Approximating Posterior Distributions by Mixtures

Authors: 
Mike West
Duke University

Nov 30 1989

Kernel density estimation techniques are used to smooth simulated samples form importance sampling functions approximations to posterior distributions, resulting in revised approximations that are mixtures of standard parametric forms, usually multivariate normal or T distributions. Adaptive refinement of such mixture approximations involves repeating this process to successively 'home-in' on the posterior. In fairly low dimensional problems, this provides a general and automatic method of approximating posteriors by mixtures so that marginal densities and other summaries may be easily computed. This is discussed and illustrated, with comment on variations and extensions suited to sequential Bayesian updating of Monte Carlo approximations, an area in which existing and alternative numerical methods are difficult to apply.

Keywords: 

Importance Sampling, Kernel Density Estimation, Mixture Distributions, Monte-Carlo Integration