Introduction_to_PyMC3.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/usr/local/anaconda/lib/python3.6/site-packages/h5py/__init__.py:34: FutureWarning: Conversion of the second argument of issubdtype from `float` to `np.floating` is deprecated. In future, it will be treated as `np.float64 == np.dtype(float).type`.\n",
      "  from ._conv import register_converters as _register_converters\n"
     ]
    }
   ],
   "source": [
    "# Data\n",
    "from pymc3 import Model, Normal, invlogit, Binomial, sample, forestplot\n",
    "import numpy as np\n",
    "n = np.ones(4)*5\n",
    "y = np.array([0, 1, 3, 5])\n",
    "dose = np.array([-.86,-.3,-.05,.73])\n",
    "\n",
    "with Model() as bioassay_model:\n",
    "\n",
    "    # Prior distributions for latent variables\n",
    "    alpha = Normal('alpha', 0, sd=100)\n",
    "    beta = Normal('beta', 0, sd=100)\n",
    "\n",
    "    # Linear combinations of parameters\n",
    "    theta = invlogit(alpha + beta*dose)\n",
    "\n",
    "    # Model likelihood\n",
    "    deaths = Binomial('deaths', n=n, p=theta, observed=y)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Probabilistic Programming Primer: Introduction to PyMC3\n",
    "\n",
    "\n",
    "Probabilistic programming (PP) allows flexible specification of Bayesian statistical models in code. PyMC3 is a new, open-source PP framework with an intuitive and readable, yet powerful, syntax that is close to the natural syntax statisticians use to describe models. It features next-generation Markov chain Monte Carlo (MCMC) sampling algorithms such as the No-U-Turn Sampler (NUTS; Hoffman, 2014), a self-tuning variant of Hamiltonian Monte Carlo (HMC; Duane, 1987). This class of samplers works well on high dimensional and complex posterior distributions and allows many complex models to be fit without specialized knowledge about fitting algorithms. HMC and NUTS take advantage of gradient information from the likelihood to achieve much faster convergence than traditional sampling methods, especially for larger models. NUTS also has several self-tuning strategies for adaptively setting the tunable parameters of Hamiltonian Monte Carlo, which means you usually don't need to have specialized knowledge about how the algorithms work. PyMC3, Stan (Stan Development Team, 2014), and the LaplacesDemon package for R are currently the only PP packages to offer HMC.\n",
    "\n",
    "### PyMC3 Features\n",
    "\n",
    "Probabilistic programming in Python confers a number of advantages including multi-platform compatibility, an expressive yet clean and readable syntax, easy integration with other scientific libraries, and extensibility via C, C++, Fortran or Cython. These features make it relatively straightforward to write and use custom statistical distributions, samplers and transformation functions, as required by Bayesian analysis.\n",
    "\n",
    "PyMC3's feature set helps to make Bayesian analysis as painless as possible. Here is a short list of some of its features:\n",
    "\n",
    "-   Fits Bayesian statistical models with Markov chain Monte Carlo, variational inference and\n",
    "    other algorithms.\n",
    "-   Includes a large suite of well-documented statistical distributions.\n",
    "-   Creates summaries including tables and plots.\n",
    "-   Traces can be saved to the disk as plain text, SQLite or pandas dataframes.\n",
    "-   Several convergence diagnostics and model checking methods are available.\n",
    "-   Extensible: easily incorporates custom step methods and unusual probability distributions.\n",
    "-   MCMC loops can be embedded in larger programs, and results can be analyzed with the full power of Python.\n",
    "\n",
    "Here, we present a primer on the use of PyMC3 for solving general Bayesian statistical inference and prediction problems. We will first see the basics of how to use PyMC3, motivated by a simple example: installation, data creation, model definition, model fitting and posterior analysis. Then we will cover two case studies and use them to show how to define and fit more sophisticated models. Finally we will show how to extend PyMC3 and discuss other useful features: the Generalized Linear Models subpackage, custom distributions, custom transformations and alternative storage backends."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Auto-assigning NUTS sampler...\n",
      "Initializing NUTS using jitter+adapt_diag...\n",
      "Multiprocess sampling (2 chains in 2 jobs)\n",
      "NUTS: [beta, alpha]\n",
      "Sampling 2 chains: 100%|██████████| 3000/3000 [00:02<00:00, 1202.69draws/s]\n",
      "The number of effective samples is smaller than 25% for some parameters.\n",
      "/usr/local/anaconda/lib/python3.6/site-packages/pymc3/plots/__init__.py:40: UserWarning: Keyword argument `varnames` renamed to `var_names`, and will be removed in pymc3 3.8\n",
      "  warnings.warn('Keyword argument `{old}` renamed to `{new}`, and will be removed in pymc3 3.8'.format(old=old, new=new))\n"
     ]
    }
   ],
   "source": [
    "with bioassay_model:\n",
    "\n",
    "    # Draw samples\n",
    "    trace = sample(1000, cores=2)\n",
    "    # Plot two parameters\n",
    "    forestplot(trace, varnames=['alpha', 'beta'])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This example will generate 1000 posterior samples."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/usr/local/anaconda/lib/python3.6/site-packages/pymc3/plots/__init__.py:40: UserWarning: Keyword argument `varnames` renamed to `var_names`, and will be removed in pymc3 3.8\n",
