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\centerline{\bf STANFORD UNIVERSITY}
\centerline{\bf DEPARTMENT OF STATISTICS}
\centerline{\bf MONTE CARLO MARKOV CHAINS IN SCIENTIFIC COMPUTING}
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\centerline{3:15 p.m., Thursday, October 12, 2000}
\centerline{Sequoia Hall Rm. 200}

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\centerline{\sl Mark Huber}
\centerline{\sl Operations Research}
\centerline{\sl Cornell University}
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\centerline{\bf Building a better Metropolis sampler}
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The vanilla Metropolis approach to creating Markov chains for sampling from
high dimensional distributions has been enormously successful.  Here we
examine methods for speeding up Metropolis for some classes of chains.
Many distributions of interest have a parameter such as temperature
governing the behavior of samples.  The omnithermal technique, developed by
Grimmett and applied more generally by Propp and Wilson, allows
samples to be taken simultaneously from all values of the temperature
parameter under a monotonicity condition satisfied by models such as the
ferromagnetic Ising and random cluster models.  Liu, Liang, and Wong have
proposed the Multiple Try Method (MTM), a version of Metropolis where it
becomes easier to specify proposal directions.  This can be combined with
local optimization techniques such as conjugate gradient for choosing
directions. For small multimodal problems numerical results indicate that
this approach
mixes faster than the straightforward Metropolis.

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