How does pymc represent the prior distribution and likelihood function?

To represent the prior, you need an instance of the Stochastic class, which has two primary attributes:

value : the variable's current valuelogp : 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 pmimport numpy as npimport theano.tensor as tx = 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.