      "  warnings.warn('Keyword argument `{old}` renamed to `{new}`, and will be removed in pymc3 3.8'.format(old=old, new=new))\n"
     ]
    }
   ],
   "source": [
    "from pymc3 import traceplot\n",
    "\n",
    "traceplot(trace[500:], varnames=['beta']);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Motivating Example: Coal mining disasters\n",
    "\n",
    "Consider the following time series of recorded coal mining disasters in the UK from 1851 to 1962 (Jarrett, 1979). The number of disasters is thought to have been affected by changes in safety regulations during this period.\n",
    "\n",
    "Let's build a model for this series and attempt to estimate when the change occurred."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
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kSZKGSmdhvKreWFV7VNUS4CjgnKp6SVflSZIkScPG+4xLkiRJPZn2BZxJtgC2r6p1U92m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\nemIYlyRJknry/wFhZuTlxtjADQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 900x252 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline \n",
    "disasters_data = np.array([4, 5, 4, 0, 1, 4, 3, 4, 0, 6, 3, 3, 4, 0, 2, 6,\n",
    "                         3, 3, 5, 4, 5, 3, 1, 4, 4, 1, 5, 5, 3, 4, 2, 5,\n",
    "                         2, 2, 3, 4, 2, 1, 3, 2, 2, 1, 1, 1, 1, 3, 0, 0,\n",
    "                         1, 0, 1, 1, 0, 0, 3, 1, 0, 3, 2, 2, 0, 1, 1, 1,\n",
    "                         0, 1, 0, 1, 0, 0, 0, 2, 1, 0, 0, 0, 1, 1, 0, 2,\n",
    "                         3, 3, 1, 1, 2, 1, 1, 1, 1, 2, 4, 2, 0, 0, 1, 4,\n",
    "                         0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 1])\n",
    "\n",
    "n_years = len(disasters_data)\n",
    "\n",
    "plt.figure(figsize=(12.5, 3.5))\n",
    "plt.bar(np.arange(1851, 1962), disasters_data, color=\"#348ABD\")\n",
    "plt.xlabel(\"Year\")\n",
    "plt.ylabel(\"Disasters\")\n",
    "plt.title(\"UK coal mining disasters, 1851-1962\")\n",
    "plt.xlim(1851, 1962);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We represent our conceptual model formally as a statistical model:\n",
    "\n",
    "$$\\begin{array}{ccc}  \n",
    "(y_t | \\tau, \\lambda_1, \\lambda_2) \\sim\\text{Poisson}\\left(r_t\\right), & r_t=\\left\\{\n",
    "\\begin{array}{lll}             \n",
    "\\lambda_1 &\\text{if}& t< \\tau\\\\ \n",
    "\\lambda_2 &\\text{if}& t\\ge \\tau             \n",
    "\\end{array}\\right.,&t\\in[t_l,t_h]\\\\         \n",
    "\\tau \\sim \\text{DiscreteUniform}(t_l, t_h)\\\\         \n",
    "\\lambda_1\\sim \\text{Exponential}(a)\\\\         \n",
    "\\lambda_2\\sim \\text{Exponential}(b)     \n",
    "\\end{array}$$\n",
    "\n",
    "Because we have defined $y$ by its dependence on $\\tau$, $\\lambda_1$ and $\\lambda_2$, the latter three are known as the *parents* of $y$ and $D$ is called their *child*. Similarly, the parents of $\\tau$ are $t_l$ and $t_h$, and $\\tau$ is the child of $t_l$ and $t_h$.\n",
    "\n",
    "## Implementing a PyMC Model\n",
    "\n",
    "At the model-specification stage (before the data are observed), $y$, $\\tau$, $\\lambda_1$, and $\\lambda_2$ are all random variables. Bayesian \"random\" variables have not necessarily arisen from a physical random process. The Bayesian interpretation of probability is **epistemic**, meaning random variable $x$'s probability distribution $p(x)$ represents our knowledge and uncertainty about $x$'s value. Candidate values of $x$ for which $p(x)$ is high are relatively more probable, given what we know. \n",
    "\n",
    "We can generally divide the variables in a Bayesian model into two types: **stochastic** and **deterministic**. The only deterministic variable in this model is $r$. If we knew the values of $r$'s parents, we could compute the value of $r$ exactly. A deterministic like $r$ is defined by a mathematical function that returns its value given values for its parents. Deterministic variables are sometimes called the *systemic* part of the model. The nomenclature is a bit confusing, because these objects usually represent random variables; since the parents of $r$ are random, $r$ is random also.\n",
    "\n",
    "On the other hand, even if the values of the parents of variables `switchpoint`, `disasters` (before observing the data), `early_mean` or `late_mean` were known, we would still be uncertain of their values. These variables are stochastic, characterized by probability distributions that express how plausible their candidate values are, given values for their parents.\n",
    "\n",
    "Let's begin by defining the unknown switchpoint as a discrete uniform random variable:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from pymc3 import DiscreteUniform\n",
    "\n",
    "with Model() as disaster_model:\n",
    "\n",
    "    switchpoint = DiscreteUniform('switchpoint', lower=0, upper=n_years)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We have done two things here. First, we have created a `Model` object; a `Model` is a Python object that encapsulates all of the variables that comprise our theoretical model, keeping them in a single container so that they may be used as a unit. After a `Model` is created, we can populate it with all of the model components that we specified when we wrote the model down. \n",
    "\n",
