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 Perfect Sampling with Markov Chains**- Mark L. Huber, Cornell University
**11:30-11:55 A Generalization of the Gibbs Sampler***Chiara Sabatti*and Jun S. Liu, Stanford University**12:00-12:25 Markov Chain Monte Carlo for Multidimensional Contingency Tables**

*Florentina Bunea*and Julian Besag, University of Washington

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