Dawn B. Woodard, Duke
University Department of Statistical Science
(with Scott C. Schmidler, and Mark
Huber )
Title:
"Conditions for Rapid and Torpid Mixing of Tempering MCMC "
Abstract:
When the posterior distribution is multimodal, many standard MCMC techniques
converge extremely slowly. Parallel and simulated tempering are sampling
methods that are designed to converge quickly for multimodal distributions; we
evaluate the extent to which this holds.
We first provide lower bounds on the convergence rates of parallel and simulated
tempering, implying a set of sufficient conditions for rapid mixing. A direct
consequence is rapid mixing for several normal mixture models in R^M as M
increases, and for the mean-field Ising model.
We also obtain upper bounds on the convergence rates, yielding a set of
sufficient conditions for torpid mixing. These conditions imply torpid mixing
on a normal mixture model with unequal covariances and on the mean-field Potts
model with q >= 3, regardless of the number and choice of temperatures, as well
as on the mean-field Ising model if an insufficient (fixed) set of temperatures
is used.