    "Notice that the `Model` above was declared using a `with` statement. This expression is used to define a Python idiom known as a **context manager**. Context managers, in general, are used to manage resources of some kind within a program. In this case, our resource is a `Model`, and we would like to add variables to it so that we can fit our statistical model. The key characteristic of the context manager is that the resources it manages are only defined within the indented block corresponding to the `with` statement. PyMC uses this idiom to automatically add defined variables to a model. Thus, any variable we define is automatically added to the `Model`, without having to explicitly add it. This avoids the repetitive syntax of `add` methods/functions that you see in some machine learning packages:\n",
    "\n",
    "```python\n",
    "model.add(a_variable)\n",
    "model.add(another_variable)\n",
    "model.add(yet_another_variable)\n",
    "model.add(and_again)\n",
    "model.add(please_kill_me_now)\n",
    "...\n",
    "```\n",
    "\n",
    "In fact, PyMC variables cannot be defined without a corresponding `Model`:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "ename": "TypeError",
     "evalue": "No model on context stack, which is needed to instantiate distributions. Add variable inside a 'with model:' block, or use the '.dist' syntax for a standalone distribution.",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mIndexError\u001b[0m                                Traceback (most recent call last)",
      "\u001b[0;32m/usr/local/anaconda/lib/python3.6/site-packages/pymc3/model.py\u001b[0m in \u001b[0;36mget_context\u001b[0;34m(cls)\u001b[0m\n\u001b[1;32m    185\u001b[0m         \u001b[0;32mtry\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 186\u001b[0;31m             \u001b[0;32mreturn\u001b[0m \u001b[0mcls\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mget_contexts\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m-\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    187\u001b[0m         \u001b[0;32mexcept\u001b[0m \u001b[0mIndexError\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;31mIndexError\u001b[0m: list index out of range",
      "\nDuring handling of the above exception, another exception occurred:\n",
      "\u001b[0;31mTypeError\u001b[0m                                 Traceback (most recent call last)",
      "\u001b[0;32m/usr/local/anaconda/lib/python3.6/site-packages/pymc3/distributions/distribution.py\u001b[0m in \u001b[0;36m__new__\u001b[0;34m(cls, name, *args, **kwargs)\u001b[0m\n\u001b[1;32m     32\u001b[0m         \u001b[0;32mtry\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 33\u001b[0;31m             \u001b[0mmodel\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mModel\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mget_context\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m     34\u001b[0m         \u001b[0;32mexcept\u001b[0m \u001b[0mTypeError\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m/usr/local/anaconda/lib/python3.6/site-packages/pymc3/model.py\u001b[0m in \u001b[0;36mget_context\u001b[0;34m(cls)\u001b[0m\n\u001b[1;32m    187\u001b[0m         \u001b[0;32mexcept\u001b[0m \u001b[0mIndexError\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 188\u001b[0;31m             \u001b[0;32mraise\u001b[0m \u001b[0mTypeError\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m\"No context on context stack\"\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    189\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;31mTypeError\u001b[0m: No context on context stack",
      "\nDuring handling of the above exception, another exception occurred:\n",
      "\u001b[0;31mTypeError\u001b[0m                                 Traceback (most recent call last)",
      "\u001b[0;32m<ipython-input-7-f6df2b3a33a9>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m()\u001b[0m\n\u001b[0;32m----> 1\u001b[0;31m \u001b[0mfoo\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mDiscreteUniform\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m'foo'\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mlower\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;36m0\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mupper\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;36m10\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m",
      "\u001b[0;32m/usr/local/anaconda/lib/python3.6/site-packages/pymc3/distributions/distribution.py\u001b[0m in \u001b[0;36m__new__\u001b[0;34m(cls, name, *args, **kwargs)\u001b[0m\n\u001b[1;32m     33\u001b[0m             \u001b[0mmodel\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mModel\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mget_context\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     34\u001b[0m         \u001b[0;32mexcept\u001b[0m \u001b[0mTypeError\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 35\u001b[0;31m             raise TypeError(\"No model on context stack, which is needed to \"\n\u001b[0m\u001b[1;32m     36\u001b[0m                             \u001b[0;34m\"instantiate distributions. Add variable inside \"\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     37\u001b[0m                             \u001b[0;34m\"a 'with model:' block, or use the '.dist' syntax \"\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;31mTypeError\u001b[0m: No model on context stack, which is needed to instantiate distributions. Add variable inside a 'with model:' block, or use the '.dist' syntax for a standalone distribution."
