{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# API quickstart"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "import numpy as np\n",
    "import theano.tensor as tt\n",
    "import pymc3 as pm\n",
    "\n",
    "import seaborn as sns\n",
    "import matplotlib.pyplot as plt\n",
    "sns.set_context('notebook')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 1. Model creation\n",
    "\n",
    "Models in PyMC3 are centered around the `Model` class. It has references to all random variables (RVs) and computes the model logp and its gradients. Usually, you would instantiate it as part of a `with` context:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "with pm.Model() as model:\n",
    "    # Model definition\n",
    "    pass"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We discuss RVs further below but let's create a simple model to explore the `Model` class."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "with pm.Model() as model:\n",
    "    mu = pm.Normal('mu', mu=0, sd=1)\n",
    "    obs = pm.Normal('obs', mu=mu, sd=1, observed=np.random.randn(100))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[mu, obs]"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model.basic_RVs"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[mu]"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model.free_RVs"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[obs]"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model.observed_RVs"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array(-139.7234487505281)"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model.logp({'mu': 0})"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Warning**\n",
    "It's worth highlighting one of the counter-intuitive design choices with logp. \n",
    "The API makes the `logp` look like an attribute, when it actually puts together a function based on the current state of the model. \n",
    "\n",
    "The current design is super maintainable, does terrible if the state stays constant, and great if the state keeps changing, for reasons of design we assume that `Model` isn't static, in fact it's best in our experience and avoids bad results. \n",
    "\n",
    "If you need to use `logp` in an inner loop and it needs to be static, simply use something like `logp = model.logp` below. You can see the caching effect with the speed up below. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "91.8 ms ± 1.95 ms per loop (mean ± std. dev. of 7 runs, 10 loops each)\n",
      "35.6 µs ± 2.01 µs per loop (mean ± std. dev. of 7 runs, 10000 loops each)\n"
     ]
    }
   ],
   "source": [
    "%timeit model.logp({mu: 0.1})\n",
    "logp = model.logp\n",
    "%timeit logp({mu: 0.1})"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 2. Probability Distributions\n",
    "\n",
    "Every probabilistic program consists of observed and unobserved Random Variables (RVs). Observed RVs are defined via likelihood distributions, while unobserved RVs are defined via prior distributions. In PyMC3, probability distributions are available from the main module space:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Help on class Normal in module pymc3.distributions.continuous:\n",
      "\n",
      "class Normal(pymc3.distributions.distribution.Continuous)\n",
      " |  Univariate normal log-likelihood.\n",
      " |  \n",
      " |  .. math::\n",
      " |  \n",
      " |     f(x \\mid \\mu, \\tau) =\n",
      " |         \\sqrt{\\frac{\\tau}{2\\pi}}\n",
      " |         \\exp\\left\\{ -\\frac{\\tau}{2} (x-\\mu)^2 \\right\\}\n",
      " |  \n",
      " |  ========  ==========================================\n",
      " |  Support   :math:`x \\in \\mathbb{R}`\n",
      " |  Mean      :math:`\\mu`\n",
      " |  Variance  :math:`\\dfrac{1}{\\tau}` or :math:`\\sigma^2`\n",
      " |  ========  ==========================================\n",
      " |  \n",
      " |  Normal distribution can be parameterized either in terms of precision\n",
      " |  or standard deviation. The link between the two parametrizations is\n",
      " |  given by\n",
      " |  \n",
      " |  .. math::\n",
      " |  \n",
      " |     \\tau = \\dfrac{1}{\\sigma^2}\n",
      " |  \n",
      " |  .. plot::\n",
      " |  \n",
      " |      import matplotlib.pyplot as plt\n",
      " |      import numpy as np\n",
      " |      import scipy.stats as st\n",
      " |      x = np.linspace(-5.0, 5.0, 1000)\n",
      " |      fig, ax = plt.subplots()\n",
      " |      f = lambda mu, sd : st.norm.pdf(x, loc=mu, scale=sd)\n",
      " |      plot_pdf = lambda a, b : ax.plot(x, f(a,b), label=r'$\\mu$={0}, $\\sigma$={1}'.format(a,b))\n",
      " |      plot_pdf(0.0, 0.4)\n",
      " |      plot_pdf(0.0, 1.0)\n",
