Markov chain Monte Carlo: How do you propose?

Speaker：Ziheng Yang

Title：Markov chain Monte Carlo: How do you propose?

Time&Venue：10:30-11:30, January 10, 2018

Abstract：Markov chain Monte Carlo has provided a computational tool for implementing sophisticated models in Bayesian inference.  The impact of the proposal kernel on the mixing efficiency of the chain is not well-studied.  We discuss a few principles to guide the design of efficient MCMC proposals for well-behaved target distributions without deeply divided peaks.  The first is to avoid positive correlation in the MCMC sample.  Thus the Gaussian random-walk is poorer than the uniform random walk, which is in turn poorer than Bactrian bimodal proposals, while the mirror move generates super efficiency as it actively introduces negative correlation.  The second principle is that a sequence of well-designed one-dimensional proposals can be more efficient than a single multi-dimensional proposal.  Thirdly, variable transform may be used as a general strategy for designing efficient MCMC algorithms.  When applied to challenging Bayesian inference problems, simple MCMC algorithms based on those ideas have higher or comparable efficiency than cutting-edge algorithms in the literature.