     ]
    }
   ],
   "source": [
    "foo = DiscreteUniform('foo', lower=0, upper=10)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "However, variables can be explicitly added to models without the use of a context manager, via the variable's optional `model` argument.\n",
    "\n",
    "```python\n",
    "disaster_model = Model()\n",
    "switchpoint = DiscreteUniform('switchpoint', lower=0, upper=110, model=disaster_model)\n",
    "```"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Or, if we just want a discrete uniform distribution, and do not need to use it in a PyMC3 model necessarily, we can create one using the `dist` classmethod."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "x = DiscreteUniform.dist(lower=0, upper=100)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\text{None} \\sim \\text{DiscreteUniform}(\\mathit{lower}=f(f()),~\\mathit{upper}=f(f()))$"
      ],
      "text/plain": [
       "<pymc3.distributions.discrete.DiscreteUniform at 0x7fe8a80e7a20>"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "`DiscreteUniform` is an object that represents uniformly-distributed discrete variables. Use of this distribution\n",
    "suggests that we have no preference *a priori* regarding the location of the switchpoint; all values are equally likely. \n",
    "\n",
    "PyMC3 includes most of the common random variable **distributions** used for statistical modeling. For example, the following discrete random variables are available."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "['Binomial',\n",
       " 'BetaBinomial',\n",
       " 'Bernoulli',\n",
       " 'DiscreteWeibull',\n",
       " 'Poisson',\n",
       " 'NegativeBinomial',\n",
       " 'ConstantDist',\n",
       " 'Constant',\n",
       " 'ZeroInflatedPoisson',\n",
       " 'ZeroInflatedBinomial',\n",
       " 'ZeroInflatedNegativeBinomial',\n",
       " 'DiscreteUniform',\n",
       " 'Geometric',\n",
       " 'Categorical',\n",
       " 'OrderedLogistic']"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from pymc3.distributions import discrete\n",
    "discrete.__all__"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "By having a library of variables that represent statistical distributions, users are relieved of having to code distrbutions themselves. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Similarly, we can create the exponentially-distributed variables `early_mean` and `late_mean` for the early and late Poisson rates, respectively (also in the context of the model `distater_model`):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from pymc3 import Exponential\n",
    "\n",
    "with disaster_model:\n",
    "    \n",
    "    early_mean = Exponential('early_mean', 1)\n",
    "    late_mean = Exponential('late_mean', 1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In this instance, we are told that the variables are being **transformed**. In PyMC3, variables with purely positive priors like `Exponential` are transformed with a log function. This makes sampling more robust. Behind the scenes, a variable in the unconstrained space (named `<variable name>_log`) is added to the model for sampling. In this model this happens behind the scenes. Variables with priors that constrain them on two sides, like `Beta` or `Uniform` (continuous), are also transformed to be unconstrained but with a log odds transform."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Next, we define the variable `rate`, which selects the early rate `early_mean` for times before `switchpoint` and the late rate `late_mean` for times after `switchpoint`. We create `rate` using the `switch` function, which returns `early_mean` when the switchpoint is larger than (or equal to) a particular year, and `late_mean` otherwise."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from pymc3.math import switch\n",
    "\n",
    "with disaster_model:\n",
    "    \n",
    "    rate = switch(switchpoint >= np.arange(n_years), early_mean, late_mean)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The last step is to define the **data likelihood**, or sampling distribution. In this case, our measured outcome is the number of disasters in each year, `disasters`. This is a stochastic variable but unlike `early_mean` and `late_mean` we have *observed* its value. To express this, we set the argument `observed` to the observed sequence of disasters. This tells PyMC that this distribution's value is fixed, and should not be changed:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from pymc3 import Poisson\n",
    "\n",
    "with disaster_model:\n",
    "    \n",
    "    disasters = Poisson('disasters', mu=rate, observed=disasters_data)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The model that we specified at the top of the page has now been fully implemented in PyMC3. Let's have a look at the model's attributes to see what we have.\n",
    "\n",
    "The stochastic nodes in the model are identified in the `vars` (*i.e.* variables) attribute:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[switchpoint, early_mean_log__, late_mean_log__]"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "disaster_model.vars"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The last two variables are the log-transformed versions of the early and late rate parameters. The original variables have become deterministic nodes in the model, since they only represent values that have been back-transformed from the transformed variable, which has been subject to fitting or sampling."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[early_mean, late_mean]"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "disaster_model.deterministics"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "You might wonder why `rate`, which is a deterministic component of the model, is not in this list. This is because, unlike the other components of the model, `rate` has not been given a name and given a formal PyMC data structure. It is essentially an **intermediate calculation** in the model, implying that we are not interested in its value when it comes to summarizing the output from the model. Most PyMC objects have a name assigned; these names are used for storage and post-processing:\n",
