Saturday, May 15

Combining Theory and Practice in Applications of Markov Chains

(Invited Minisymposium)

10:30 AM-12:30 PM
Room: Capitol South

Development of theory for the convergence of Markov chains has provided ways to improve efficiency of the Monte Carlo Markov Chain methodsused in statistics (through the Gibbs sampler for instance) and in physics (Ising model). However, monitoring the simulation's progress also provides insight into the behaviour of the chain. Combining these two types of information is the subject of this minisymposium. The speakers will present examples of applications to biology and physics where insight can be gained from both theory and practice. For instance one can do the beginning of a theoretical expansion and fill in some unkown parameters by their estimates. Or one can estimate the second eigenvalue of the Markov Chain transition matrix through a simulation run. This has already been put in practice for instance by using nonreversible versions of a chain that converge faster than the original one, this idea was inspired by practical work from chemistry simulations(hybrid Monte Carlo).

Organizer: Susan P. Holmes
Stanford University

10:30-10:55 Combining Theoretical and Simulation-Based Insight in Monte Carlo Markov Chains
Susan P. Holmes, Organizer
11:00-11:25 UpdatedPerfect Sampling with Markov Chains
Mark L. Huber, Cornell University
11:30-11:55 NewA Generalization of the Gibbs Sampler
Chiara Sabatti and Jun S. Liu, Stanford University
12:00-12:25 NewMarkov Chain Monte Carlo for Multidimensional Contingency Tables
Florentina Bunea and Julian Besag, University of Washington

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tjf, 1/20/99, MMD, 3/25/99