{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Using PyMC3\n",
    "\n",
    "PyMC3 is a Python package for doing MCMC using a variety of samplers, including Metropolis, Slice and Hamiltonian Monte Carlo. See [Probabilistic Programming in Python using PyMC](http://arxiv.org/abs/1507.08050) for a description. The GitHub [site](https://github.com/pymc-devs/pymc3) also has many examples and links for further exploration."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "```bash\n",
    "! pip install --quiet arviz\n",
    "! pip install --quiet pymc3\n",
    "! pip install --quiet daft\n",
    "! pip install --quiet seaborn\n",
    "```"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "```bash\n",
    "! conda install --yes --quiet mkl-service\n",
    "```"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import warnings\n",
    "\n",
    "warnings.simplefilter('ignore', UserWarning)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Other resources**\n",
    "\n",
    "Some examples are adapted from:\n",
    "\n",
    "- [Probabilistic Programming & Bayesian Methods for Hackers](http://camdavidsonpilon.github.io/Probabilistic-Programming-and-Bayesian-Methods-for-Hackers/)\n",
    "- [MCMC tutorial series](https://theclevermachine.wordpress.com/2012/11/19/a-gentle-introduction-to-markov-chain-monte-carlo-mcmc/)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/cliburn/anaconda3/lib/python3.6/site-packages/dask/config.py:168: YAMLLoadWarning: calling yaml.load() without Loader=... is deprecated, as the default Loader is unsafe. Please read https://msg.pyyaml.org/load for full details.\n",
      "  data = yaml.load(f.read()) or {}\n",
      "/Users/cliburn/anaconda3/lib/python3.6/site-packages/distributed/config.py:20: YAMLLoadWarning: calling yaml.load() without Loader=... is deprecated, as the default Loader is unsafe. Please read https://msg.pyyaml.org/load for full details.\n",
      "  defaults = yaml.load(f)\n"
     ]
    }
   ],
   "source": [
    "import numpy as np\n",
    "import numpy.random as rng\n",
    "import matplotlib.pyplot as plt\n",
    "import seaborn as sns\n",
    "import pandas as pd\n",
    "import pymc3 as pm\n",
    "import scipy.stats as stats\n",
    "import daft\n",
    "import arviz as az"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "import theano\n",
    "theano.config.warn.round=False"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "sns.set_context('notebook')\n",
    "plt.style.use('seaborn-darkgrid')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Introduction to PyMC3"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Distributions in pymc3"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "AR\n",
      "AR1\n",
      "Bernoulli\n",
      "Beta\n",
      "BetaBinomial\n",
      "Binomial\n",
      "Bound\n",
      "Categorical\n",
      "Cauchy\n",
      "ChiSquared\n",
      "Constant\n",
      "ConstantDist\n",
      "Continuous\n",
      "DensityDist\n",
      "Dirichlet\n",
      "Discrete\n",
      "DiscreteUniform\n",
      "DiscreteWeibull\n",
      "Distribution\n",
      "ExGaussian\n",
      "Exponential\n",
      "Flat\n",
      "GARCH11\n",
      "Gamma\n",
      "GaussianRandomWalk\n",
      "Geometric\n",
      "Gumbel\n",
      "HalfCauchy\n",
      "HalfFlat\n",
      "HalfNormal\n",
      "HalfStudentT\n",
      "Interpolated\n",
      "InverseGamma\n",
      "KroneckerNormal\n",
      "Kumaraswamy\n",
      "LKJCholeskyCov\n",
      "LKJCorr\n",
      "Laplace\n",
      "Logistic\n",
      "LogitNormal\n",
      "Lognormal\n",
      "MatrixNormal\n",
      "Mixture\n",
      "Multinomial\n",
      "MvGaussianRandomWalk\n",
      "MvNormal\n",
      "MvStudentT\n",
      "MvStudentTRandomWalk\n",
      "NegativeBinomial\n",
      "NoDistribution\n",
      "Normal\n",
      "NormalMixture\n",
      "OrderedLogistic\n",
      "Pareto\n",
      "Poisson\n",
      "Rice\n",
      "SkewNormal\n",
      "StudentT\n",
      "TensorType\n",
      "Triangular\n",
      "TruncatedNormal\n",
      "Uniform\n",
      "VonMises\n",
      "Wald\n",
      "Weibull\n",
      "Wishart\n",
      "WishartBartlett\n",
      "ZeroInflatedBinomial\n",
      "ZeroInflatedNegativeBinomial\n",
      "ZeroInflatedPoisson\n"
     ]
    }
   ],
   "source": [
    "print('\\n'.join([d for d in dir(pm.distributions) if d[0].isupper()]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "d = pm.Normal.dist(mu=0, sd=1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\text{None} \\sim \\text{Normal}(\\mathit{mu}=0,~\\mathit{sd}=1.0)$"
      ],
      "text/plain": [
       "<pymc3.distributions.continuous.Normal at 0x11fc118d0>"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "d.dist()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Random samples"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([-1.04374916,  0.82779499,  0.63210758, -1.25758947,  0.54865016])"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "d.random(size=5)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Log probability"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array(-0.91893853)"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "d.logp(0).eval()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Custom distributions\n",
    "\n",
    "The pymc3 algorithms generally only work with the log probability of a distribution. Hence it is easy to define custom distributions to use in your models by providing a `logp` function."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "def logp(x, μ=0, σ=1):\n",
    "    \"\"\"Normal distribtuion.\"\"\"\n",
    "    return -0.5*np.log(2*np.pi) - np.log(σ) - (x-μ)**2/(2*σ**2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "d = pm.DensityDist.dist(logp)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-0.9189385332046727"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "d.logp(0)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example: Estimating coin bias\n",
    "\n",
    "We start with the simplest model - that of determining the bias of a coin from observed outcomes."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Setting up the model    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "n = 100\n",
    "heads = 61"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Analytical solution"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "a, b = 10, 10\n",