    "\n",
    "-   as keys in on-disk databases,\n",
    "-   as axis labels in plots of traces,\n",
    "-   as table labels in summary statistics.\n",
    "\n",
    "If we wish to include `rate` in our output, we need to make it a `Deterministic` object, and give it a name:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from pymc3 import Deterministic\n",
    "\n",
    "with disaster_model:\n",
    "    \n",
    "    rate = Deterministic('rate', switch(switchpoint >= np.arange(n_years), early_mean, late_mean))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now, `rate` is included in the `Model`'s deterministics list, and the model will retain its samples during MCMC sampling, for example."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[early_mean, late_mean, rate]"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "disaster_model.deterministics"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "> ### Why are data and unknown variables represented by the same object?\n",
    "\n",
    ">Since its represented by PyMC random variable object, `disasters` is defined by its dependence on its parent `rate` even though its value is **fixed**. This isn't just a quirk of PyMC's syntax; Bayesian hierarchical notation itself makes no distinction between random variables and data. The reason is simple: to use Bayes' theorem to compute the posterior, we require the likelihood. Even though `disasters`'s value is known and fixed, we need to formally assign it a *probability distribution* as if it were a random variable. Remember, the likelihood and the probability function are essentially the same, except that the former is regarded as a function of the parameters and the latter as a function of the data. This point can be counterintuitive at first, as many peoples' instinct is to regard data as fixed a priori and unknown variables as dependent on the data. \n",
    "\n",
    "> One way to understand this is to think of statistical models as predictive models for data, or as models of the processes that gave rise to data. Before observing the value of `disasters`, we could have sampled from its prior predictive distribution $p(y)$ (*i.e.* the marginal distribution of the data) as follows:\n",
    "\n",
    "> -   Sample `early_mean`, `switchpoint` and `late_mean` from their\n",
    ">     priors.\n",
    "> -   Sample `disasters` conditional on these values.\n",
    "\n",
    "> Even after we observe the value of `disasters`, we need to use this process model to make inferences about `early_mean` , `switchpoint` and `late_mean` because its the only information we have about how the variables are related.\n",
    "\n",
    "> We will see later that we can sample from this fixed stochastic random variable, to obtain predictions after having observed our data."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## PyMC3 Variables\n",
    "\n",
    "Each of the built-in statistical variables are subclasses of the generic `Distribution` class in PyMC3. The `Distribution` carries relevant **attributes** about the probability distribution, such as the data type (called `dtype`), any relevant transformations (`transform`, see below), and initial values (`init_value`)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'int64'"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "disasters.dtype"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array(0.69314718)"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "early_mean.init_value"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "PyMC's built-in distribution variables can also be used to generate **random values** from that variable. For example, the `switchpoint`, which is a discrete uniform random variable, can generate random draws:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([104.,  97.,  97.,  90., 103.,  99.,  93.,  95., 110., 112.]),\n",
       " array([  0. ,  11.1,  22.2,  33.3,  44.4,  55.5,  66.6,  77.7,  88.8,\n",
       "         99.9, 111. ]),\n",
       " <a list of 10 Patch objects>)"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAXcAAAD4CAYAAAAXUaZHAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nSQ39L4QcDS0u4Ar3AAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.hist(switchpoint.random(size=1000))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As we noted earlier, some variables have undergone **transformations** prior to sampling. Such variables will have `transformed` attributes that points to the variable that it has been transformed to."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "early_mean_log__"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "early_mean.transformed"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Variables will usually have an associated distribution, as determined by the constructor used to create it. For example, the `switchpoint` variable was created by calling `DiscreteUniform()`. Hence, its distribution is `DiscreteUniform`:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\text{None} \\sim \\text{DiscreteUniform}(\\mathit{lower}=f(f()),~\\mathit{upper}=f(f()))$"
      ],
      "text/plain": [
       "<pymc3.distributions.discrete.DiscreteUniform at 0x7fe8a4483e48>"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "switchpoint.distribution"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As with all Python objects, the underlying type of a variable can be exposed with the `type()` function:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "pymc3.model.FreeRV"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "type(switchpoint)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "pymc3.model.ObservedRV"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "type(disasters)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We will learn more about these types in an upcoming section."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Variable log-probabilities\n",
