MCMC: Does It Work? How Can We Tell?

• Activity Number: 452
• Type: Invited
• Date/Time: Wednesday, August 5, 2009 : 10:30 AM to 12:20 PM
• Sponsor: IMS
• Author(s): Charles J. Geyer*+
• Companies: The University of Minnesota
• Keywords: Markov chain Monte Carlo ; programming ; convergence ; diagnostics

Abstract

Markov chain Monte Carlo (MCMC) is the only method that perhaps works for many complicated problems, but in practice it has two severe difficulties. When the only thing known about a probability distribution is what one learns from an MCMC sampler that purports to sample that distribution, it is very difficult to debug or validate the sampler and very difficult to know how long to run the sampler. In practice, most samplers are so complicated that theorems about convergence do not apply or do not give useful information. Much of the literature discusses toy problems for which a few thousand iterations suffice. In real applications, billions of iterations may not be enough. We provide some help with the debugging issue, giving guidelines for writing MCMC code. We can provide only negative information about diagnostics. Other than perfect sampling, no valid MCMC diagnostics exist.