    "prior = stats.beta(a, b)\n",
    "post = stats.beta(heads+a, n-heads+b)\n",
    "ci = post.interval(0.95)\n",
    "\n",
    "xs = np.linspace(0, 1, 100)\n",
    "plt.plot(prior.pdf(xs), label='Prior')\n",
    "plt.plot(post.pdf(xs), c='green', label='Posterior')\n",
    "plt.axvline(100*heads/n, c='red', alpha=0.4, label='MLE')\n",
    "plt.xlim([0, 100])\n",
    "plt.axhline(0.3, ci[0], ci[1], c='black', linewidth=2, label='95% CI');\n",
    "plt.legend()\n",
    "pass"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Graphical model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 141.732x170.079 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "pgm = daft.PGM(shape=[2.5, 3.0], origin=[0, -0.5])\n",
    "\n",
    "pgm.add_node(daft.Node(\"alpha\", r\"$\\alpha$\", 0.5, 2, fixed=True))\n",
    "pgm.add_node(daft.Node(\"beta\", r\"$\\beta$\", 1.5, 2, fixed=True))\n",
    "pgm.add_node(daft.Node(\"p\", r\"$p$\", 1, 1))\n",
    "pgm.add_node(daft.Node(\"n\", r\"$n$\", 2, 0, fixed=True))\n",
    "pgm.add_node(daft.Node(\"y\", r\"$y$\", 1, 0, observed=True))\n",
    "\n",
    "pgm.add_edge(\"alpha\", \"p\")\n",
    "pgm.add_edge(\"beta\", \"p\")\n",
    "pgm.add_edge(\"n\", \"y\")\n",
    "pgm.add_edge(\"p\", \"y\")\n",
    "\n",
    "pgm.render()\n",
    "pass"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### The Model context\n",
    "\n",
    "When you specify a model, you are adding nodes to a computation graph. When executed, the graph is compiled via Theno. Hence, `pymc3` uses the Model context manager to automatically add new nodes."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "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: [p]\n",
      "Sampling 2 chains: 100%|██████████| 5000/5000 [00:03<00:00, 1456.13draws/s]\n"
     ]
    }
   ],
   "source": [
    "niter = 2000\n",
    "with pm.Model() as coin_context:\n",
    "    p = pm.Beta('p', alpha=2, beta=2)\n",
    "    y = pm.Binomial('y', n=n, p=p, observed=heads)\n",
    "    trace = pm.sample(niter)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$$\n",
       "            \\begin{array}{rcl}\n",
       "            \\text{p} &\\sim & \\text{Beta}(\\mathit{alpha}=2,~\\mathit{beta}=2)\\\\\\text{y} &\\sim & \\text{Binomial}(\\mathit{n}=100,~\\mathit{p}=\\text{p})\n",
       "            \\end{array}\n",
       "            $$"
      ],
      "text/plain": [
       "<pymc3.model.Model at 0x1c299bf4a8>"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "coin_context"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Transformed prior variables"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[p_logodds__]"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "coin_context.free_RVs"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Prior variables"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[p]"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "coin_context.deterministics"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Variables in likelihood"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[y]"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "coin_context.observed_RVs"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Under the hood"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Theano\n",
    "\n",
    "Theano builds functions as mathematical expression graphs and compiles them into C for actual computation, making use of GPU resources where available.\n",
    "\n",
    "Performing calculations in Theano generally follows the following 3 steps (from official docs):\n",
    "\n",
    "- declare variables (a,b) and give their types\n",
    "- build expressions for how to put those variables together\n",
    "- compile expression graphs to functions in order to use them for computation."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [],
   "source": [
    "import theano\n",
    "import theano.tensor as tt\n",
    "theano.config.compute_test_value = \"off\""
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This part builds symbolic expressions."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [],
   "source": [
    "a = tt.iscalar('a')\n",
    "b = tt.iscalar('x')\n",
    "c = a + b"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This step compiles a function whose inputs are [a, b] and outputs are [c]."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [],
   "source": [
    "f = theano.function([a, b], [c])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<theano.compile.function_module.Function at 0x1c2a3d6fd0>"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "f"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[array(7, dtype=int32)]"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "f(3, 4)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Within a model context, \n",
    "\n",
    "- when you add an unbounded variable, it is defined as a Theano variable and added to the prior part of the log posterior function\n",
    "- when you add a bounded variable, a transformed version is defined as a Theano variable and and added to the log posterior function\n",
    "    - The inverse transformation is used to define the original variable - this is a deterministic variable\n",
    "- when you add an observed variable bound to data, the data is added to the likelihood part of the log posterior\n",
    "\n",
    "See [PyMC3 and Theano](https://docs.pymc.io/PyMC3_and_Theano.html) for details."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "scrolled": false
   },
   "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, nuts_kwargs=None, step_kwargs=None, progressbar=True, model=None, random_seed=None, live_plot=False, discard_tuned_samples=True, live_plot_kwargs=None, compute_convergence_checks=True, use_mmap=False, **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' if 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' defaults to 1). Keep in mind that some chains might\n",
      "        themselves be multithreaded via openmp or BLAS. In those cases it might be faster to set\n",
      "        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",
      "    nuts_kwargs : dict\n",
      "        Options for the NUTS sampler. See the docstring of NUTS for a complete list of options.\n",