    "\n",
    "All PyMC3 stochastic variables can evaluate their probability mass or density functions at a particular value, given the values of their parents. The **logarithm** of a stochastic object's probability mass or density can be\n",
    "accessed via the `logp` method. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array(-4.71849887)"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "switchpoint.logp({'switchpoint':55, 'early_mean_log__':1, 'late_mean_log__':1})"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "For **vector-valued** variables like `disasters`, the `logp` attribute returns the **sum** of the logarithms of\n",
    "the joint probability or density of all elements of the value."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array(-225.5380749)"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "disasters.logp({'switchpoint':55, 'early_mean_log__':1, 'late_mean_log__':1})"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Custom variables\n",
    "\n",
    "Though we created the variables in `disaster_model` using well-known probability distributions that are available in PyMC3, its possible to create custom distributions by **wrapping** functions that compute an arbitrary log-probability using the `DensityDist` function. For example, one example we'll see will show an exponential survival function, which accounts for censored data. If we pass this function as the `logp` argument for `DensityDist`, we can use it as the data likelihood in a survival model:\n",
    "\n",
    "```python\n",
    "def logp(failure, value):\n",
    "    return (failure * log(lam) - lam * value).sum()\n",
    "\n",
    "x = DensityDist('x', logp, observed={'failure':failure, 'value':t})\n",
    "```\n",
    "\n",
    "Users are thus not\n",
    "limited to the set of of statistical distributions provided by PyMC."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Fitting the model with MCMC\n",
    "\n",
    "PyMC3's `sample` function will fit probability models (linked collections of variables) like ours using Markov chain Monte Carlo (MCMC) sampling. Unless we manually assign particular algorithms to variables in our model, PyMC will assign algorithms that it deems appropriate (it usually does a decent job of this):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Multiprocess sampling (2 chains in 2 jobs)\n",
      "CompoundStep\n",
      ">Metropolis: [switchpoint]\n",
      ">NUTS: [late_mean, early_mean]\n",
      "Sampling 2 chains: 100%|██████████| 5000/5000 [00:03<00:00, 1295.56draws/s]\n",
      "The number of effective samples is smaller than 25% for some parameters.\n"
     ]
    }
   ],
   "source": [
    "with disaster_model:\n",
    "    trace = sample(2000)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This returns the Markov chain of draws from the model in a data structure called a **trace**."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<MultiTrace: 2 chains, 2000 iterations, 6 variables>"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "trace"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The `sample()` function always takes at least one argument, `draws`, which specifies how many samples to draw. However, there are a number of additional optional arguments that are worth knowing about:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Help on function sample in module pymc3.sampling:\n",
      "\n",
      "sample(draws=500, step=None, init='auto', n_init=200000, start=None, trace=None, chain_idx=0, chains=None, cores=None, tune=500, progressbar=True, model=None, random_seed=None, discard_tuned_samples=True, compute_convergence_checks=True, **kwargs)\n",
      "    Draw samples from the posterior using the given step methods.\n",
      "    \n",
      "    Multiple step methods are supported via compound step methods.\n",
      "    \n",
      "    Parameters\n",
      "    ----------\n",
      "    draws : int\n",
      "        The number of samples to draw. Defaults to 500. The number of tuned samples are discarded\n",
      "        by default. See discard_tuned_samples.\n",
      "    step : function or iterable of functions\n",
      "        A step function or collection of functions. If there are variables without a step methods,\n",
      "        step methods for those variables will be assigned automatically.\n",
      "    init : str\n",
      "        Initialization method to use for auto-assigned NUTS samplers.\n",
      "    \n",
      "        * auto : Choose a default initialization method automatically.\n",
      "          Currently, this is `'jitter+adapt_diag'`, but this can change in the future.\n",
      "          If you depend on the exact behaviour, choose an initialization method explicitly.\n",
      "        * adapt_diag : Start with a identity mass matrix and then adapt a diagonal based on the\n",
      "          variance of the tuning samples. All chains use the test value (usually the prior mean)\n",
      "          as starting point.\n",
      "        * jitter+adapt_diag : Same as `adapt_diag`, but add uniform jitter in [-1, 1] to the\n",
      "          starting point in each chain.\n",
      "        * advi+adapt_diag : Run ADVI and then adapt the resulting diagonal mass matrix based on the\n",
      "          sample variance of the tuning samples.\n",
      "        * advi+adapt_diag_grad : Run ADVI and then adapt the resulting diagonal mass matrix based\n",
      "          on the variance of the gradients during tuning. This is **experimental** and might be\n",
      "          removed in a future release.\n",
      "        * advi : Run ADVI to estimate posterior mean and diagonal mass matrix.\n",
      "        * advi_map: Initialize ADVI with MAP and use MAP as starting point.\n",
