To represent the prior, you need an instance of the Stochastic class, which has two primary attributes:
value : the variable's current value
logp : the log probability of the variable's current value given the values of its parents
You can initialize a prior with the name of the distribution you are using.
To represent the likelihood, you need a so-called Data Stochastic. That is, an instance of class Stochastic whose observed
flag is set to True
. The value of this variable cannot be changed and it will not be sampled. Again, you can initialize the likelihood with the name of the distribution you are using (but don't forget to set the observed
flag to True
).
Say we have the following setup:
import pymc as pm
import numpy as np
import theano.tensor as t
x = np.array([1,2,3,4,5,6])
y = np.array([0,1,0,1,1,1])
We can run a simple logistic regression with the following:
with pm.Model() as model:
#Priors
b0 = pm.Normal("b0", mu=0, tau=1e-6)
b1 = pm.Normal("b1", mu=0, tau=1e-6)
#Likelihood
z = b0 + b1 * x
yhat = pm.Bernoulli("yhat", 1 / (1 + t.exp(-z)), observed=y)
# Sample from the posterior
trace = pm.sample(10000, pm.Metropolis())
Most of the above came from Chris Fonnesbeck's iPython notebook here.