      "        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",
      "        If you want to pass options to other step methods, please use `step_kwargs`.\n",
      "    step_kwargs : dict\n",
      "        Options for step methods. Keys are the lower case names of the step method, values are\n",
      "        dicts of keyword arguments. You can find a full list of arguments in the docstring of the\n",
      "        step methods. If you want to pass arguments only to nuts, you can use `nuts_kwargs`.\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",
      "    live_plot : bool\n",
      "        Flag for live plotting the trace while sampling. Ignored when using 'SMC'.\n",
      "    live_plot_kwargs : dict\n",
      "        Options for traceplot. Example: live_plot_kwargs={'varnames': ['x']}.\n",
      "        Ignored when using 'SMC'\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",
      "    use_mmap : bool, default=False\n",
      "        Whether to use joblib's memory mapping to share numpy arrays when sampling across multiple\n",
      "        cores. Ignored when using 'SMC'\n",
      "    \n",
      "    Returns\n",
      "    -------\n",
      "    trace : pymc3.backends.base.MultiTrace\n",
      "        A `MultiTrace` object that contains the samples.\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(pm.sample)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Specifying sampler (step) and multiple chains"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Multiprocess sampling (8 chains in 2 jobs)\n",
      "Metropolis: [p]\n",
      "Sampling 8 chains: 100%|██████████| 20000/20000 [00:05<00:00, 3712.51draws/s]\n",
      "The number of effective samples is smaller than 25% for some parameters.\n"
     ]
    }
   ],
   "source": [
    "with coin_context:\n",
    "    step = pm.Metropolis()\n",
    "    t = pm.sample(niter, step=step, chains=8, random_seed=123)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Samplers available\n",
    "\n",
    "For continuous distributions, it is hard to beat NUTS and hence this is the default. To learn more, see [A Conceptual Introduction to Hamiltonian Monte Carlo](https://arxiv.org/pdf/1701.02434.pdf)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "BinaryGibbsMetropolis\n",
      "BinaryMetropolis\n",
      "CSG\n",
      "CategoricalGibbsMetropolis\n",
      "CauchyProposal\n",
      "CompoundStep\n",
      "DEMetropolis\n",
      "ElemwiseCategorical\n",
      "EllipticalSlice\n",
      "HamiltonianMC\n",
      "LaplaceProposal\n",
      "Metropolis\n",
      "MultivariateNormalProposal\n",
      "NUTS\n",
      "NormalProposal\n",
      "PoissonProposal\n",
      "SGFS\n",
      "SMC\n",
      "Slice\n"
     ]
    }
   ],
   "source": [
    "print('\\n'.join(m for m in dir(pm.step_methods) if m[0].isupper()))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Generally, the sampler will be automatically selected based on the type of the variable (discrete or continuous), but there are many samples that you can explicitly specify if you want to learn more about them or understand why an alternative would be better than the default for your problem."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Multiprocess sampling (2 chains in 2 jobs)\n",
      "CompoundStep\n",
      ">Slice: [mu]\n",
      ">Metropolis: [sd]\n",
      "Sampling 2 chains: 100%|██████████| 5000/5000 [00:02<00:00, 1691.48draws/s]\n",
      "The number of effective samples is smaller than 10% for some parameters.\n"
     ]
    }
   ],
   "source": [
    "niter = 2000\n",
    "with pm.Model() as normal_context:\n",
    "    mu = pm.Normal('mu', mu=0, sd=100)\n",
    "    sd = pm.HalfCauchy('sd', beta=2)\n",
    "    y = pm.Normal('y', mu=mu, sd=sd, observed=xs)\n",
    "    \n",
    "    step1 = pm.Slice(vars=mu)\n",
    "    step2 = pm.Metropolis(vars=sd)\n",
    "    \n",
    "    t = pm.sample(niter, step=[step1, step2])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 864x288 with 4 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "pm.traceplot(t)\n",
    "pass"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### MAP estimate"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/cliburn/anaconda3/lib/python3.6/site-packages/pymc3/tuning/starting.py:61: UserWarning: find_MAP should not be used to initialize the NUTS sampler, simply call pymc3.sample() and it will automatically initialize NUTS in a better way.\n",
      "  warnings.warn('find_MAP should not be used to initialize the NUTS sampler, simply call pymc3.sample() and it will automatically initialize NUTS in a better way.')\n",
      "logp = -4.5407, ||grad|| = 11: 100%|██████████| 6/6 [00:00<00:00, 563.70it/s]\n"
     ]
    }
   ],
   "source": [
    "with pm.Model() as m:\n",
    "    p = pm.Beta('p', alpha=2, beta=2)\n",
    "    y = pm.Binomial('y', n=n, p=p, observed=heads)\n",
    "    θ = pm.find_MAP()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{'p_logodds__': array(0.43825493), 'p': array(0.60784314)}"
      ]
     },
     "execution_count": 34,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "θ"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Getting values from the trace"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "All the information about the posterior is in the trace, and it also provides statistics about the sampler."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Help on MultiTrace in module pymc3.backends.base object:\n",
      "\n",
      "class MultiTrace(builtins.object)\n",
      " |  Main interface for accessing values from MCMC results\n",
      " |  \n",
      " |  The core method to select values is `get_values`. The method\n",
      " |  to select sampler statistics is `get_sampler_stats`. Both kinds of\n",
      " |  values can also be accessed by indexing the MultiTrace object.\n",
      " |  Indexing can behave in four ways:\n",
      " |  \n",
      " |  1. Indexing with a variable or variable name (str) returns all\n",
      " |     values for that variable, combining values for all chains.\n",
      " |  \n",
      " |     >>> trace[varname]\n",
      " |  \n",
      " |     Slicing after the variable name can be used to burn and thin\n",
      " |     the samples.\n",
