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 Java applets. We then discuss adaptive MCMC, and present examples and theorems concerning its ergodicity and efficiency.

Jeffrey Rosenthal is a professor of Statistics at the University of Toronto. He received his PhD from Harvard University in 1992. He was awarded the CRM-SSC Prize in 2006, the COPSS Presidents' Award in 2007, and teaching awards in 1991 and 1998. His book for the general public, Struck by Lightning: The Curious World of Probabilities, was published in sixteen editions and ten languages, and was a bestseller in Canada. His web site is www.probability.ca, and on Twitter he is @ProbabilityProf.