Institute of Statistics and Decision Sciences
Duke University
presents:
David Hidgon
Institute of Statistics & Decision Sciences, Duke University
"MCMC, Auxiliary Variables, and Applications"
Abstract: Swendsen and Wang (1987) unveiled a revolutionary algorithm for sampling from the Ising model of statistical physics. From a statistical standpoint, they use a Markov Chain Monte Carlo technique in which the state space is augmented by auxiliary variables. This auxiliary variable framework lends insight to simple algorithms such as Metropolis, and can be extended to handle other spatial processes.
Instead of sampling from a distribution p(x), one can define p(u|x), giving a joint distribution p(x,u) = p(x)p(u|x) whose marginal distribution is p(x). Augmenting the state space with can lead to greatly improved performance of the sampler. This talk will discuss auxiliary variable methods, from simple to rather complicated.
Such methods are particularly useful Bayesian image analysis where prior distributions often exhibit phase transition. These distributions are notoriously difficult to handle with standard MCMC tools, however auxiliary variable methods can lead to more efficient sampling methods. We'll look at applications from spatial statistics and medical imaging.
Friday, October 13, 1995
11:45 - 12:45
116 Old Chemistry Building Any questions concerning the seminar may be addressed to Cheryl McGhee @ (919) 684-8029, e-mail cheryl@isds.duke.edu, or finger seminar@isds.duke.edu.