      " |  \n",
      " |     >>> trace[varname, 1000:]\n",
      " |  \n",
      " |     For convenience during interactive use, values can also be\n",
      " |     accessed using the variable as an attribute.\n",
      " |  \n",
      " |     >>> trace.varname\n",
      " |  \n",
      " |  2. Indexing with an integer returns a dictionary with values for\n",
      " |     each variable at the given index (corresponding to a single\n",
      " |     sampling iteration).\n",
      " |  \n",
      " |  3. Slicing with a range returns a new trace with the number of draws\n",
      " |     corresponding to the range.\n",
      " |  \n",
      " |  4. Indexing with the name of a sampler statistic that is not also\n",
      " |     the name of a variable returns those values from all chains.\n",
      " |     If there is more than one sampler that provides that statistic,\n",
      " |     the values are concatenated along a new axis.\n",
      " |  \n",
      " |  For any methods that require a single trace (e.g., taking the length\n",
      " |  of the MultiTrace instance, which returns the number of draws), the\n",
      " |  trace with the highest chain number is always used.\n",
      " |  \n",
      " |  Methods defined here:\n",
      " |  \n",
      " |  __getattr__(self, name)\n",
      " |  \n",
      " |  __getitem__(self, idx)\n",
      " |  \n",
      " |  __init__(self, straces)\n",
      " |      Initialize self.  See help(type(self)) for accurate signature.\n",
      " |  \n",
      " |  __len__(self)\n",
      " |  \n",
      " |  __repr__(self)\n",
      " |      Return repr(self).\n",
      " |  \n",
      " |  add_values(self, vals, overwrite=False)\n",
      " |      add variables to traces.\n",
      " |      \n",
      " |      Parameters\n",
      " |      ----------\n",
      " |      vals : dict (str: array-like)\n",
      " |           The keys should be the names of the new variables. The values are expected to be\n",
      " |           array-like object. For traces with more than one chain the length of each value\n",
      " |           should match the number of total samples already in the trace (chains * iterations),\n",
      " |           otherwise a warning is raised.\n",
      " |      overwrite : bool\n",
      " |          If `False` (default) a ValueError is raised if the variable already exists.\n",
      " |          Change to `True` to overwrite the values of variables\n",
      " |  \n",
      " |  get_sampler_stats(self, varname, burn=0, thin=1, combine=True, chains=None, squeeze=True)\n",
      " |      Get sampler statistics from the trace.\n",
      " |      \n",
      " |      Parameters\n",
      " |      ----------\n",
      " |      varname : str\n",
      " |      sampler_idx : int or None\n",
      " |      burn : int\n",
      " |      thin : int\n",
      " |      \n",
      " |      Returns\n",
      " |      -------\n",
      " |      If the `sampler_idx` is specified, return the statistic with\n",
      " |      the given name in a numpy array. If it is not specified and there\n",
      " |      is more than one sampler that provides this statistic, return\n",
      " |      a numpy array of shape (m, n), where `m` is the number of\n",
      " |      such samplers, and `n` is the number of samples.\n",
      " |  \n",
      " |  get_values(self, varname, burn=0, thin=1, combine=True, chains=None, squeeze=True)\n",
      " |      Get values from traces.\n",
      " |      \n",
      " |      Parameters\n",
      " |      ----------\n",
      " |      varname : str\n",
      " |      burn : int\n",
      " |      thin : int\n",
      " |      combine : bool\n",
      " |          If True, results from `chains` will be concatenated.\n",
      " |      chains : int or list of ints\n",
      " |          Chains to retrieve. If None, all chains are used. A single\n",
      " |          chain value can also be given.\n",
      " |      squeeze : bool\n",
      " |          Return a single array element if the resulting list of\n",
      " |          values only has one element. If False, the result will\n",
      " |          always be a list of arrays, even if `combine` is True.\n",
      " |      \n",
      " |      Returns\n",
      " |      -------\n",
      " |      A list of NumPy arrays or a single NumPy array (depending on\n",
      " |      `squeeze`).\n",
      " |  \n",
      " |  point(self, idx, chain=None)\n",
      " |      Return a dictionary of point values at `idx`.\n",
      " |      \n",
      " |      Parameters\n",
      " |      ----------\n",
      " |      idx : int\n",
      " |      chain : int\n",
      " |          If a chain is not given, the highest chain number is used.\n",
      " |  \n",
      " |  points(self, chains=None)\n",
      " |      Return an iterator over all or some of the sample points\n",
      " |      \n",
      " |      Parameters\n",
      " |      ----------\n",
      " |      chains : list of int or N\n",
      " |          The chains whose points should be inlcuded in the iterator.  If\n",
      " |          chains is not given, include points from all chains.\n",
      " |  \n",
      " |  remove_values(self, name)\n",
      " |      remove variables from traces.\n",
      " |      \n",
      " |      Parameters\n",
      " |      ----------\n",
      " |      name : str\n",
      " |          Name of the variable to remove. Raises KeyError if the variable is not present\n",
      " |  \n",
      " |  ----------------------------------------------------------------------\n",
      " |  Data descriptors defined here:\n",
      " |  \n",
      " |  __dict__\n",
      " |      dictionary for instance variables (if defined)\n",
      " |  \n",
      " |  __weakref__\n",
      " |      list of weak references to the object (if defined)\n",
      " |  \n",
      " |  chains\n",
      " |  \n",
      " |  nchains\n",
      " |  \n",
      " |  report\n",
      " |  \n",
      " |  stat_names\n",
      " |  \n",
      " |  varnames\n",
      "\n"
     ]
    }
   ],
   "source": [
    "help(trace)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{'depth',\n",
       " 'diverging',\n",
       " 'energy',\n",
       " 'energy_error',\n",
       " 'max_energy_error',\n",
       " 'mean_tree_accept',\n",
