All Times EDT
Keywords: MCMC, Markov chain Monte Carlo, Adaptation, Metropolis algorithm, Gibbs sampler
Markov chain Monte Carlo (MCMC) algorithms, such as the Metropolis Algorithm and the Gibbs Sampler, are an extremely useful and popular method of approximately sampling from complicated probability distributions. Adaptive MCMC attempts to automatically modify the algorithm while it runs, to improve its performance on the fly. However, such adaptation often destroys the ergodicity properties necessary for the algorithm to be valid. In this talk, we first illustrate MCMC algorithms using simple graphical examples. We then discuss adaptive MCMC, and present examples and theorems concerning its ergodicity and efficiency.