Thermodynamic Integration and Path Sampling: Abstract
July 6, 1998
Statistical Engineering Division
Thermodynamic Integration and Path Sampling
Xiao-Li Meng
Department of Statistics
The University of Chicago
Thermodynamic Integration (TI) is a powerful and thus popular method
in statistical physics for computing absolute free energies and
free-energy differences via Markov chain Monte Carlo. Path sampling
(Gelman and Meng, Statistical Science, 1998) is a
general formulation of TI with the introduction of flexible path along
which the integration will be made. The method also includes
Ogata's method for very high dimension (e.g., 1,000) integrations.
This talk provides a general overview of path sampling with both theoretical
and empirical investigation. We present some general
theory regarding the optimal path, which turns out to be closely related
to Jeffreys' prior, Rao's distance, and Hellinger's distance between
distributions. We also present examples to
illustrate the power of path sampling for high-dimension integrations.
If time permits, we will also show how path sampling evolves, with the
help of bridge sampling (Meng and Wong, Statistica Sinica, 1996),
from importance sampling, which is in routine use in statistics for dealing
with analytically intractable integrations.
Regardless of an audience's particular interests,
the speaker guarantees that the audience will walk away with some
simple and useful identities that are verifiable on the back of an
envelope, and that these identities will be remembered for at least 30
work-days.