       " 'model_logp',\n",
       " 'step_size',\n",
       " 'step_size_bar',\n",
       " 'tree_size',\n",
       " 'tune'}"
      ]
     },
     "execution_count": 36,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "trace.stat_names"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sns.distplot(trace.get_sampler_stats('model_logp'))\n",
    "pass"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(4000,)"
      ]
     },
     "execution_count": 38,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "p = trace.get_values('p')\n",
    "p.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(4000,)"
      ]
     },
     "execution_count": 39,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "trace['p'].shape"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Convert to `pandas` data frame for downstream processing"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [
    {
     "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>p</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0.597814</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>0.588101</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>0.576538</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>0.577302</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>0.550194</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "          p\n",
       "0  0.597814\n",
       "1  0.588101\n",
       "2  0.576538\n",
       "3  0.577302\n",
       "4  0.550194"
      ]
     },
     "execution_count": 40,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df = pm.trace_to_dataframe(trace)\n",
    "df.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Posterior distribution"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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7+alyR1GU8ekmnGji3ox0HsuaQupkcycO1LTjvmk5vLB4jcZeOBVyigs7EcuaQuztg3UwatW4Z3KW3FEUJzU+DqPTjDxvTQB4UwyFyPrSRjjcvdhWYcX1w5KwvdImdyRFum1MGv60twatrh5enI1xHFlTyByoaYcAMD0vSe4oijV3TBoEgM9PcXQd6ziyppDweH04Uu/A+HQTkgxaueMoVmmDA8kGLf52uAGQvl2lsJinlWIOR9YUEkfrHfB4/Zg5nGtWD4UkSRiXYcK5ti509/rkjkMyYllT0Hl9fuyvaUdesgFZiXq54yjeuHQT/AKo4lohMY1lTUH3aWULHG4vbhjOc9XBkJWgQ4Jeg0prp9xRSEYsawoqIQTePlCHFKMW+WnxcseJCpIkYWy6CdWtXfB4/XLHIZmwrCmoDtV1oMLaiZnDkyFJ3LYrWMalm+DzC5zmSnwxi2VNQfX2gTokG7SYmGWWO0pUyU3SIz5OjYpmngqJVSxrCpozrV3YXd2G70/Lhoa3lgeVSpIwPsOEUy0ueLycFRKL+BVFQbPuYB10GhXuncI5wKFQkGmGzy9w0spTIbGIZU1BYXN68PGJZiwuzEAyN8MNiZxEPZIMGpxocsodhWTAsqageGvvWfT6BJZflyN3lKglSRIKMs0429qFVleP3HEozFjWNGTuXh/e+uocbh2diuEpRrnjRLXCTDMEgE9OcmGsWBPw2iAvvfQS7HY7XnzxxVDmIQVZX9oIADhU2w57Vy+GJRv6HqPQSDPpkG6Kw9YKK+7jTzExJaCR9d69e1FSUhLqLKRAfiGwr6YduckG5Cbx1vJwKMwy41ijE3Xt3Ew3lgxY1u3t7Xj11VexZs2acOQhhTllc8He1Ytbxlh4E0yYTMg4P4d9WwVPhcSSAcv6n/7pn/Dkk08iISEhHHlIYb4+Z0eSQYOCLL4/wiXRoMW0nARsKbdCCCF3HAqTq56zfv/995GVlYVZs2Zh/fr1/T4vOdkIjUYd0AtaLJF7Z1skZwMiL5/D24C6djeKJmVBrZJgNkX2aZBoyrdsRh6e23AcNq9AYXZ4vlFG2vvvuyI5XzCyXbWsP/roI9hsNixduhQdHR3o6urCr371KzzzzDOXPM9u7wroxSwWM2y2yJwjGsnZgMjMt+tkM7RqCWNTDQAAZ2fk7sJtNumjKt9t+WlQqyT8bc9ZPD5nVAiTnReJ77+LRXK+q2W7lhK/aln/+c9/7vv/9evXY9++fZcVNcUme1cPTjR1Ykp2AvTawH6qouBJMmoxa0QytlZY8eNbR0LF6wVRj/OsaVA2HGuCzy9w/TCuWS2XBePTYe3sweG6DrmjUBgEPM+6uLgYxcXFocxCCuH1C/z30UaMSDEgzcRby+Vya34qjFo1Pj5h5TfNGMCRNV2zXada0Oz0sCBkZtCqcfvYNGw/aeP+jDGAZU3X7L8ONyA7QYd8C3eCkdviiRno6vXhs6oWuaNQiLGs6ZpU2TpxqK4D907N5kWtCDAtJxG5SXpsPt4kdxQKMZY1XZP3DjdAp1HhromZckchnF+Jb3FhBg7UdqC+g7efRzOWNQXM4e7Fx+VWLJiQjkSDVu449I2iggxIAD4qs8odhUIo4NkgFLsurKT39Vk7PF4/0uLjuLpeBMlM0GNGXhI+LGvCj2bl8fRUlOLImgIihMDhug4MS9Ij3ayTOw59x+KJGWhweHColnOuoxVH1hSQGns37N29mD06Re4oBFz2k02vzw+dRoUPy5owPY9TKqMRR9YUkCP1HdBrVBiXbpI7Cl2BVq3ChAwTPq1sgavHK3ccCgGWNQ2oq8eHk80uFGaZoVXzLROpJmUnwO3149OTnHMdjfiVRwMqa3LAJwSm5iTKHYWuIidRj+HJBmwu45zraMSypqsSQuBovQNZCTpeWIxwF+ZcH6l3oMbOOdfRhhcY6aqONzph6+zBwgnpckehAEiSBAnAbz47hTn5aZf8WfHkLHlCUVBwZE1XtfFYE7RqCRMyI3cXDvqWWa/ByFQjjjU44eeWX1GFZU39cvV4se2kFQUZZug0fKsoxeTsBDg9XpxtC2wHJ1IGfgVSv7ZW2NDd68eUXF5YVJIxlnjoNSoca3DIHYWCiGVN/dp4rAmj04zITuCFRSXRqFUoyDSj0uqCm+tcRw2WNV1RpbUTJ5qcuHtSFiSuNaE4k7MT4PULlDd3yh2FgoSzQajPxbcwb6uwQq2S4ONFKkXKTNDBYopDaYMD03gaKypwZE2X6fX5UdboxLh0EwzcuVyRJEnCpKwENHS40dLZI3ccCgKWNV3mpLUTbq8fU3MS5I5CQzAxywxJAo418kJjNGBZ02WO1DmQbNAiL9kgdxQagnidBqNT43GswQG/n6ezlI5lTZdodfWgtr0bU3ISeGExCkzOSYCrx4fqVs65VjqWNV3iaL0DKun8Cm6kfPlp8TBo1ZxzHQVY1tTH5xc41uBAviUeJh0nCkUDtUpCYZYZVTYX2rt75Y5DQ8Cypj4nrZ3o6vVhGpdCjSqTsxPgEwLbKrihrpKxrKnP4boOJBm0GJlqlDsKBVGGWYcMsw6bjzfLHYWGgGVNAIDqVhdq7N2YlssLi9FoUnYCKqydqLLxjkalYlkTAGD90UaoJQmTeWExKhVmmqFRSfiwjKNrpWJZE7p7ffifE80Yl2GCMY4XFqORMU6NW0an4uMTVnh9frnj0CCwrAnbKqzo9PhwHdeQiGpLCjNg7+7F7uo2uaPQILCsCf99tBGjUo3ITdLLHYVCaNbIFKQYtTwVolAs6xh3osmJ8uZOLJvCpVCjnUYlYVFBBnafaUNbFxd3UhqWdYxbf7QReo0Kiwoy5I5CYbBkYgZ8foEt5ZxzrTQs6xjmdHuxpcKK+RPSecdijBiVGo/CTDM2H2+G4FrlisKv0Bj20YlmeLx+LJuSJXcUCoMLm0vkJumxtcKG1788i6wEPYon899fCTiyjlF+IfD+kQYUZJoxIcMsdxwKowmZZqhVEkq5uJOisKxj1N4zdpyzd+P+67LljkJhZtCqMS49HicanejlnGvFCKisX3vtNRQVFaGoqAgvv/xyqDNRGLx7qA4WUxzuGGuROwrJYGpOItxePyq4oa5iDFjWe/bswe7du1FSUoINGzagrKwM27dvD0c2CpFTLS58fa4d35+aDa2aP1zForxkA5INWhyp75A7CgVowK9Ui8WCtWvXIi4uDlqtFqNHj0ZDQ0M4slGI/O1QPXQaFe7hhaWYJUkSpuYmoq7djepWl9xxKAADlvWYMWMwdepUAMDZs2fx8ccfY86cOSEPRqFh7+rBlnIrigoykGTQyh2HZDQ52wyVBGwobZI7CgVAEgFOtqyqqsLq1avxD//wD7jnnnsu+TOv1weNRh2SgBRcP/zzPnx+0oaf3DEWFrNO7jgks3f31aCmrQtfP3M79Fp+DUeygOZZHzx4EI8//jieeeYZFBUVXfbndntgm3FaLGbYbM5rSxgmkZwNCE6+To8XX51uxdh0E/SSgLPTHaR0gNmkD+rnCzbmu7JJmSYcq+/AO7ursWRiZr/Pi4Wvj1C5WjaLJfBpswOeBmlsbMTf//3f49e//vUVi5qUo6S0EW6vH7NGJMsdhSJEXrIB+WnxePdQPe9ojHADlvWbb74Jj8eDF198EUuXLsXSpUvx7rvvhiMbBZHH68e6g/UYkWJAViJX16PzJEnC8utyUGVz4VAdZ4ZEsgFPgzz33HN47rnnwpGFQuh/yprQ6urBvHE5ckehCDN/Qjr+7YszePdgPa4fliR3HOoHJ9nGgB6vH//xdS0mZZkxPMUgdxyKMDqNCsumZGHX6VbUtXfLHYf6wbKOARuONaLZ6cHqm0dwzWq6onunZEGtkvDOwXq5o1A/WNZRzt3rw398XYvrchNxQx5/xKUrSzPpUFSYgY3HGmHr9Mgdh66AZR3l3j/SgFZXD9ZwVE0D+LuZw+ATwH/uq5U7Cl0ByzqKOdy9+M99tbhxeDKmcTNcGkBOogGLCzJQUsrRdSRiWUep9aWNWLu5HB1uLwqyzFhf2ti3+DxRf37I0XXEYllHqVZXDw7WtmNqTgIyeFs5BSg36dvRdX0HZ4ZEEm7rFaU+rbRBq1bh1vxUuaNQhPvuT1y5yXoIAfzbrjN4cUmBTKnouziyjkJfnG7F6ZYu3DwyBfFx/H5M1yZBr8WNI5PxaWULDta2yx2HvsGyjjKdHi9e/KQKafFxmM6pejRIM4cnI9Osw28+Ow2fn2uGRAKWdZT5f7uq0eLqQVFhBtQqTtWjwdGqVXh8zihU2Vz44Ag3G4kELOsocqCmHSWlTVh+XS6yuVgTDdEdY9Nw44hk/G73GdS2BbYMMoUOyzpKdHT34hdbTmJYkh5rbh4udxyKApIk4dk7x0AlSfjHD0rh5xKqsmJZRwEhBF7YWokWVw9+WTSBO35Q0GQm6PHEnFHYW92K9Uc5T19OLOso8O6heuw63YrH54xCQWbgO08QBeLuSZm4ZUwa/vXzam6uKyPO61K4//t5Nd49WIexlnjEqSXepUhBc/F76