log-transform to x_2 and added transformed x_2_log_ to model.\n",
      "Applied log-transform to x_3 and added transformed x_3_log_ to model.\n",
      "Applied log-transform to x_4 and added transformed x_4_log_ to model.\n",
      "Applied log-transform to x_5 and added transformed x_5_log_ to model.\n",
      "Applied log-transform to x_6 and added transformed x_6_log_ to model.\n",
      "Applied log-transform to x_7 and added transformed x_7_log_ to model.\n",
      "Applied log-transform to x_8 and added transformed x_8_log_ to model.\n",
      "Applied log-transform to x_9 and added transformed x_9_log_ to model.\n"
     ]
    }
   ],
   "source": [
    "N = 10\n",
    "x = np.ones(N, dtype=object)\n",
    "with pm.Model() as model:\n",
    "    for i in range(0, N):\n",
    "        x[i] = pm.Exponential('x_%i' % i, (i+1.0)**2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The remainder of this chapter examines some practical examples of PyMC3 and PyMC3 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",
   "execution_count": 45,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "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"
     ]
    },
    {
     "data": {
      "image/png": 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LcCQwgtCbPgr4aNFFuoiIiIiIBLkvz+juj7j75939aHc/w90f7omA1KOeDvW2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\nBzNBWL/hM4KOAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fa09b3dd320>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "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\");\n"
   ]
  },
  {
   "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",
   "execution_count": 46,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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TDXry27i2JJ/OUdExoWbGhJq5ekYM20sa+CavmvUFtaSXNpJe2sgz6/dxwohA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\nDQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fa09b3fc128>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "figsize(12, 3)\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();"
   ]
  },
  {
   "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",
   "execution_count": 47,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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i1x3L1wHThBB3HrVOEPAxMAoIAq4UQnxx7LaO1yZRV1cHQHh4+ID5ZzSYCSGo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\nRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fa09b3e9080>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "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\");"
   ]
  },
  {
   "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 PyMC3. 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",
   "execution_count": 48,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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s0BrZMTFC2kCnhvtAcY312EIV6VwqZUNcpDZsjLk4iGVu6o1YlFJKqb5uf1E1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\neZzqAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fa09b115940>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "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\");"
   ]
  },
  {
   "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",
   "execution_count": 49,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "import pymc3 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",
    "with pm.Model() as model:\n",
    "    beta = pm.Normal(\"beta\", mu=0, tau=0.001, testval=0)\n",
    "    alpha = pm.Normal(\"alpha\", mu=0, tau=0.001, testval=0)\n",
    "    p = pm.Deterministic(\"p\", 1.0/(1. + tt.exp(beta*temperature + alpha)))"
   ]
  },
  {
   "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 PyMC3. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      " [-------100%-------] 120000 of 120000 in 16.5 sec. | SPS: 7283.1 | ETA: 0.0"
     ]
    }
   ],
   "source": [
    "# connect the probabilities in `p` with our observations through a\n",
    "# Bernoulli random variable.\n",
    "with model:\n",
    "    observed = pm.Bernoulli(\"bernoulli_obs\", p, observed=D)\n",
    "    \n",
    "    # Mysterious code to be explained in Chapter 3\n",
    "    start = pm.find_MAP()\n",
    "    step = pm.Metropolis()\n",
    "    trace = pm.sample(120000, step=step, start=start)\n",
    "    burned_trace = trace[100000::2]"
   ]
  },
  {
   "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",
   "execution_count": 51,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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fzMixhzP80CF5HJ0Ugj5DJSHvibqZnQVcA9SY2RJihcJfd/cn831sERGRvmbX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\n1+gHouX2t9q23mt+VXYXWoq6z1zIIw+yyIU88tj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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fa08eb8f320>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "alpha_samples = burned_trace[\"alpha\"][:, None]  # best to make them 1d\n",
    "beta_samples = burned_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\", density=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\", density=True)\n",
    "plt.legend();"
   ]
  },
  {
   "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",
   "execution_count": 52,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "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)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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JAYkTikieNoGkqeP79dArpZRSSg3WsG60n4hun6G+vYf69p5jel6c20VqnJu0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\nO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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fa09b2632b0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "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\");"
   ]
  },
  {
   "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",
   "execution_count": 54,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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rAdixY8dp7a63azuxbc235ns4tzXf6dHuuF5cXAzA8uXLWbduHV05WdNuA/uI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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fa09b458588>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "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. $t$\");"
