Metropolis-Hastings algorithms with adaptive proposals
by
Bo Cai
University of Auckland
Coauthors: Renate Meyer (University of Auckland), Francois Perron (University of Montreal)

Monte Carlo methods are fundamental tools of computational statistics. In modern Bayesian inference, for instance, sampling from the posterior distribution and computing posterior quantities of interest are the two main tasks. For sampling from high-dimensional distributions, Markov chain Monte Carlo (MCMC) techniques have been developed. By regarding the distribution of interest as the stationary distribution of a Markov chain, relevant samples from this distribution can be generated through simulating the Markov chain. The Gibbs sampler is a specific MCMC technique that generates from the joint multidimensional distribution by generating from univariate full conditional distributions in a cyclic way. A general purpose method (ARMS) to sample from any univariate density was proposed by Gilks et al.(1995), combining a derivative-free method of adaptive rejection sampling with the Metropolis-Hastings algorithm. Although ARMS is a very efficient general sampling algorithm for sampling from univariate distributions, some potential weaknesses should be noticed. We discuss two new general random number generation algorithms based on Markov chains and compare them with ARMS.

Date received: May 26, 2002

Copyright © 2002 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cajj-13.