      "        * map : Use the MAP as starting point. This is discouraged.\n",
      "        * nuts : Run NUTS and estimate posterior mean and mass matrix from the trace.\n",
      "    n_init : int\n",
      "        Number of iterations of initializer. Only works for 'nuts' and 'ADVI'.\n",
      "        If 'ADVI', number of iterations, if 'nuts', number of draws.\n",
      "    start : dict, or array of dict\n",
      "        Starting point in parameter space (or partial point)\n",
      "        Defaults to trace.point(-1)) if there is a trace provided and model.test_point if not\n",
      "        (defaults to empty dict). Initialization methods for NUTS (see `init` keyword) can\n",
      "        overwrite the default. For 'SMC' it should be a list of dict with length `chains`.\n",
      "    trace : backend, list, or MultiTrace\n",
      "        This should be a backend instance, a list of variables to track, or a MultiTrace object\n",
      "        with past values. If a MultiTrace object is given, it must contain samples for the chain\n",
      "        number `chain`. If None or a list of variables, the NDArray backend is used.\n",
      "        Passing either \"text\" or \"sqlite\" is taken as a shortcut to set up the corresponding\n",
      "        backend (with \"mcmc\" used as the base name). Ignored when using 'SMC'.\n",
      "    chain_idx : int\n",
      "        Chain number used to store sample in backend. If `chains` is greater than one, chain\n",
      "        numbers will start here. Ignored when using 'SMC'.\n",
      "    chains : int\n",
      "        The number of chains to sample. Running independent chains is important for some\n",
      "        convergence statistics and can also reveal multiple modes in the posterior. If `None`,\n",
      "        then set to either `cores` or 2, whichever is larger. For SMC the number of chains is the\n",
      "        number of draws.\n",
      "    cores : int\n",
      "        The number of chains to run in parallel. If `None`, set to the number of CPUs in the\n",
      "        system, but at most 4 (for 'SMC' ignored if `pm.SMC(parallel=False)`. Keep in mind that\n",
      "        some chains might themselves be multithreaded via openmp or BLAS. In those cases it might\n",
      "        be faster to set this to 1.\n",
      "    tune : int\n",
      "        Number of iterations to tune, defaults to 500. Ignored when using 'SMC'. Samplers adjust\n",
      "        the step sizes, scalings or similar during tuning. Tuning samples will be drawn in addition\n",
      "        to the number specified in the `draws` argument, and will be discarded unless\n",
      "        `discard_tuned_samples` is set to False.\n",
      "    progressbar : bool\n",
      "        Whether or not to display a progress bar in the command line. The bar shows the percentage\n",
      "        of completion, the sampling speed in samples per second (SPS), and the estimated remaining\n",
      "        time until completion (\"expected time of arrival\"; ETA).\n",
      "    model : Model (optional if in `with` context)\n",
      "    random_seed : int or list of ints\n",
      "        A list is accepted if `cores` is greater than one.\n",
      "    discard_tuned_samples : bool\n",
      "        Whether to discard posterior samples of the tune interval. Ignored when using 'SMC'\n",
      "    compute_convergence_checks : bool, default=True\n",
      "        Whether to compute sampler statistics like gelman-rubin and effective_n.\n",
      "        Ignored when using 'SMC'\n",
      "    \n",
      "    Returns\n",
      "    -------\n",
      "    trace : pymc3.backends.base.MultiTrace\n",
      "        A `MultiTrace` object that contains the samples.\n",
      "    \n",
      "    Notes\n",
      "    -----\n",
      "    \n",
      "    Optional keyword arguments can be passed to `sample` to be delivered to the \n",
      "    `step_method`s used during sampling. In particular, the NUTS step method accepts\n",
      "    a number of arguments. Common options are:\n",
      "    \n",
      "        * target_accept: float in [0, 1]. The step size is tuned such that we approximate this\n",
      "          acceptance rate. Higher values like 0.9 or 0.95 often work better for problematic\n",
      "          posteriors.\n",
      "        * max_treedepth: The maximum depth of the trajectory tree.\n",
      "        * step_scale: float, default 0.25\n",
      "          The initial guess for the step size scaled down by `1/n**(1/4)`.\n",
      "    \n",
      "    You can find a full list of arguments in the docstring of the step methods.\n",
      "    \n",
      "    Examples\n",
      "    --------\n",
      "    .. code:: ipython\n",
      "    \n",
      "        >>> import pymc3 as pm\n",
      "        ... n = 100\n",
      "        ... h = 61\n",
      "        ... alpha = 2\n",
      "        ... beta = 2\n",
      "    \n",
      "    .. code:: ipython\n",
      "    \n",
      "        >>> with pm.Model() as model: # context management\n",
      "        ...     p = pm.Beta('p', alpha=alpha, beta=beta)\n",
      "        ...     y = pm.Binomial('y', n=n, p=p, observed=h)\n",
      "        ...     trace = pm.sample(2000, tune=1000, cores=4)\n",
      "        >>> pm.summary(trace)\n",
      "               mean        sd  mc_error   hpd_2.5  hpd_97.5\n",
      "        p  0.604625  0.047086   0.00078  0.510498  0.694774\n",
      "\n"
     ]
    }
   ],
   "source": [
    "help(sample)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The `step` argument is what allows users to manually override the sampling algorithms used to fit the model. For example, if we wanted to use a **slice sampler** to sample the `early_mean` and `late_mean` variables, we could specify it:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Multiprocess sampling (2 chains in 2 jobs)\n",
      "CompoundStep\n",
      ">CompoundStep\n",
      ">>Slice: [late_mean]\n",
