Add sample_prior function

RELEASE-NOTES.md

@@ -11,8 +11,7 @@
   Gaussian Process implementation for efficient inference, along with
   lower-level functions such as `cartesian` and `kronecker` products.
 - Added `Coregion` covariance function.
-- Add new 'pairplot' function, for plotting scatter or hexbin matrices of sampled parameters.
-  Optionally it can plot divergences.
+- Add new 'pairplot' function, for plotting scatter or hexbin matrices of sampled parameters. Optionally it can plot divergences.
 - Plots of discrete distributions in the docstrings
 - Add logitnormal distribution
 - Densityplot: add support for discrete variables
@@ -21,6 +20,7 @@
 - Changed the `compare` function to accept a dictionary of model-trace pairs instead of two separate lists of models and traces.
 - add test and support for creating multivariate mixture and mixture of mixtures
 - `distribution.draw_values`, now is also able to draw values from conditionally dependent RVs, such as autotransformed RVs (Refer to PR #2902).
+- New function `pm.sample_prior` which generates test data from a model in the absence of data.
 
 ### Fixes
 

pymc3/distributions/distribution.py

@@ -210,7 +210,7 @@ def random(self, *args, **kwargs):
 
 
 
-def draw_values(params, point=None):
+def draw_values(params, point=None, size=None):
     """
     Draw (fix) parameter values. Handles a number of cases:
 
@@ -254,7 +254,7 @@ def draw_values(params, point=None):
 
     # Init givens and the stack of nodes to try to `_draw_value` from
     givens = {}
-    stored = set([])  # Some nodes 
+    stored = set()  # Some nodes 
     stack = list(leaf_nodes.values())  # A queue would be more appropriate
     while stack:
         next_ = stack.pop(0)
@@ -279,13 +279,14 @@ def draw_values(params, point=None):
             # The named node's children givens values must also be taken
             # into account.
             children = named_nodes_children[next_]
-            temp_givens = [givens[k] for k in givens.keys() if k in children]
+            temp_givens = [givens[k] for k in givens if k in children]
             try:
                 # This may fail for autotransformed RVs, which don't
                 # have the random method
                 givens[next_.name] = (next_, _draw_value(next_,
                                                          point=point,
-                                                         givens=temp_givens))
+                                                         givens=temp_givens,
+                                                         size=size))
                 stored.add(next_.name)
             except theano.gof.fg.MissingInputError:
                 # The node failed, so we must add the node's parents to
@@ -295,10 +296,27 @@ def draw_values(params, point=None):
                               if node is not None and
                               node.name not in stored and
                               node not in params])
-    values = []
-    for param in params:
-        values.append(_draw_value(param, point=point, givens=givens.values()))
-    return values
+
+    # Funny dance to resolve missing nodes
+    params = dict(enumerate(params))  # some nodes are not hashable
+    evaluated = {}
+    to_eval = set()
+    missing_inputs = set(params)
+    while to_eval or missing_inputs:
+        if to_eval == missing_inputs:
+            raise ValueError('Cannot resolve inputs for {}'.format([str(params[j]) for j in to_eval]))
+        to_eval = set(missing_inputs)
+        missing_inputs = set()
+        for param in to_eval:
+            try:  # might evaluate in a bad order,
+                evaluated[param] = _draw_value(params[param], point=point, givens=givens.values(), size=size)
+                if any(params[param] in j for j in named_nodes_children.values()):
+                    givens[params[param].name] = (params[param], evaluated[param])
+            except theano.gof.fg.MissingInputError:
+                missing_inputs.add(param)
+
+
+    return [evaluated[j] for j in params] # set the order back
 
 
 @memoize
@@ -326,7 +344,7 @@ def _compile_theano_function(param, vars, givens=None):
                     allow_input_downcast=True)
 
 
-def _draw_value(param, point=None, givens=None):
+def _draw_value(param, point=None, givens=None, size=None):
     """Draw a random value from a distribution or return a constant.
 