eb8NBw8Z8ePPziG9Y/M4E9vMuDIWsHq2rux/mgDkgxaFBVmcKEmCpkEvRZLJmbA1tmD33x2Wu44MYllrVCdHi9+WlIGIYDvT8vmSIdCblRqPGaNSMaGY03YfLxJ7jgxh6dBFMjd68NTG8tQ096N+6ZlI8UYJ3ckihG3jk6F1y/w4idVGJVqRGFWgtyRYgZH1grj9fnxzIflOFTbgecXjMXwFKPckSiGqFQSflU0AWnxcfjHTSfQ4uqRO1LMYFkriP+bKXpfVLfhZ7fnY+GEDLkjUQxKMmrxytJCONxe/GxjGdy9PrkjxQSeBlEIIQR+s+M0Pi634tGbR+D7U7PljkQx6sIskUWFGVh/tBEr/3YU90zOhCRJKJ6cJXO66MWRtUK8+kkV3jvSgBXX5+LvZg6TOw4RxqWbcPvYNJy0duKzqha540Q9jqwV4M9f1+D13Wdx18QMPDFnJKfoUcSYkZcEe1cvvj7Xjvg4DUfWIcSRdYT7095zeH33WSydmo2n7xzLoqaIIkkS7hxvwfgME3ZUtWDjMd6UFSocWUeQi+8YE0Lgi+o2fFndholZZvz2f01FW2unjOmIrkwlSbhrYiY83gb8ansV9Bo15k9IlztW1GFZRyAhBHadbsWeM3ZMzk7AwoJ0/Nf+Wjg73XJHI7oitUpC8ZQsfFbZgv/zUQV6fH4smZgpd6yowtMgEUYIgZ2nzhf1lJwELCpIh4qnPkgB4tQq/GvxRMwcnowXtlbivcPctCCYWNYRxOcX+OiEFV+dtWNabiIWTkjnOWpSFL1WjV/fXYhbR6filR2n8OpObgsWLCzrCOHq8eKDIw0obXDg5lEpmD/ewqImRdJpVHjprgLcNy0b7xysxz9uOoFOj1fuWIrHc9YR4FSLC09vPoFz9m4sKkjHlJxEuSMRDcrFF8lHpcXjznEWfFJpw4q3DuFXReO5lsgQcGQtIyEENh1vwg/XHYbD7cXy63JY1BRVpucl4cHpufD7BX70t6N486tz6PX55Y6lSBxZy+RcWxde/PQUDtS04/phifhl0QTsOt0qdyyioMtNMuD+63OwtdyKP3x5Dh8cacTCgnTkJhl4E801YFmHWaPDjb/uq8XG403QaVRYe0c+7pmcxRkfFNUMWjXunpyFQlsntpbb8Nb+OkzIMGHm8CTkJBrkjqcILOsw8PkFvj5nx/+UNePTqhZIABYXZmD1zSOQFs+1qCl2jLGYkJdsxFdn7dh3zo7v//kAigoy8OD0XC73OwCWdYh0erw4WNuOL6rbsLu6Da2uHiToNfj+1GysuD4HmQl6uSMSyUKnUWFOfiquy01Eo8ONzcebsPFYE743Jg0Pz8jlRch+sKyDpLvXh6P1HThQ24GDte0ob3LCJ4D4ODVmjUjBneMtmD0yBXEaFTe1JQJg1mvw8A1j8L9nDcd7h+vx/pFGfFbVgmm5ibh7Uia+l58GYxy3q7uAZT1I7l4fjjU68PaBetTYu9DQ4YZfACoJyE7UY+aIFDw0PRdTcxKgUXPSDVF/UuPj8OjskfjBDcOw8VgT/utwA57/+CS06kqMSzdhUlYC8lIMfdd1YvV/6tQ3AAAJ30lEQVSiJMs6QA53L441OHG0oQNH6x043uhAj09AApCZoMMNw5MxPNmA3CQD4jTny7mmvRs17d3yBidSiPg4DR64PhfLr8vB0XoHfrf7DMqbO3G80Yn4ODVGp8VjdJoR9q5UJMfgvqMBlfXmzZvx+9//Hl6vFw8//DBWrFgR6lyyEULA1tmD060uVLd04VSLC2VNTpxp7QIASBKQYdZham4ihicbMSxZD52GP6oRDcbVTgkuLMjAHeMsqLK5UGntxElrJ0obHCgpbUJesgETMkwYnRaPkSlGjHX7sL20AfFxaqhUl8+siobR+IBl3dzcjFdffRXr169HXFwc7r//fsycORP5+fnhyBcUXr+Ay+OFq8eHzot+dbi9sHZ6YOvsQXuPD3WtLtS1u+G86NbY1Pg4jE83IS/ZgJxEPbIS9YjjaQ2isNCqVSjINKMg0wyfX6DR4UaiXouj9R04Uu/A1grbZR8TH6dGfJwaeq0aeo0Keq0a59q6kKjXwqzXIEGnOf+rXoMEvRYJOg1Meg00Vyj5SDJgWe/Zswc33ngjkpKSAADz58/Hli1b8OMf/3jIL97s9GBbhRU+v4DA+Q1h/eL86PbiXy/+f6/fjx6fHz1ePzxe8e3/f/Nrj88Pj/f8fz1eP7p7fXB7r37HVIJeg6xEA5INWui1alhMcbDExyHNpOMFDqIIoVZJF91Ic35ru06PF7Xt3ehRqfHB/hp0erx9AzJ3rw/27l64HR5UWjsH7IH4ODXMugslroH5myKP16mhliSoVRJUKglq6fwa3mqVhES9BosLM/tOfYbSgGVttVphsVj6fp+eno7S0tJLnmOxmAN+wYufa7GYMXFUWsAfS0R0MQuAkbnJAIA7CjLkDXMV19KR/Rnw24Hf779k9TchBFeDIyIKswHLOjMzEzbbt+eFbDYb0tO5ZQ8RUTgNWNY33XQT9u7di7a2NnR3d2Pbtm249dZbw5GNiIi+MWBZZ2Rk4Mknn8QPfvAD3H333Vi8eDEmT558yXM2b96MRYsWYd68eVi3bl2/n2vnzp247bbb+n7vcDiwatUqLFy4ECtWrLhkBB9Mg823b98+zJw5E0uXLsXSpUvx9NNPy5Lvtddew9y5c/tyXHhOeXk5iouLMX/+fDz77LPwekOzwPtg8/X3eLjzVVdX46GHHsJdd92FH/3oR+jo6AAANDQ0YMWKFViwYAEeffRRuFyuiMpXUlKC2bNn9x2/V199NazZysvL+1576dKluOWWW7B48WIAkXHsrpYvHMduoHwAUFZWhmXLluGuu+7C6tWr4XA4AAyy+8QQNTU1iblz5wq73S5cLpdYsmSJqKqquux5NptNLFiwQMydO7fvsV/84hfijTfeEEIIUVJSIp544omhxglqvjfffFP84Q9/CHqma823evVqcejQocs+tqioSBw+fFgIIcTTTz8t1q1bF1H5+ns8nPn8fr+YN2+e+Pzzz4UQQrzyyivi5ZdfFkIIsWrVKvHhhx8KIYR47bXX+h6PlHwvvPCC2Lx5c9AzBZrtYl1dXaKoqEjs379fCBEZx+5q+UJ97ALNt3z5crFz504hhBD/8i//In77298KIQbXfUOeb3Lx1D6j0dg3te+7nnvuucum++3cuRNLliwBACxevBi7du1Cb2/vUCMFLd+xY8ewe/duLFmyBGvWrEFjY/DX9Agk3/Hjx/HGG29gyZIleOGFF+DxeFBfXw+3242pU6cCAIqLi6/495Ir39UeD2e+srIyGI3GvlN3a9aswYoVK9Db24v9+/dj/vz5AOQ7fv3lA86//0pKSrBkyRI89dRTfSPucGW72BtvvIEZM2Zg+vTpEXPs+ssHhP7YBZrP7/f3/dTR3d0Nvf78Am6D6b4hl/WVpvY1Nzdf8py//vWvKCgowJQpU/r9WI1GA5PJhLa2tqFGClo+s9mMhx56CJs3b8acOXPw5JNPBjVbIPlcLhcmTJiAn/3sZygpKYHD4cDrr79+2cdZLJbL/l5y5uvv8XDnq6mpQVpaGp555hncc889eP7552E0GmG322EymaDRnJ+9Ktfx6y/fhUyPPfYYNm3ahKysLLzwwgthzXaB0+nEe++91zeYiZRj11++C5lCeewCzbd27Vo899xzmD17Nvbs2YP777//so8NtPuGXNYDTe2rrKzEtm3b8Nhjjw34uYQQUKmCO7l8KPleeOEFzJs3DwCwfPlynDp1Ck6nM6z54uPj8e///u8YPXo0NBoNHnnkEXz++edhm1I52Hz9PR7ufF6vF/v27cPy5ctRUlKCYcOG4cUXX7zi8ZLj+PWXDwB+97vf4frrr4ckSVi5ciW++OKLsGa7YNOmTbjjjjuQmpra7/PkOHb95QNCf+wCyed2u/Hss8/iL3/5C3bv3o0HHngAP//5z6/4uQLpviE340BT+7Zs2QKbzYZly5Zh1apVsFqteOCBBwCc/07U0tIC4Pyb1uVy9d0pGSyDzef3+/H73/8ePp/vks+nVgf3jsaB8jU0NOCDDz7o+70QAhqN5rKPa2lpCcmUysHm6+/xcOezWCwYPnw4Jk2aBOD8j5ylpaVISUmB0+ns+/cN1ZTUweZzOp34y1/+0vc8IUTY33sXfPLJJ1i0aFHf7yPl2PWXLxzHLpB8lZWV0Ol0fRMy7rvvPuzbtw/A4LpvyGU90NS+xx9/HFu3bsXGjRvxxz/+Eenp6XjnnXcAAHPmzMGGDRsAAB999BGmT58OrVY71EhByadSqbB9+3Zs3boVALBhwwZMmTKl70fUcOXT6/V45ZVXUFtbCyEE1q1bhzvvvBM5OTnQ6XQ4ePAgAGDjxo0hmVI52Hz9PR7ufNOmTUNbWxsqKioAADt27EBhYSG0Wi2mT5+Ojz76CMD5f185jl9/+YxGI/70pz/h6NGjAIC333476McvkGm5QgiUlZVh2rRpfY9FyrHrL184jl0g+YYPH46mpiZUV1cDAD799NO+b8qD6r5BXgi9xKZNm0RRUZGYN2+e+OMf/yiEEGLlypWitLT0kufV1tZeMtvCbreL1atXi0WLFon77rtP1NbWBiNO0PJVVlaK++67TyxatEg8+OCDoqGhQZZ8W7Zs6fvztWvXCo/HI4QQory8XCxbtkzMnz9f/PSnP+17PFLy9fd4uPMdOXJELFu2TCxatEg88sgjoqWlRQghRF1dnXjwwQfFwoULxSOPPCLa29sjKt/+/fvF3XffLRYsWCDWrFkjHA5H2LO1tLSIm2666bKPi5Rj11++cBy7QPLt3LlTLFmyRCxevFg8/PDDoqamRggxuO6ThBAi6N9yiIgoqLjWJxGRArCsiYgUgGVNRKQALGsiIgVgWRMRKQDLmohIAVjWREQKwLImIlKA/w+hKQSxGSYuXgAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sns.distplot(trace['p'])\n",
    "pass"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Autocorrelation plot"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 864x144 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "pm.autocorrplot(trace, varnames=['p'])\n",
    "pass"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Calculate effective sample size\n",
    "\n",
    "$$\n",
    "\\hat{n}_{eff} = \\frac{mn}{1 + 2 \\sum_{t=1}^T \\hat{\\rho}_t}\n",
    "$$\n",
    "\n",
    "where $m$ is the number of chains, $n$ the number of steps per chain, $T$ the time when the autocorrelation first becomes negative, and $\\hat{\\rho}_t$ the autocorrelation at lag $t$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{'p': 1639.0804767244163}"
      ]
     },
     "execution_count": 44,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pm.effective_n(trace)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Evaluate convergence"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### Gelman-Rubin\n",
    "\n",
    "$$\n",
    "\\hat{R} = \\frac{\\hat{V}}{W}\n",
    "$$\n",
    "\n",
    "where $W$ is the within-chain variance and $\\hat{V}$ is the posterior variance estimate for the pooled traces.  Values greater than one indicate that one or more chains have not yet converged.\n",
