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Colloquium - 15 Oct 1998

Department of Statistics
Texas A&M University

ABSTRACT: The Metropolis algorithm provides a scheme for simulating a Markov chain whose long-run frequencies match a desired distribution, when this distribution is known only up to a proportionality constant. In many applications, particularly in statistical physics, there are states of high probability separated by large sets of states which have low probability, which can cause the Metropolis algorithm to converge to the correct distribution far too slowly to provide sufficient precision in reasonable run-times. Importance-weighted [non-Boltzmann] Metropolis can be used to great advantage in these cases. By adding a simple bookkeeping step to the algorithm, greater information can be extracted from the dynamics of the chain. This information provides unbiased estimators of canonical [Boltzmann] transition probabilities (CTPs), which can be used to estimate the desired distribution. These CTPs are de-coupled from the importance weights, allowing adaptivity of importance weights and extrapolation to other reference distributions [temperatures]. In addition, CTPs improve parallelization and reduce the variance of estimates of system properties.

Refreshments will be served in the Blocker Building, Room 447, at 3:30 p.m.

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