      " |      plot_pdf(0.0, 2.0)\n",
      " |      plot_pdf(-2.0, 0.4)\n",
      " |      plt.legend(loc='upper right', frameon=False)\n",
      " |      ax.set(xlim=[-5,5], ylim=[0,1.2], xlabel='x', ylabel='f(x)')\n",
      " |      plt.show()\n",
      " |  \n",
      " |  Parameters\n",
      " |  ----------\n",
      " |  mu : float\n",
      " |      Mean.\n",
      " |  sd : float\n",
      " |      Standard deviation (sd > 0).\n",
      " |  tau : float\n",
      " |      Precision (tau > 0).\n",
      " |  \n",
      " |  Method resolution order:\n",
      " |      Normal\n",
      " |      pymc3.distributions.distribution.Continuous\n",
      " |      pymc3.distributions.distribution.Distribution\n",
      " |      builtins.object\n",
      " |  \n",
      " |  Methods defined here:\n",
      " |  \n",
      " |  __init__(self, mu=0, sd=None, tau=None, **kwargs)\n",
      " |      Initialize self.  See help(type(self)) for accurate signature.\n",
      " |  \n",
      " |  logp(self, value)\n",
      " |  \n",
      " |  random(self, point=None, size=None, repeat=None)\n",
      " |  \n",
      " |  ----------------------------------------------------------------------\n",
      " |  Methods inherited from pymc3.distributions.distribution.Distribution:\n",
      " |  \n",
      " |  __getnewargs__(self)\n",
      " |  \n",
      " |  __latex__ = _repr_latex_(self, name=None, dist=None)\n",
      " |      Magic method name for IPython to use for LaTeX formatting.\n",
      " |  \n",
      " |  default(self)\n",
      " |  \n",
      " |  get_test_val(self, val, defaults)\n",
      " |  \n",
      " |  getattr_value(self, val)\n",
      " |  \n",
      " |  logp_nojac(self, *args, **kwargs)\n",
      " |      Return the logp, but do not include a jacobian term for transforms.\n",
      " |      \n",
      " |      If we use different parametrizations for the same distribution, we\n",
      " |      need to add the determinant of the jacobian of the transformation\n",
      " |      to make sure the densities still describe the same distribution.\n",
      " |      However, MAP estimates are not invariant with respect to the\n",
      " |      parametrization, we need to exclude the jacobian terms in this case.\n",
      " |      \n",
      " |      This function should be overwritten in base classes for transformed\n",
      " |      distributions.\n",
      " |  \n",
      " |  logp_sum(self, *args, **kwargs)\n",
      " |      Return the sum of the logp values for the given observations.\n",
      " |      \n",
      " |      Subclasses can use this to improve the speed of logp evaluations\n",
      " |      if only the sum of the logp values is needed.\n",
      " |  \n",
      " |  ----------------------------------------------------------------------\n",
      " |  Class methods inherited from pymc3.distributions.distribution.Distribution:\n",
      " |  \n",
      " |  dist(*args, **kwargs) from builtins.type\n",
      " |  \n",
      " |  ----------------------------------------------------------------------\n",
      " |  Static methods inherited from pymc3.distributions.distribution.Distribution:\n",
      " |  \n",
      " |  __new__(cls, name, *args, **kwargs)\n",
      " |      Create and return a new object.  See help(type) for accurate signature.\n",
      " |  \n",
      " |  ----------------------------------------------------------------------\n",
      " |  Data descriptors inherited from pymc3.distributions.distribution.Distribution:\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"
     ]
    }
   ],
   "source": [
    "help(pm.Normal)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In the PyMC3 module, the structure for probability distributions looks like this:\n",
    "\n",
    "[pymc3.distributions](../api/distributions.rst)\n",
    "- [continuous](../api/distributions/continuous.rst)\n",
    "- [discrete](../api/distributions/discrete.rst)\n",
    "- [timeseries](../api/distributions/timeseries.rst)\n",
    "- [mixture](../api/distributions/mixture.rst)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "['Discrete',\n",
       " 'Distribution',\n",
       " 'Mixture',\n",
       " 'Normal',\n",
       " 'NormalMixture',\n",
       " '__builtins__',\n",
       " '__cached__',\n",
       " '__doc__',\n",
       " '__file__',\n",
       " '__loader__',\n",
       " '__name__',\n",
       " '__package__',\n",
       " '__spec__',\n",
       " 'all_discrete',\n",
       " 'bound',\n",
       " 'draw_values',\n",
       " 'generate_samples',\n",
       " 'get_tau_sd',\n",
       " 'get_variable_name',\n",
       " 'logsumexp',\n",
       " 'np',\n",
