Stratification and Markov chain Monte Carlo
In stratified survey sampling, one divides a population into homogeneous subgroups and then draws samples from each subgroup independently. Stratification often permits accurate computation of statistics from a sample much smaller than required otherwise. One can stratify Markov chain Monte Carlo (MCMC) simulations as well as surveys. This idea arose in computational statistical physics, and stratified MCMC has been instrumental in resolving important questions related to ion channels and protein folding. I will explain how to use stratified MCMC for a broader class of problems, including both the computation of averages with respect to an arbitrary target distribution and the computation of dynamical quantities such as rates of chemical reactions. I will then present theoretical results and numerical experiments which demonstrate the advantages of stratified MCMC. In addition to explaining the successes of stratified MCMC in statistical physics, I will show that stratification enables the efficient computation of tail probabilities and that it may be applied to computational problems in statistics.