      ">>Slice: [early_mean]\n",
      ">Metropolis: [switchpoint]\n",
      "Sampling 2 chains: 100%|██████████| 3000/3000 [00:02<00:00, 1112.63draws/s]\n",
      "The number of effective samples is smaller than 25% for some parameters.\n"
     ]
    }
   ],
   "source": [
    "from pymc3 import Slice\n",
    "\n",
    "with disaster_model:\n",
    "    trace = sample(1000, step=Slice(vars=[early_mean, late_mean]))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Accessing the samples\n",
    "\n",
    "The output of the `sample` function is a `MultiTrace` object, which stores the sequence of samples for each variable in the model. These traces can be accessed using dict-style indexing:\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.89825551, 0.93391033, 0.82333143, ..., 0.91174755, 1.10464976,\n",
       "       0.89170921])"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "trace['late_mean']"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The trace can also be sliced using the NumPy array slice `[start:stop:step]`. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.9121513 , 1.00214478, 0.97034371, 0.93429576, 0.90940391,\n",
       "       0.7655077 , 0.77096137, 0.91174755, 1.10464976, 0.89170921])"
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "trace['late_mean', -5:]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Sampling output\n",
    "\n",
    "You can examine the marginal posterior of any variable by plotting a\n",
    "histogram of its trace:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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lpDXEf1+AdwCfBk7m/2+HZrg/42i3TVh1xJiXAy9P8s9Jbk9y4diqG71h5vtnwG8m2cdg\ntfOO8ZQ2EcP8fvRqC4O/tXQrySrgN4BrJ13LuBjuC7OMwdbM64C3An+bZPlEK1pabwU+UlWrGWxb\nfDSJPzMdSfJ6BuH+nknXssTeD7ynqn406ULGxX+s4xnD3DZhH4O9yf8D/j3JtxiE/Z3jKXGkhpnv\nFuBCgKr6lySnMbgJU49/rX3e3TYjyS8CHwIuqqrHJ13PEpsBPpkEBj/DG5McqqrPTbaspeMq7BnD\n3DbhcwxW7SRZwWCb5sFxFjlCw8z3P4ANAEl+ATgNODjWKsdnJ3B5+9TMeuCpqnpk0kUtlSRrgc8A\nb6+qb026nqVWVedU1XRVTQM3Ar/bc7CDK/cfq2PcNiHJXwC7q2pnO/emJPcBPwT+8GRd8Qw533cz\n2Hr6AwZvrv5WtY8dnGySfILBH8wr2nsI7wVeCFBVf8PgPYWNwCzwNHDFZCodjSHm+6fAWcBft9Xs\noTqJ75w4xHyfd7z9gCR1yG0ZSeqQ4S5JHTLcJalDhrskdchwl6QOGe6S1CHDXZI69P/1quMQvdy+\ngwAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.hist(trace['late_mean']);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "PyMC has its own plotting functionality dedicated to plotting MCMC output. For example, we can obtain a time series plot of the trace and a histogram using `traceplot`:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/usr/local/anaconda/lib/python3.6/site-packages/pymc3/plots/__init__.py:40: UserWarning: Keyword argument `varnames` renamed to `var_names`, and will be removed in pymc3 3.8\n",
      "  warnings.warn('Keyword argument `{old}` renamed to `{new}`, and will be removed in pymc3 3.8'.format(old=old, new=new))\n"
     ]
    },
    {
     "data": {
      "image/png": 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ISCzEcccfYefKaR8jgFSx617EJFMsDSjSjJO8tiZb18QItCOML9+5iUd3DPL/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gybxxeEEO1H9UQWAGIWPkA6fs0x0+9KOnazR6Pfh3T8jgKUUjM+gJuA1wMnApuBbwG7gM5p9vk/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\naqApiqIoiqIoiqIcEv5/OPFnkflH/78AAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 864x432 with 6 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from pymc3 import traceplot\n",
    "\n",
    "traceplot(trace[500:], varnames=['early_mean', 'late_mean', 'switchpoint']);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The upper left-hand pane of each figure shows the temporal series of the\n",
    "samples from each parameter, while below is an autocorrelation plot of\n",
    "the samples. The right-hand pane shows a histogram of the trace. The\n",
    "trace is useful for evaluating and diagnosing the algorithm's\n",
    "performance, while the histogram is useful for\n",
    "visualizing the posterior.\n",
    "\n",
    "For a non-graphical summary of the posterior, simply call the `stats` method."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/usr/local/anaconda/lib/python3.6/site-packages/pymc3/stats.py:991: FutureWarning: The join_axes-keyword is deprecated. Use .reindex or .reindex_like on the result to achieve the same functionality.\n",
      "  axis=1, join_axes=[dforg.index])\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>mean</th>\n",
       "      <th>sd</th>\n",
       "      <th>mc_error</th>\n",
       "      <th>hpd_2.5</th>\n",
       "      <th>hpd_97.5</th>\n",
       "      <th>n_eff</th>\n",
       "      <th>Rhat</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>early_mean</th>\n",
       "      <td>3.068889</td>\n",
       "      <td>0.289303</td>\n",
       "      <td>0.011469</td>\n",
       "      <td>2.559729</td>\n",
       "      <td>3.662162</td>\n",
       "      <td>635.842063</td>\n",
       "      <td>0.999273</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>late_mean</th>\n",
       "      <td>0.932517</td>\n",
       "      <td>0.116916</td>\n",
       "      <td>0.004617</td>\n",
       "      <td>0.697093</td>\n",
       "      <td>1.148656</td>\n",
       "      <td>615.843803</td>\n",
       "      <td>1.000680</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                mean        sd  mc_error   hpd_2.5  hpd_97.5       n_eff  \\\n",
       "early_mean  3.068889  0.289303  0.011469  2.559729  3.662162  635.842063   \n",
       "late_mean   0.932517  0.116916  0.004617  0.697093  1.148656  615.843803   \n",
       "\n",
       "                Rhat  \n",
       "early_mean  0.999273  \n",
       "late_mean   1.000680  "
      ]
     },
     "execution_count": 35,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from pymc3 import summary\n",
    "\n",
    "summary(trace[500:], varnames=['early_mean', 'late_mean'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
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