       " 'tt']"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "dir(pm.distributions.mixture)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Unobserved Random Variables"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Every unobserved RV has the following calling signature: name (str), parameter keyword arguments. Thus, a normal prior can be defined in a model context like this:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "with pm.Model():\n",
    "    x = pm.Normal('x', mu=0, sd=1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As with the model, we can evaluate its logp:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array(-0.9189385332046727)"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x.logp({'x': 0})"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Observed Random Variables"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Observed RVs are defined just like unobserved RVs but require data to be passed into the `observed` keyword argument:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "with pm.Model():\n",
    "    obs = pm.Normal('x', mu=0, sd=1, observed=np.random.randn(100))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "`observed` supports lists, `numpy.ndarray`, `theano` and `pandas` data structures."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Deterministic transforms"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "PyMC3 allows you to freely do algebra with RVs in all kinds of ways:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "with pm.Model():\n",
    "    x = pm.Normal('x', mu=0, sd=1)\n",
    "    y = pm.Gamma('y', alpha=1, beta=1)\n",
    "    plus_2 = x + 2\n",
    "    summed = x + y\n",
    "    squared = x**2\n",
    "    sined = pm.math.sin(x)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "While these transformations work seamlessly, its results are not stored automatically. Thus, if you want to keep track of a transformed variable, you have to use `pm.Determinstic`:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "with pm.Model():\n",
    "    x = pm.Normal('x', mu=0, sd=1)\n",
    "    plus_2 = pm.Deterministic('x plus 2', x + 2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Note that `plus_2` can be used in the identical way to above, we only tell PyMC3 to keep track of this RV for us."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Automatic transforms of bounded RVs\n",
    "\n",
    "In order to sample models more efficiently, PyMC3 automatically transforms bounded RVs to be unbounded."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "with pm.Model() as model:\n",
    "    x = pm.Uniform('x', lower=0, upper=1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "When we look at the RVs of the model, we would expect to find `x` there, however:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[x_interval__]"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model.free_RVs"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "`x_interval__` represents `x` transformed to accept parameter values between -inf and +inf. In the case of an upper and a lower bound, a `LogOdd`s transform is applied. Sampling in this transformed space makes it easier for the sampler. PyMC3 also keeps track of the non-transformed, bounded parameters. These are common determinstics (see above): "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[x]"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model.deterministics"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "When displaying results, PyMC3 will usually hide transformed parameters. You can pass the `include_transformed=True` parameter to many functions to see the transformed parameters that are used for sampling.\n",
    "\n",
    "You can also turn transforms off:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[x]\n"
     ]
    }
   ],
   "source": [
    "with pm.Model() as model:\n",
    "    x = pm.Uniform('x', lower=0, upper=1, transform=None)\n",
    "    \n",
    "print(model.free_RVs)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Lists of RVs / higher-dimensional RVs\n",
    "\n",
    "Above we have seen how to create scalar RVs. In many models, you want multiple RVs. There is a tendency (mainly inherited from PyMC 2.x) to create list of RVs, like this:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "with pm.Model():\n",
    "    x = [pm.Normal('x_{}'.format(i), mu=0, sd=1) for i in range(10)] # bad"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "However, even though this works it is quite slow and not recommended. Instead, use the `shape` kwarg:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "with pm.Model() as model:\n",
    "    x = pm.Normal('x', mu=0, sd=1, shape=10) # good"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "`x` is now a random vector of length 10. We can index into it or do linear algebra operations on it:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "with model:\n",