   ]
  },
  {
   "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",
   "execution_count": 55,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fa09b46c630>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "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, density=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\");"
   ]
  },
  {
   "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, observed=D)\n",
    "\n",
    "Hence we create:\n",
    "    \n",
    "    simulated_data = pm.Bernoulli(\"simulation_data\", p)\n",
    "\n",
    "Let's simulate 10 000:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Assigned BinaryGibbsMetropolis to bernoulli_sim\n",
      " [-------100%-------] 10000 of 10000 in 27.8 sec. | SPS: 359.1 | ETA: 0.0"
     ]
    }
   ],
   "source": [
    "N = 10000\n",
    "with pm.Model() as model:\n",
    "    beta = pm.Normal(\"beta\", mu=0, tau=0.001, testval=0)\n",
    "    alpha = pm.Normal(\"alpha\", mu=0, tau=0.001, testval=0)\n",
    "    p = pm.Deterministic(\"p\", 1.0/(1. + tt.exp(beta*temperature + alpha)))\n",
    "    observed = pm.Bernoulli(\"bernoulli_obs\", p, observed=D)\n",
    "    \n",
    "    simulated = pm.Bernoulli(\"bernoulli_sim\", p, shape=p.tag.test_value.shape)\n",
    "    step = pm.Metropolis(vars=[p])\n",
    "    trace = pm.sample(N, step=step)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(10000, 23)\n"
     ]
    },
    {
     "data": {
      "image/png": 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E8LfABuAPETyniIiIiEhVK8uCR2Z2NvBxd78XOO7YHM2jHg7dKR4W5REW5REO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\nRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fa09b3a57b8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "figsize(12.5, 5)\n",
    "\n",
    "simulations = 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)"
   ]
  },
  {
   "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](https://onlinelibrary.wiley.com/doi/10.1111/j.1540-5907.2011.00525.x), 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",
   "execution_count": 58,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "posterior prob of defect | realized defect \n",
      "0.40                     |   0\n",
      "0.25                     |   1\n",
      "0.28                     |   0\n",
      "0.32                     |   0\n",
      "0.36                     |   0\n",
      "0.19                     |   0\n",
      "0.17                     |   0\n",
      "0.25                     |   0\n",
      "0.73                     |   1\n",
      "0.53                     |   1\n",
      "0.25                     |   1\n",
      "0.10                     |   0\n",
      "0.36                     |   0\n",
      "0.80                     |   1\n",
      "0.36                     |   0\n",
      "0.13                     |   0\n",
      "0.25                     |   0\n",
      "0.07                     |   0\n",
      "0.12                     |   0\n",
      "0.09                     |   0\n",
      "0.13                     |   1\n",
      "0.12                     |   0\n",
      "0.71                     |   1\n"
     ]
    }
   ],
   "source": [
    "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]))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Next we sort each column by the posterior probabilities:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "probb | defect \n",
      "0.07  |   0\n",
      "0.09  |   0\n",
      "0.10  |   0\n",
      "0.12  |   0\n",
      "0.12  |   0\n",
      "0.13  |   1\n",
      "0.13  |   0\n",
      "0.17  |   0\n",
      "0.19  |   0\n",
      "0.25  |   1\n",
      "0.25  |   0\n",
      "0.25  |   1\n",
      "0.25  |   0\n",
      "0.28  |   0\n",
      "0.32  |   0\n",
      "0.36  |   0\n",
      "0.36  |   0\n",
      "0.36  |   0\n",
      "0.40  |   0\n",
      "0.53  |   1\n",
      "0.71  |   1\n",
      "0.73  |   1\n",
      "0.80  |   1\n"
     ]
    }
   ],
   "source": [
    "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]]))"
   ]
  },
  {
   "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",
   "execution_count": 60,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fa086f4f080>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from separation_plot import separation_plot\n",
    "\n",
    "\n",
    "figsize(11., 1.5)\n",
    "separation_plot(posterior_probability, D)"
   ]
  },
  {
   "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",
   "execution_count": 61,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fa0a3cd1940>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fa0a3cd1b38>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fa09b481160>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fa08c089978>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "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\");"
   ]
  },
  {
   "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",
   "execution_count": 62,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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Iw8OOYhF8X/3mIxEtigWV3HQtMItFtc4UUR3/ygo0Go6lJc32Z7Oa8W+11O7S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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fa08cb8d518>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#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\"$\\beta$\");"
   ]
  },
  {
   "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: 357–376, 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",
   "execution_count": 1,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
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     "execution_count": 1,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "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()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "anaconda-cloud": {},
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.5.2"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 0
}