A General MCMC Method for Bayesian Inference in Logic-Based Probabilistic Modeling

Taisuke Sato

Abstract: We propose a generalMCMC method for Bayesian inference in logic-based probabilistic modeling. It covers a broad class of generativemodels including Bayesian networks and PCFGs. The idea is to generalize an MCMC method for PCFGs to the one for a Turing-complete probabilistic modeling language PRISM in the context of statistical abduction where parse trees are replaced with explanations. We describe how to estimate the marginal probability of data from MCMC samples and how to perform Bayesian Viterbi inference using an example of Naive Bayesmodel augmentedwith a hidden variable.