    "    y = x[0] * x[1] # full indexing is supported\n",
    "    x.dot(x.T) # Linear algebra is supported"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Initialization with test_values\n",
    "\n",
    "While PyMC3 tries to automatically initialize models it is sometimes helpful to define initial values for RVs. This can be done via the `testval` kwarg:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 0.,  0.,  0.,  0.,  0.])"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "with pm.Model():\n",
    "    x = pm.Normal('x', mu=0, sd=1, shape=5)\n",
    "\n",
    "x.tag.test_value"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 0.421665  , -1.63966614,  0.92402752,  0.14413675, -1.39721381])"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "with pm.Model():\n",
    "    x = pm.Normal('x', mu=0, sd=1, shape=5, testval=np.random.randn(5))\n",
    "\n",
    "x.tag.test_value"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This technique is quite useful to identify problems with model specification or initialization."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 3. Inference\n",
    "\n",
    "Once we have defined our model, we have to perform inference to approximate the posterior distribution. PyMC3 supports two broad classes of inference: sampling and variational inference.\n",
    "\n",
    "### 3.1 Sampling\n",
    "\n",
    "The main entry point to MCMC sampling algorithms is via the `pm.sample()` function. By default, this function tries to auto-assign the right sampler(s) and auto-initialize if you don't pass anything."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Auto-assigning NUTS sampler...\n",
      "Initializing NUTS using jitter+adapt_diag...\n",
      "100%|██████████| 1500/1500 [00:01<00:00, 1026.78it/s]\n"
     ]
    }
   ],
   "source": [
    "with pm.Model() as model:\n",
    "    mu = pm.Normal('mu', mu=0, sd=1)\n",
    "    obs = pm.Normal('obs', mu=mu, sd=1, observed=np.random.randn(100))\n",
    "    \n",
    "    trace = pm.sample(1000, tune=500)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As you can see, on a continuous model, PyMC3 assigns the NUTS sampler, which is very efficient even for complex models. PyMC3 also runs variational inference (i.e. ADVI) to find good starting parameters for the sampler. Here we draw 1000 samples from the posterior and allow the sampler to adjust its parameters in an additional 500 iterations. These 500 samples are discarded by default:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1000"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "len(trace)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "You can also run multiple chains in parallel using the `cores` kwarg:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Auto-assigning NUTS sampler...\n",
      "Initializing NUTS using jitter+adapt_diag...\n",
      "100%|██████████| 1000/1000 [00:01<00:00, 851.68it/s]\n"
     ]
    }
   ],
   "source": [
    "with pm.Model() as model:\n",
    "    mu = pm.Normal('mu', mu=0, sd=1)\n",
    "    obs = pm.Normal('obs', mu=mu, sd=1, observed=np.random.randn(100))\n",
    "    \n",
    "    trace = pm.sample(cores=4)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Note, that we are now drawing 2000 samples, 500 samples for 4 chains each. The 500 tuning samples are discarded by default."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(2000,)"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "trace['mu'].shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "4"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "trace.nchains"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(500,)"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "trace.get_values('mu', chains=1).shape # get values of a single chain"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "PyMC3, offers a variety of other samplers, found in `pm.step_methods`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "['BinaryGibbsMetropolis',\n",
       " 'BinaryMetropolis',\n",
       " 'CategoricalGibbsMetropolis',\n",
       " 'CauchyProposal',\n",
       " 'CompoundStep',\n",
       " 'ElemwiseCategorical',\n",
       " 'EllipticalSlice',\n",
       " 'HamiltonianMC',\n",
       " 'LaplaceProposal',\n",
       " 'Metropolis',\n",
       " 'MultivariateNormalProposal',\n",
       " 'NUTS',\n",
       " 'NormalProposal',\n",
       " 'PoissonProposal',\n",
       " 'SGFS',\n",
       " 'SMC',\n",
