Computing normalizing constants: A bridge between Statistical Physics and Statistical Computing
Markov Chains in Algorithms and Statistical Physics
February 01, 2005 04:30 PM to 05:30 PM
Speakers:
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Abstract: |
Computing normalizing constants, known as partition functions in
statistical physics, is a fundamental computational problem in
statistics and in scientific studies in general. In this talk I will
provide an overview of some Monte Carlo methods developed in
statistics, namely, bridge sampling, path sampling, and warp bridge
sampling, during the past decade or so, and show their close
connections with several well-known methods in statistical physics,
namely acceptance ratio method, thermodynamic integration, and Voter's
displacement method. A theoretical framework is provided to show how
all these methods can be viewed as building bridge/overlap between
underlying probability densities or configuration spaces. The emphasis
will be on further development of warp bridge sampling, which aims to
improve Monte Carlo efficiency by warping geometrical shapes of the
underlying densities, and hence increasing their overlap, without
altering their normalizing constants. |
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