Example of using pymc to display and fit a graphical model

PymcGraphExample.py

from numpy import sqrt,exp,log,pi
import numpy as np
import pymc

#Example script showing how to fit 


#Generate some fake data to fit.
#Use fixed mean and variance
true_mu = 2.4
true_sigma = 0.7
N = 100
observations = np.random.randn(N)*true_sigma + true_mu


#Generate the PyMC nodes (random variables).
#The first two declare only the priors.
#The last gives the dependence of the probability on the parents
#and sets the observed value - this is the data.
mu = pymc.Uniform('mu',lower=-5,upper=5)
sigma = pymc.Uniform('sigma',lower=0.01,upper=2.0)
P = pymc.Normal('Observed Samples', mu=mu, tau=sigma**-2, value=observations, observed=True)

#Build a model out of these three variables
model = pymc.Model([mu,sigma,P])


#Make a slightly pretty graph out of it
graph = pymc.graph.graph(model)
graph.write_png("graph.png")

#Get the maximum posterior fit to the model
#We could also sample in various ways and do other things with it instead.
fitter = pymc.MAP(model)
fitter.fit()
print "Maximum posterior mu = ", mu.value
print "Maximum posterior sigma = ", sigma.value