    "\n",
    "Discrad burn-in steps for each chain. The idea is to see if the starting values of each chain come from the same distribution as the stationary state. \n",
    "\n",
    "- $W$ is the number of chains $m \\times$ the variacne of each individual chain\n",
    "- $B$ is the number of steps $n \\times$ the variance of the chain means\n",
    "- $\\hat{V}$ is the weigthed average $(1 - \\frac{1}{n})W + \\frac{1}{n}B$\n",
    "\n",
    "The idea is that $\\hat{V}$ is an unbiased estimator of $W$ if the starting values of each chain come from the same distribution as the stationary state. Hence if $\\hat{R}$ differs significantly from 1, there is probsbly no convergence and we need more iterations. This is done for each parameter $\\theta$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{'p': 1.0011843767338002}"
      ]
     },
     "execution_count": 45,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pm.gelman_rubin(trace)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### Geweke\n",
    "\n",
    "Compares mean of initial with later segments of a trace for a parameter. Should have absolute value less than 1 at convergence."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(pm.geweke(trace['p'])[:,1], 'o')\n",
    "plt.axhline(1, c='red')\n",
    "plt.axhline(-1, c='red')\n",
    "plt.gca().margins(0.05)\n",
    "pass"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Textual summary"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {},
   "outputs": [
    {
     "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>p</th>\n",
       "      <td>0.607161</td>\n",
       "      <td>0.047751</td>\n",
       "      <td>0.001174</td>\n",
       "      <td>0.513838</td>\n",
       "      <td>0.699736</td>\n",
       "      <td>1639.080477</td>\n",
       "      <td>1.001184</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "       mean        sd  mc_error   hpd_2.5  hpd_97.5        n_eff      Rhat\n",
       "p  0.607161  0.047751  0.001174  0.513838  0.699736  1639.080477  1.001184"
      ]
     },
     "execution_count": 47,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pm.summary(trace, varnames=['p'])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Visual summary"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x144 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "pm.traceplot(trace, varnames=['p'])\n",
    "pass"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "pm.forestplot(trace)\n",
    "pass"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "pm.plot_posterior(trace)\n",
    "pass"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Prior predictive samples"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {},
   "outputs": [],
   "source": [
    "with coin_context:\n",
    "    ps = pm.sample_prior_predictive(samples=1000)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sns.distplot(ps['y'])\n",
    "plt.axvline(heads, c='red')\n",
    "pass"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Posterior predictive samples"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 1000/1000 [00:00<00:00, 1386.64it/s]\n"
     ]
    }
   ],
   "source": [
    "with coin_context:\n",
    "    ps = pm.sample_posterior_predictive(trace, samples=1000)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sns.distplot(ps['y'])\n",
    "plt.axvline(heads, c='red')\n",
    "pass"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Saving traces"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'my_trace'"
      ]
     },
     "execution_count": 59,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pm.save_trace(trace, 'my_trace', overwrite=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "You need to re-initialize the model when reloading."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "metadata": {},
   "outputs": [],
   "source": [
    "with pm.Model() as my_trace:\n",
    "    p = pm.Beta('p', alpha=2, beta=2)\n",
    "    y = pm.Binomial('y', n=n, p=p, observed=heads)\n",
    "    tr = pm.load_trace('my_trace')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "metadata": {},
   "outputs": [
    {
     "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>p</th>\n",
       "      <td>0.607161</td>\n",
       "      <td>0.047751</td>\n",
       "      <td>0.001174</td>\n",
       "      <td>0.513838</td>\n",
       "      <td>0.699736</td>\n",
       "      <td>1639.080477</td>\n",
       "      <td>1.001184</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "       mean        sd  mc_error   hpd_2.5  hpd_97.5        n_eff      Rhat\n",
       "p  0.607161  0.047751  0.001174  0.513838  0.699736  1639.080477  1.001184"
      ]
     },
     "execution_count": 61,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pm.summary(tr)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "It is probably a good practice to make model reuse convenient"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "metadata": {},
   "outputs": [],
   "source": [
    "def build_model():\n",
    "    with pm.Model() as m:\n",
    "        p = pm.Beta('p', alpha=2, beta=2)\n",
    "        y = pm.Binomial('y', n=n, p=p, observed=heads)\n",
    "    return m"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "metadata": {},
   "outputs": [],
   "source": [
    "m = build_model()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "metadata": {},
   "outputs": [],
   "source": [
    "with m:\n",
    "    tr1 = pm.load_trace('my_trace')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "metadata": {},
   "outputs": [
    {
     "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>p</th>\n",
       "      <td>0.607161</td>\n",
       "      <td>0.047751</td>\n",
       "      <td>0.001174</td>\n",
       "      <td>0.513838</td>\n",
       "      <td>0.699736</td>\n",
       "      <td>1639.080477</td>\n",
       "      <td>1.001184</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "       mean        sd  mc_error   hpd_2.5  hpd_97.5        n_eff      Rhat\n",
       "p  0.607161  0.047751  0.001174  0.513838  0.699736  1639.080477  1.001184"
      ]
     },
     "execution_count": 65,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pm.summary(tr1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Sampling from prior\n",
    "\n",