       " 'Slice']"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "list(filter(lambda x: x[0].isupper(), dir(pm.step_methods)))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Commonly used step-methods besides NUTS are `Metropolis` and `Slice`. **For almost all continuous models, `NUTS` should be preferred.** There are hard-to-sample models for which `NUTS` will be very slow causing many users to use `Metropolis` instead. This practice, however, is rarely successful. NUTS is fast on simple models but can be slow if the model is very complex or it is badly initialized. In the case of a complex model that is hard for NUTS, Metropolis, while faster, will have a very low effective sample size or not converge properly at all. A better approach is to instead try to improve initialization of NUTS, or reparameterize the model.\n",
    "\n",
    "For completeness, other sampling methods can be passed to sample:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 1500/1500 [00:00<00:00, 5511.71it/s]\n"
     ]
    }
   ],
   "source": [
    "with pm.Model() as model:\n",
    "    mu = pm.Normal('mu', mu=0, sd=1)\n",
    "    obs = pm.Normal('obs', mu=mu, sd=1, observed=np.random.randn(100))\n",
    "    \n",
    "    step = pm.Metropolis()\n",
    "    trace = pm.sample(1000, step=step)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "You can also assign variables to different step methods."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 10500/10500 [00:13<00:00, 774.35it/s]\n"
     ]
    }
   ],
   "source": [
    "with pm.Model() as model:\n",
    "    mu = pm.Normal('mu', mu=0, sd=1)\n",
    "    sd = pm.HalfNormal('sd', sd=1)\n",
    "    obs = pm.Normal('obs', mu=mu, sd=sd, observed=np.random.randn(100))\n",
    "    \n",
    "    step1 = pm.Metropolis(vars=[mu])\n",
    "    step2 = pm.Slice(vars=[sd])\n",
    "    trace = pm.sample(10000, step=[step1, step2], cores=4)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 3.2 Analyze sampling results\n",
    "\n",
    "The most common used plot to analyze sampling results is the so-called trace-plot:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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L7wbksgar1xz/qrtcwJibT+czKg6V0uJ66iwllbLD1HiJeDzKpm29yy3OSaFmHJkGrOhp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ywMA1Bkm0WRrfeImqJAlj2TTEfv0WZFUcgrziMnzY6ekzHg/fdkSh3Z1icd+08VTXUxc17OIEdP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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x114fd9390>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "pm.traceplot(trace);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Another common metric to look at is R-hat, also known as the Gelman-Rubin statistic:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{'mu': 1.0001326715972627,\n",
       " 'sd': 0.99995267558629874,\n",
       " 'sd_log__': 0.99995398290485815}"
      ]
     },
     "execution_count": 35,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pm.gelman_rubin(trace)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "These are also part of the `forestplot`:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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AjsQUlaGio2MUHBxgdwwAAByJgmOoN95YxRocAAB8YIoKAAD4HUZwDLVlyyeKiQnXddc1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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x115edccf8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "pm.forestplot(trace);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Finally, for a plot of the posterior that is inspired by the book [Doing Bayesian Data Analysis](http://www.indiana.edu/~kruschke/DoingBayesianDataAnalysis/), you can use the:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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a50WpNQIys1U6z4/KzMmDWpPfmEptneDfaVKJsUhtnSCxtseLQ+fkj69PzR9fb+0ghzIz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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1150fabe0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "pm.plot_posterior(trace);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "For high-dimensional models it becomes cumbersome to look at all parameter's traces. When using `NUTS` we can look at the energy plot to assess problems of convergence:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Auto-assigning NUTS sampler...\n",
      "Initializing NUTS using jitter+adapt_diag...\n",
      "100%|██████████| 1000/1000 [00:05<00:00, 198.29it/s]\n"
     ]
    },
    {
     "data": {
      "image/png": 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jfB3jqVEKczKBuVdWyoosJIEpsl4ylebRdY1o/n6cyotb95ld0qJhUVZWOE4l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\npAr/D5sxC0pR9egRAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1169d7358>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "with pm.Model() as model:\n",
    "    x = pm.Normal('x', mu=0, sd=1, shape=100)    \n",
    "    trace = pm.sample(cores=4)\n",
    "    \n",
