Convergence of Parallel and Simulated Tempering on Multimodal Distributions

Dawn Woodard
Department of Statistics
Duke University
ABSTRACT:
Sampling methods such as Markov chain Monte Carlo are ubiquitous in Bayesian statistics, statistical mechanics, and theoretical computer science. However, when the distribution being sampled is multimodal many of these techniques require long running times to obtain reliable answers. In statistics, multimodal posterior distributions arise in model selection problems, mixture models, and change point models among others. Parallel and simulated tempering (PT and ST) are Markov chain methods that are designed to sample efficiently from multimodal distributions; we address the extent to which this holds.