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Abstract:
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Markov chain Monte Carlo (MCMC) algorithms provide a very general recipe for estimating properties of complicated distributions. While their use has become commonplace, users have several difficult and time consuming decisions to make: how to construct a good algorithm, deciding whether an MCMC algorithm is producing accurate estimates, and determining an appropriate length (stopping rule) for the Markov chain. I will describe some approaches for automating these decisions in the context of spatial generalized linear models, an important class of models that result in challenging posterior distributions. These approaches combine analytical approximations for constructing provably fast mixing MCMC algorithms and take advantage of innovations in modern parallel computing capabilities. I will describe the application of these algorithms to several models and data sets.
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