Fall 2002 Seminar Series - December 4, 2002
University of Minnesota
School of Statistics
College of Liberal Arts
Perfect Sampling: Basic Ideas and an Interesting
Connection
Jim Hobert
Department of Statistics
University of Florida
Wednesday, December 4, 2002
3:30 PM, 2-650
Moos Tower
Minneapolis, East Bank Campus
Social at 3:00 PM, A434
Mayo
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 pi . 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 pi under the assumption that
the Markov chain satisfies a minorization condition. When the minorization
holds on the entire state space, our mixture representation of pi 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.
Seminar jointly sponsored by School of Statistics and Division of Biostatistics