Merge pull request #1546 from usptact/master

Adding hierarhical partial pooling example

Author: fonnesbeck

.gitignore

@@ -23,4 +23,4 @@ _build
 mcmc.sqlite
 
 # Docker development
-notebooks/
+#notebooks/

docs/source/notebooks/hierarchical_partial_pooling.ipynb

@@ -0,0 +1,37 @@
+#
+# Demonstrates the usage of hierarchical partial pooling
+# See http://mc-stan.org/documentation/case-studies/pool-binary-trials.html for more details
+#
+
+import pymc3 as pm
+import numpy as np
+
+data = np.loadtxt( 'data/efron-morris-75-data.tsv', delimiter="\t", skiprows=1, usecols=(2,3) )
+
+atBats = data[:,0]
+hits = data[:,1]
+
+N = len( hits )
+
+model = pm.Model()
+
+# we want to bound the kappa below
+BoundedKappa = pm.Bound( pm.Pareto, lower=1.0 )
+
+with model:
+    phi = pm.Uniform( 'phi', lower=0.0, upper=1.0 )
+    kappa = BoundedKappa( 'kappa', alpha=1.0001, m=1.5 )
+    thetas = pm.Beta( 'thetas', alpha=phi*kappa, beta=(1.0-phi)*kappa, shape=N )
+    ys = pm.Binomial( 'ys', n=atBats, p=thetas, observed=hits )
+
+def run( n=100000 ):
+    with model:
+        # initialize NUTS() with ADVI under the hood
+        trace = pm.sample( n )
+
+    # drop some first samples as burnin
+    pm.traceplot( trace[1000:] )
+
+if __name__ == '__main__':
+    run()
+

pymc3/examples/baseball.py

@@ -0,0 +1,19 @@
+FirstName	LastName	At-Bats	Hits	BattingAverage	RemainingAt-Bats	RemainingAverage	SeasonAt-Bats	SeasonHits	SeasonAverage
+Roberto	Clemente	45	18	0.4	367	0.346	412	145	0.352
+Frank	Robinson	45	17	0.378	426	0.2981	471	144	0.306
+Frank	Howard	45	16	0.356	521	0.2764	566	160	0.283
+Jay	Johnstone	45	15	0.333	275	0.2218	320	76	0.238
+Ken	Berry	45	14	0.311	418	0.2727	463	128	0.276
+Jim	Spencer	45	14	0.311	466	0.2704	511	140	0.274
+Don	Kessinger	45	13	0.289	586	0.2645	631	168	0.266
+Luis	Alvarado	45	12	0.267	138	0.2101	183	41	0.224
+Ron	Santo	45	11	0.244	510	0.2686	555	148	0.267
+Ron	Swaboda	45	11	0.244	200	0.23	245	57	0.233
+Rico	Petrocelli	45	10	0.222	538	0.2639	583	152	0.261
+Ellie	Rodriguez	45	10	0.222	186	0.2258	231	52	0.225
+George	Scott	45	10	0.222	435	0.3034	480	142	0.296
+Del	Unser	45	10	0.222	277	0.2635	322	83	0.258
+Billy	Williams	45	10	0.222	591	0.3299	636	205	0.251
+Bert	Campaneris	45	9	0.2	558	0.2849	603	168	0.279
+Thurman	Munson	45	8	0.178	408	0.3162	453	137	0.302
+Max	Alvis	45	7	0.156	70	0.2	115	21	0.183