Arbitrary deterministic function added. (#2514)

* Arbitray deterministic function added.

* Typo fixed (\mu insted of \eta)

* Typo fixed (nu instead of mu)

* Added sensible default value for eps in stick_breaking transform

* add stacking and bb-pseudo-bma to the docs (#2512)

* add stacking and bb-pseudo-bma to the docs

* fix typo

* fix typo

* Created disaster_model.py example file

* Rename disaster_model_arbitrary_deterministic.py to disaster_model_theano_op.py

* Update getting_started.ipynb

Replace PyMC with PyMC3.
Replace the hyperlink to https://github.com/pymc-devs/pymc3/blob/master/pymc3/examples/disaster_model_arbitrary_deterministic.py with https://github.com/pymc-devs/pymc3/blob/master/pymc3/examples/disaster_model_theano_op.py

* Converted eps value to floatX fixes test failures of #2515 and lowered precision requirements for test_transforms on float32 machines (#2517)

* Arbitray deterministic function added.

* Typo fixed (\mu insted of \eta)

* Typo fixed (nu instead of mu)

* Created disaster_model.py example file

* Rename disaster_model_arbitrary_deterministic.py to disaster_model_theano_op.py

* Update getting_started.ipynb

Replace PyMC with PyMC3.
Replace the hyperlink to https://github.com/pymc-devs/pymc3/blob/master/pymc3/examples/disaster_model_arbitrary_deterministic.py with https://github.com/pymc-devs/pymc3/blob/master/pymc3/examples/disaster_model_theano_op.py

Author: mcavallaro

docs/source/notebooks/BEST.ipynb

@@ -160,7 +160,7 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "We follow Kruschke by making the prior for $\\mu$ exponentially distributed with a mean of 30; this allocates high prior probability over the regions of the parameter that describe the range from normal to heavy-tailed data under the Student-T distribution."
+    "We follow Kruschke by making the prior for $\\nu$ exponentially distributed with a mean of 30; this allocates high prior probability over the regions of the parameter that describe the range from normal to heavy-tailed data under the Student-T distribution."
    ]
   },
   {

docs/source/notebooks/getting_started.ipynb

@@ -1113,7 +1113,7 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "An important drawback of this approach is that it is not possible for `theano` to inspect these functions in order to compute the gradient required for the Hamiltonian-based samplers. Therefore, it is not possible to use the HMC or NUTS samplers for a model that uses such an operator. However, it is possible to add a gradient if we inherit from `theano.Op` instead of using `as_op`. The PyMC example set includes [a more elaborate example of the usage of as_op](https://github.com/pymc-devs/pymc3/blob/master/pymc3/examples/disaster_model_arbitrary_deterministic.py)."
+    "An important drawback of this approach is that it is not possible for `theano` to inspect these functions in order to compute the gradient required for the Hamiltonian-based samplers. Therefore, it is not possible to use the HMC or NUTS samplers for a model that uses such an operator. However, it is possible to add a gradient if we inherit from `theano.Op` instead of using `as_op`. The PyMC example set includes [a more elaborate example of the usage of as_op](https://github.com/pymc-devs/pymc3/blob/master/pymc3/examples/disaster_model_theano_op.py)."
    ]
   },
   {
@@ -1122,7 +1122,7 @@
    "source": [
     "## Arbitrary distributions\n",
     "\n",
-    "Similarly, the library of statistical distributions in PyMC3 is not exhaustive, but PyMC allows for the creation of user-defined functions for an arbitrary probability distribution. For simple statistical distributions, the `DensityDist` function takes as an argument any function that calculates a log-probability $log(p(x))$. This function may employ other random variables in its calculation. Here is an example inspired by a blog post by Jake Vanderplas on which priors to use for a linear regression (Vanderplas, 2014). \n",
+    "Similarly, the library of statistical distributions in PyMC3 is not exhaustive, but PyMC3 allows for the creation of user-defined functions for an arbitrary probability distribution. For simple statistical distributions, the `DensityDist` function takes as an argument any function that calculates a log-probability $log(p(x))$. This function may employ other random variables in its calculation. Here is an example inspired by a blog post by Jake Vanderplas on which priors to use for a linear regression (Vanderplas, 2014). \n",
     "\n",
     "```python\n",
     "import theano.tensor as tt\n",

