Seminars: Dept Seminar
Monte Carlo Methods for Improper Target Distributions
Monte Carlo methods for estimating means with respect to a proper target distribution (that is, a probability distribution) are well developed in the statistics literature. In this talk, Monte Carlo methods are considered that work for any (proper or improper) target distribution. It can be shown that when the target is improper, the standard "time average" Markov chain Monte Carlo (MCMC) estimator based on a Harris recurrent Markov chain converges to zero almost surely and hence is not appropriate. In this presentation, several algorithms are considered that can be used when the target is proper or improper. Some relevant limit theorems are proved. Applications of this to Gibbs sampler, importance sampling and MCMC for Bayesian inference are discussed.
(This is a joint work with Krishna Athreya.)