    "Just omit the `observed=` argument."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Multiprocess sampling (2 chains in 2 jobs)\n",
      "CompoundStep\n",
      ">Metropolis: [mu]\n",
      ">Metropolis: [sigma]\n",
      "Sampling 2 chains: 100%|██████████| 5000/5000 [00:01<00:00, 2753.43draws/s]\n",
      "The number of effective samples is smaller than 10% for some parameters.\n"
     ]
    }
   ],
   "source": [
    "with pm.Model() as prior_context:\n",
    "    sigma = pm.Gamma('sigma', alpha=2.0, beta=1.0)\n",
    "    mu = pm.Normal('mu', mu=0, sd=sigma)\n",
    "    trace = pm.sample(niter, step=pm.Metropolis())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 68,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x288 with 4 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "pm.traceplot(trace, varnames=['mu', 'sigma'])\n",
    "pass"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Sampling from posterior"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 69,
   "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: [sd, mu]\n",
      "Sampling 2 chains: 100%|██████████| 5000/5000 [00:03<00:00, 1307.56draws/s]\n"
     ]
    }
   ],
   "source": [
    "niter = 2000\n",
    "with pm.Model() as normal_context:\n",
    "    mu = pm.Normal('mu', mu=0, sd=100)\n",
    "    sd = pm.HalfCauchy('sd', beta=2)\n",
    "    y = pm.Normal('y', mu=mu, sd=sd, observed=xs)\n",
    "    trace = pm.sample(niter)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Find Highest Posterior Density (Credible intervals)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 70,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.44162207, 0.55971851])"
      ]
     },
     "execution_count": 70,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "hpd = pm.hpd(trace['mu'], alpha=0.05)\n",
    "hpd"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 72,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x144 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "ax = pm.traceplot(trace, varnames=['mu'],)\n",
    "\n",
    "ymin, ymax = ax[0,0].get_ylim()\n",
    "y = ymin + 0.05*(ymax-ymin)\n",
    "ax[0, 0].plot(hpd, [y,y], c='red')\n",
    "pass"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Evaluating goodness-of-fit\n",
    "\n",
    "DIC, WAIC and BPIC are approximations to the out-of-sample error and can be used for model comparison. Likelihood is dependent on model complexity and should not be used for model comparisons."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 73,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "mu          0.500164\n",
       "sd_log__   -1.218045\n",
       "sd          0.296556\n",
       "Name: mean, dtype: float64"
      ]
     },
     "execution_count": 73,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "post_mean = pm.summary(trace, varnames=trace.varnames)['mean']\n",
    "post_mean"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Likelihood"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 74,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array(-26.57766616)"
      ]
     },
     "execution_count": 74,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "normal_context.logp(post_mean)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Cross-validation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 75,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/cliburn/anaconda3/lib/python3.6/site-packages/pymc3/stats.py:167: FutureWarning: arrays to stack must be passed as a \"sequence\" type such as list or tuple. Support for non-sequence iterables such as generators is deprecated as of NumPy 1.16 and will raise an error in the future.\n",
      "  return np.stack(logp)\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "LOO_r(LOO=40.743463301462626, LOO_se=8.891566223871754, p_LOO=1.3902023282742455, shape_warn=0)\n"
     ]
    }
   ],
   "source": [
    "with normal_context:\n",
    "    print(pm.loo(trace))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### WAIC"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 76,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "WAIC_r(WAIC=40.74205569255692, WAIC_se=8.891356706673374, p_WAIC=1.3894985238213904, var_warn=0)\n"
     ]
    }
   ],
   "source": [
    "with normal_context:\n",
    "    print(pm.waic(trace))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Using a custom likelihood"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 77,
   "metadata": {},
   "outputs": [],
   "source": [
    "def logp(x, μ=0, σ=1):\n",
    "    \"\"\"Normal distribtuion.\"\"\"\n",
    "    return -0.5*np.log(2*np.pi) - np.log(σ) - (x-μ)**2/(2*σ**2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 78,
   "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: [sd, mu]\n",
      "Sampling 2 chains: 100%|██████████| 5000/5000 [00:03<00:00, 1316.85draws/s]\n"
     ]
    }
   ],
   "source": [
    "with pm.Model() as prior_context:\n",
    "    mu = pm.Normal('mu', mu=0, sd=100)\n",
    "    sd = pm.HalfCauchy('sd', beta=2)\n",
    "    y = pm.DensityDist('y', logp, observed=dict(x=xs, μ=mu, σ=sd))\n",
    "    custom_trace = pm.sample(niter)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 79,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "mu    0.499692\n",
       "sd    0.296759\n",
       "dtype: float64"
      ]
     },
     "execution_count": 79,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pm.trace_to_dataframe(custom_trace).mean()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Variational methods available\n",
    "\n",
    "To use a variational method, use `pm.fit` instead of `pm.sample`. We'll see examples of usage in another notebook."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 80,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "ADVI\n",
      "ASVGD\n",
      "Approximation\n",
      "Empirical\n",
      "FullRank\n",
      "FullRankADVI\n",
      "Group\n",
      "ImplicitGradient\n",
      "Inference\n",
      "KLqp\n",
      "MeanField\n",
      "NFVI\n",
      "NormalizingFlow\n",
      "SVGD\n",
      "Stein\n"
     ]
    }
   ],
   "source": [
    "print('\\n'.join(m for m in dir(pm.variational) if m[0].isupper()))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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