    "pm.energyplot(trace);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "For more information on sampler stats and the energy plot, see [here](sampler-stats.ipynb). For more information on identifying sampling problems and what to do about them, see [here](Diagnosing_biased_Inference_with_Divergences.ipynb)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 3.3 Variational inference\n",
    "\n",
    "PyMC3 supports various Variational Inference techniques. While these methods are much faster, they are often also less accurate and can lead to biased inference. The main entry point is `pymc3.fit()`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Average Loss = 150.94: 100%|██████████| 10000/10000 [00:03<00:00, 2988.43it/s]\n",
      "Finished [100%]: Average Loss = 150.93\n"
     ]
    }
   ],
   "source": [
    "with pm.Model() as model:\n",
    "    mu = pm.Normal('mu', mu=0, sd=1)\n",
    "    sd = pm.HalfNormal('sd', sd=1)\n",
    "    obs = pm.Normal('obs', mu=mu, sd=sd, observed=np.random.randn(100))\n",
    "    \n",
    "    approx = pm.fit()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The returned `Approximation` object has various capabilities, like drawing samples from the approximated posterior, which we can analyse like a regular sampling run:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<MultiTrace: 1 chains, 500 iterations, 3 variables>"
      ]
     },
     "execution_count": 40,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "approx.sample(500)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The `variational` submodule offers a lot of flexibility in which VI to use and follows an object oriented design. For example, full-rank ADVI estimates a full covariance matrix:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Average Loss = 0.0068883: 100%|██████████| 10000/10000 [00:08<00:00, 1233.38it/s]\n",
      "Finished [100%]: Average Loss = 0.0065707\n"
     ]
    }
   ],
   "source": [
    "mu = pm.floatX([0., 0.])\n",
    "cov = pm.floatX([[1, .5], [.5, 1.]])\n",
    "with pm.Model() as model:\n",
    "    pm.MvNormal('x', mu=mu, cov=cov, shape=2)\n",
    "    approx = pm.fit(method='fullrank_advi')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "An equivalent expression using the object-oriented interface is:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Average Loss = 0.01127: 100%|██████████| 10000/10000 [00:08<00:00, 1225.82it/s] \n",
      "Finished [100%]: Average Loss = 0.011343\n"
     ]
    }
   ],
   "source": [
    "with pm.Model() as model:\n",
    "    pm.MvNormal('x', mu=mu, cov=cov, shape=2)\n",
    "    approx = pm.FullRankADVI().fit()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x11817c908>"
      ]
     },
     "execution_count": 43,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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AF9SW8MXJLRwrSAFA5ejOnfEzmBObhKPSodtgFJPZxPn6Qo6Vn+NkZRpVrfWd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\nhDn4dK54ZdNLtyuA3mykzaSnzaRHa+7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lu1DI5Fw9ZJbXORVttWwu3UtiSIzfWu/KQ+tp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\nsx3MhiE+NXaL286m+hzkyJgbPdbr+L6mfKqtRiZFDCehRy3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XP32DIE0Qv1/+BOkJqT6f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zrOJ7s/IyUjBYDQoFB+MedWpsRM6dH6yM7O4u233yQ5OQkHB0cef/z3zJwZO6Bau+L6IeErrknz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\nhBBCqOz/A9ovAiWVtI6tAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11812c978>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure()\n",
    "trace = approx.sample(10000)\n",
    "sns.kdeplot(trace['x'])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Stein Variational Gradient Descent (SVGD) uses particles to estimate the posterior:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 10000/10000 [01:21<00:00, 123.44it/s]\n"
     ]
    }
   ],
   "source": [
    "w = pm.floatX([.2, .8])\n",
    "mu = pm.floatX([-.3, .5])\n",
    "sd = pm.floatX([.1, .1])\n",
    "with pm.Model() as model:\n",
    "    pm.NormalMixture('x', w=w, mu=mu, sd=sd)\n",
    "    approx = pm.fit(method=pm.SVGD(n_particles=200, jitter=1.))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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HG4YwESW86iY7ZIKA/MzoDmGzXoU0swY1zXaIoih1OTQBGMJElND8gSDq2nqRa+mffRzt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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11741a860>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure()\n",
    "trace = approx.sample(10000)\n",
    "sns.distplot(trace['x']);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "For more information on variational inference, see [these examples](http://pymc-devs.github.io/pymc3/examples.html#variational-inference)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 4. Posterior Predictive Sampling\n",
