Jim Hobert, Ph.D.
Department of Statistics
University of Florida
Wednesday, December 4, 2002
3:30 PM
Moos Tower 2-650
Minneapolis Campus
Abstract:
A perfect sampler is an algorithm that allows one to use a Markov chain with stationary density to make exact (or perfect) draws from p . This talk begins with basic explanations of two perfect sampling algorithms called coupling from the past (CFTP) (Propp & Wilson 1996) and the multigamma coupler (Murdoch & Green 1998). The multigamma coupler requires a minorization condition on the underlying Markov chain. Our result is a mixture representation of p under the assumption that the Markov chain satisfies a minorization condition. When the minorization holds on the entire state space, our mixture representation of p reduces to a simple formula from which samples can easily be drawn. Interestingly, despite the fact that the derivation of this formula involves no coupling or backward simulation arguments, the formula can be used to reconstruct perfect sampling algorithms such as the multigamma coupler and Wilson's (2000) Read-Once CFTP algorithm. This is joint work with Christian Robert, Universite Paris Dauphine.