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"Adaptive MCMC For Everyone"
Jeffrey Rosenthal, University of Toronto
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. We close with
some recent ideas which make adaptive MCMC more widely applicable
in broader contexts.