    "\n",
    "The `sample_ppc()` function performs prediction on hold-out data and posterior predictive checks."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Auto-assigning NUTS sampler...\n",
      "Initializing NUTS using jitter+adapt_diag...\n",
      " 97%|█████████▋| 968/1000 [00:01<00:00, 1050.37it/s]/Users/ferres/dev/pymc3/pymc3/step_methods/hmc/nuts.py:451: UserWarning: The acceptance probability in chain 0 does not match the target. It is 0.886449584522, but should be close to 0.8. Try to increase the number of tuning steps.\n",
      "  % (self._chain_id, mean_accept, target_accept))\n",
      "100%|██████████| 1000/1000 [00:01<00:00, 949.39it/s]\n"
     ]
    }
   ],
   "source": [
    "data = np.random.randn(100)\n",
    "with pm.Model() as model:\n",
    "    mu = pm.Normal('mu', mu=0, sd=1)\n",
    "    sd = pm.HalfNormal('sd', sd=1)\n",
    "    obs = pm.Normal('obs', mu=mu, sd=sd, observed=data)\n",
    "    \n",
    "    trace = pm.sample()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 500/500 [00:01<00:00, 484.68it/s]\n"
     ]
    }
   ],
   "source": [
    "with model:\n",
    "    post_pred = pm.sample_ppc(trace, samples=500, size=len(data))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "`sample_ppc()` returns a dict with a key for every observed node:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(500, 100)"
      ]
     },
     "execution_count": 48,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "post_pred['obs'].shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x11a8af940>"
      ]
     },
     "execution_count": 49,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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npUCt4rIkKWQl6+HximhsH96mHUTRjkWYIsanxydknRchZwaHo97rwjXNHJIm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\nRK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11a7ec630>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure()\n",
    "ax = sns.distplot(post_pred['obs'].mean(axis=1), label='Posterior predictive means')\n",
    "ax.axvline(data.mean(), color='r', ls='--', label='True mean')\n",
    "ax.legend()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 4.1 Predicting on hold-out data\n",
    "\n",
    "In many cases you want to predict on unseen / hold-out data. This is especially relevant in Probabilistic Machine Learning and Bayesian Deep Learning. While we plan to improve the API in this regard, this can currently be achieved with a `theano.shared` variable. These are theano tensors whose values can be changed later. Otherwise they can be passed into PyMC3 just like any other numpy array or tensor.\n",
    "\n",
    "This distinction is significant since internally all models in PyMC3 are giant symbolic expressions. When you pass data directly into a model, you are giving Theano permission to treat this data as a constant and optimize it away as it sees fit. If you need to change this data later you might not have a way to point at it in the symbolic expression. Using `theano.shared` offers a way to point to a place in that symbolic expression, and change what is there."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Auto-assigning NUTS sampler...\n",
      "Initializing NUTS using jitter+adapt_diag...\n",
      "100%|██████████| 1000/1000 [00:00<00:00, 1369.19it/s]\n"
     ]
    }
   ],
   "source": [
    "import theano\n",
    "\n",
    "x = np.random.randn(100)\n",
    "y = x > 0\n",
    "\n",
    "x_shared = theano.shared(x)\n",
    "y_shared = theano.shared(y)\n",
    "\n",
    "with pm.Model() as model:\n",
    "    coeff = pm.Normal('x', mu=0, sd=1)\n",
    "    logistic = pm.math.sigmoid(coeff * x_shared)\n",
    "    pm.Bernoulli('obs', p=logistic, observed=y_shared)\n",
    "    trace = pm.sample()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now assume we want to predict on unseen data. For this we have to change the values of `x_shared` and `y_shared`. Theoretically we don't need to set `y_shared` as we want to predict it but it has to match the shape of `x_shared`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 500/500 [00:01<00:00, 463.31it/s]\n"
     ]
    }
   ],
   "source": [
    "x_shared.set_value([-1, 0, 1.])\n",
    "y_shared.set_value([0, 0, 0]) # dummy values\n",
    "\n",
    "with model:\n",
    "    post_pred = pm.sample_ppc(trace, samples=500)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 0.026,  0.516,  0.966])"
      ]
     },
     "execution_count": 52,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "post_pred['obs'].mean(axis=0)"
   ]
  }
 ],
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