pymc3/examples/disaster_model.py

@@ -0,0 +1,47 @@
+"""
+A model for the disasters data with a changepoint
+
+changepoint ~ U(1851, 1962)
+early_mean ~ Exp(1.)
+late_mean ~ Exp(1.)
+disasters[t] ~ Poi(early_mean if t <= switchpoint, late_mean otherwise)
+
+"""
+
+
+import pymc3 as pm
+import theano.tensor as tt
+from numpy import arange, array
+
+
+__all__ = ['disasters_data', 'switchpoint', 'early_mean', 'late_mean', 'rate',
+           'disasters']
+
+
+# Time series of recorded coal mining disasters in the UK from 1851 to 1962
+disasters_data = array([4, 5, 4, 0, 1, 4, 3, 4, 0, 6, 3, 3, 4, 0, 2, 6,
+                        3, 3, 5, 4, 5, 3, 1, 4, 4, 1, 5, 5, 3, 4, 2, 5,
+                        2, 2, 3, 4, 2, 1, 3, 2, 2, 1, 1, 1, 1, 3, 0, 0,
+                        1, 0, 1, 1, 0, 0, 3, 1, 0, 3, 2, 2, 0, 1, 1, 1,
+                        0, 1, 0, 1, 0, 0, 0, 2, 1, 0, 0, 0, 1, 1, 0, 2,
+                        3, 3, 1, 1, 2, 1, 1, 1, 1, 2, 4, 2, 0, 0, 1, 4,
+                        0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 1])
+year = arange(1851, 1962)
+
+with pm.Model() as model:
+
+    switchpoint = pm.DiscreteUniform('switchpoint', lower=year.min(), upper=year.max())
+    early_mean = pm.Exponential('early_mean', lam=1.)
+    late_mean = pm.Exponential('late_mean', lam=1.)
+
+    # Allocate appropriate Poisson rates to years before and after current
+    # switchpoint location
+    rate = tt.switch(switchpoint >= year, early_mean, late_mean)
+    
+    disasters = pm.Poisson('disasters', rate, observed=disasters_data)
+
+    # Initial values for stochastic nodes
+    start = {'early_mean': 2., 'late_mean': 3.}
+    
+    tr = pm.sample(1000, tune=500, start=start)
+    pm.traceplot(tr)

pymc3/examples/disaster_model_arbitrary_deterministic.py renamed to pymc3/examples/disaster_model_theano_op.py

@@ -7,7 +7,7 @@
 
 import pymc3 as pm
 import theano.tensor as tt
-from numpy import arange, array
+from numpy import arange, array, empty
 
 __all__ = ['disasters_data', 'switchpoint', 'early_mean', 'late_mean', 'rate',
            'disasters']
@@ -22,6 +22,15 @@
                         0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 1])
 years = len(disasters_data)
 
+
+@as_op(itypes=[tt.lscalar, tt.dscalar, tt.dscalar], otypes=[tt.dvector])
+def rate_(switchpoint, early_mean, late_mean):
+    out = empty(years)
+    out[:switchpoint] = early_mean
+    out[switchpoint:] = late_mean
+    return out
+
+
 with pm.Model() as model:
 
     # Prior for distribution of switchpoint location
@@ -33,8 +42,8 @@
     # Allocate appropriate Poisson rates to years before and after current
     # switchpoint location
     idx = arange(years)
-    rate = tt.switch(switchpoint >= idx, early_mean, late_mean)
-    
+    rate = rate_(switchpoint, early_mean, late_mean)
+
     # Data likelihood
     disasters = pm.Poisson('disasters', rate, observed=disasters_data)