Jeffrey Rosenthal - The mathematics of Markov chain Monte Carlo algorithms

Markov chain Monte Carlo ( MCMC) algorithms, such as the Gibbs sampler and the Metropolis-Hastings algorithm, are now widely used in statistics, computer science, physics, and chemistry to understand complicated probability distributions. While the implementation of these algorithms is often routine, many fundamental questions--such as convergence rates--are much more difficult. In this talk, we will review some of these issues and the partial progress that has been made towards resolving them.