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Monte Carlo methods have been crucial in many scientific endeavors, ranging from physics to biochemistry, and have recently become very popular in the statistics community. Both Markov chain Monte Carlo (MCMC) and sequential Monte Carlo (SMC) techniques will be discussed with an emphasis on their applications in bioinformatics. The presenter will explain the idea of Metropolis et al. (1953) and its close "cousin" Gibbs sampling, which are fundamental rules for constructing a Markov chain whose equilibrium distribution is the one prescribed in advance. Then the presenter will focus on some advanced ideas such as parallel tempering, multigrid Monte Carlo (MGMC), evolutionary Monte Carlo, etc. These ideas aim at constructing Markov chains with better mixing properties and are very helpful in many practical problems. The presenter will also describe SMC techniques, whose basic idea is to construct a sampling distribution sequentially and to use resampling (or pruning and splitting) to further improve the method. They are often known in the engineering and statistics literature as the "bootstrap filter", the "particle filter", etc., and in the biophysics literature as the Rosenbluth method. These ideas are particularly attractive for dealing with dynamic structures, such as the nonlinear state-space models and molecular structure prediction. The presenter will describe applications of these Monte Carlo techniques in both statistical and bioinformatic problems such as nonlinear filtering, variable selection, contingency table analysis, gene regulatory analysis, inference of differentially expressed genes, and biopolymer structure optimization. OPTIONAL TEXTBOOK AVAILABLE
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= Applied Session,
= Theme Session,
= Presenter