     Parameters
@@ -355,14 +373,19 @@ def _draw_value(param, point=None, givens=None):
         if point and hasattr(param, 'model') and param.name in point:
             return point[param.name]
         elif hasattr(param, 'random') and param.random is not None:
-            return param.random(point=point, size=None)
+            return param.random(point=point, size=size)
+        elif hasattr(param, 'distribution') and hasattr(param.distribution, 'random') and param.distribution.random is not None:
+            return param.distribution.random(point=point, size=size)
         else:
             if givens:
                 variables, values = list(zip(*givens))
             else:
                 variables = values = []
             func = _compile_theano_function(param, variables)
-            return func(*values)
+            if size is None:
+                return func(*values)
+            else:
+                return np.array([func(*value) for value in zip(*values)])
     else:
         raise ValueError('Unexpected type in draw_value: %s' % type(param))
 

pymc3/sampling.py

@@ -11,11 +11,12 @@
 
 from .backends.base import BaseTrace, MultiTrace
 from .backends.ndarray import NDArray
+from .distributions import draw_values
 from .model import modelcontext, Point, all_continuous
 from .step_methods import (NUTS, HamiltonianMC, Metropolis, BinaryMetropolis,
                            BinaryGibbsMetropolis, CategoricalGibbsMetropolis,
                            Slice, CompoundStep, arraystep)
-from .util import update_start_vals
+from .util import update_start_vals, is_transformed_name, get_untransformed_name, get_default_varnames
 from .vartypes import discrete_types
 from pymc3.step_methods.hmc import quadpotential
 from pymc3 import plots
@@ -25,7 +26,7 @@
 import sys
 sys.setrecursionlimit(10000)
 
-__all__ = ['sample', 'iter_sample', 'sample_ppc', 'sample_ppc_w', 'init_nuts']
+__all__ = ['sample', 'iter_sample', 'sample_ppc', 'sample_ppc_w', 'init_nuts', 'sample_generative']
 
 STEP_METHODS = (NUTS, HamiltonianMC, Metropolis, BinaryMetropolis,
                 BinaryGibbsMetropolis, Slice, CategoricalGibbsMetropolis)
@@ -1206,6 +1207,50 @@ def sample_ppc_w(traces, samples=None, models=None, weights=None,
     return {k: np.asarray(v) for k, v in ppc.items()}
 
 
+def sample_generative(samples=500, model=None, vars=None, random_seed=None):
+    """Generate samples from the generative model.
+
+    Parameters
+    ----------
+    samples : int
+        Number of samples from the prior to generate. Defaults to 500.
+    model : Model (optional if in `with` context)
+    vars : iterable
+        Variables for which to compute the posterior predictive samples.
+        Defaults to `model.named_vars`.
+    random_seed : int
+        Seed for the random number generator.
+
+    Returns
+    -------
+    dict
+        Dictionary with the variables as keys. The values are arrays of prior samples.
+    """
+    model = modelcontext(model)
+
+    if vars is None:
+        vars = set(model.named_vars.keys())
+
+    if random_seed is not None:
+        np.random.seed(random_seed)
+
+    names = get_default_varnames(model.named_vars, include_transformed=False)
+    # draw_values fails with auto-transformed variables. transform them later!
+    values = draw_values([model[name] for name in names], size=samples)
+
+    data = {k: v for k, v in zip(names, values)}
+
+    prior = {}
+    for var_name in vars:
+        if var_name in data:
+            prior[var_name] = data[var_name]
+        elif is_transformed_name(var_name):
+            untransformed = get_untransformed_name(var_name)
+            if untransformed in data:
+                prior[var_name] = model[untransformed].transformation.forward(data[untransformed]).eval()
+    return prior
+
+
 def init_nuts(init='auto', chains=1, n_init=500000, model=None,
               random_seed=None, progressbar=True, **kwargs):
     """Set up the mass matrix initialization for NUTS.

pymc3/tests/test_sampling.py

@@ -302,3 +302,17 @@ def test_exec_nuts_init(method):
         assert len(start) == 2
         assert isinstance(start[0], dict)
         assert 'a' in start[0] and 'b_log__' in start[0]
+
+
+def test_sample_generative():
+    observed = np.random.normal(10, 1, size=200)
+    with pm.Model():
+        # Use a prior that's way off to show we're actually sampling from it
+        mu = pm.Normal('mu', mu=-10, sd=1)
+        positive_mu = pm.Deterministic('positive_mu', np.abs(mu))
+        pm.Normal('x_obs', mu=mu, sd=1, observed=observed)
+        prior = pm.sample_generative()
+
+    assert (prior['mu'] < 0).all()
+    assert (prior['positive_mu'] > 0).all()
+    assert (prior['x_obs'] < 0).all()