pymc-submodels: Common Bayesian submodels for PyMC

:Author: Daniel E. Acuna [email protected] Copyright (c) 2010-2011 :URL: http://blog.principiapredictiva.com

Description

Common submodels used in Bayesian modeling, implemented in PyMC.

Contents

1. Truncated GEM distribution (sticks) for Dirichlet Process
2. Gaussian finite and infinite mixtures (based on truncated GEM distribution)

Example

Infinite mixture::

import numpy as np import pymc as pm from pymc_submodels import infty_mixture_model as imm

data = np.array([10., 11., 12., -10., -11., -12.])

Precision of Gaussian likelihood

tau_like = 0.5

Mean and precision of Gaussian base distribution

mu_base = 0. tau_base = 0.01

Concentration parameter of Dirichlet process

alpha = 1.

Construct model using pymc_submodels package

mdl = imm.model(data, tau_like, mu_base, tau_base, alpha)

Call PyMC

mcmc = pm.MCMC(mdl)

Sample

mcmc.sample(10000, 1000, 2)

Stochastic 'z' component membership of each data point

print np.mean(mcmc.trace('z')[:], 0)