Markov Chain Monte Carlo with Linchpin Variables

• Activity Number: 376
• Type: Contributed
• Date/Time: Tuesday, August 6, 2013 : 10:30 AM to 12:20 PM
• Sponsor: Section on Statistical Computing
• Author(s): Felipe Acosta Archila*+ and Galin Jones
• Companies: University of Minnesota and University of Minnesota
• Keywords: MCMC ; Bayesian ; GLMM

Abstract

Markov chain Monte Carlo methods provide a useful way to explore the space of distributions that otherwise are intractable. For a two variable joint distribution we propose a MCMC method in which we use a Metropolis-Hastings step on the marginal distribution of one of the variables to then sample from the conditional distribution of the other variable. We show that qualitative results from the joint chain can be derived from the subchain where the Metropolis-Hastings step is being performed. As an example we apply the method to a Bayesian hierarchical linear model and show that it yields a uniformly ergodic Markov chain which offers a qualitative improvement from the more often used Gibbs sampler which usually has a geometrically ergodic convergence rate.