Efficient MCMC Schemes for Computationally Expensive Posterior Distributions

• Activity Number: 390
• Type: Invited
• Date/Time: Tuesday, August 2, 2011 : 2:00 PM to 3:50 PM
• Sponsor: Technometrics
• Author(s): David Nott*+ and Mark Fielding and Shie-Yui Liong
• Companies: National University of Singapore and University of Wollongong and National University of Singapore
• Keywords: Computer models ; Hybrid Monte Carlo ; Markov chain Monte Carlo ; Parallel tempering

Abstract

We consider Markov chain Monte Carlo (MCMC) computational schemes intended to minimize the number of evaluations of the posterior distribution in Bayesian inference when the posterior is computationally expensive to evaluate. Our motivation is Bayesian calibration of computationally expensive computer models. An algorithm suggested previously in the literature based on hybrid Monte Carlo and a Gaussian process approximation to the target distribution is extended in three ways. First, we consider combining the original method with tempering schemes. Second, we consider replacing the original target posterior distribution with the Gaussian process approximation, which requires less computation to evaluate. Third, we consider in the context of tempering schemes the replacement of the true target distribution with the approximation in the high temperature chains while retaining the true target in the lowest temperature chain. This retains the correct target distribution in the lowest temperature chain while avoiding the computational expense of running the computer model in moves involving the high temperatures.