Dawn Woodard
Department of Statistical Science
Duke University
"Bayesian Computation for Multimodal Posterior Distributions"
3:00 Refreshments in 241 Schaeffer Hall
3:30 Talk in 1505 Seamans Center
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, high-dimensional distributions; we address the extent to which this holds.
We obtain general bounds on the convergence rate of PT and ST. We apply these to evaluate the running time of PT and ST as a function of the parameter dimension, for multimodal examples including several normal mixture and discrete Markov random field distributions. We categorize the distributions into those for which PT and ST are rapidly mixing, meaning that the running time increases polynomially in the parameter dimension, and those for which PT and ST are torpidly mixing, meaning that the running time increases exponentially.
