Fall Seminar Series - October 7, 2004
University of Minnesota
School of Statistics
College of Liberal Arts
Fixed-Volume
Output Analysis in Markov Chain Monte Carlo
Galin Jones
School of Statistics
University of Minnesota
Thursday, October 7, 2004
NOTE NEW TIME
3:30 PM, 115
Ford Hall
Minneapolis, East Bank Campus
Social at 3:00 PM, 300 Ford Hall
Abstract
Markov
chain Monte Carlo is a method of producing a correlated sample from a
target distribution. Features of the target distribution are then
estimated via simple ergodic averages based on this sample. Thus a
fundamental question in MCMC is when should the sampling stop? That is,
when are the ergodic averages accurate estimates of the desired
quantities? I will introduce a method that stops the MCMC sampling when
the volume of a confidence region based on the ergodic averages is less
than a user-specified value. Hence calculating Monte Carlo standard
errors of the ergodic averages is a critical step in assessing the
output of the simulation. In this talk I will give an overview of
fixed-volume methodology as well as methods for calculating Monte Carlo
standard errors and the resulting confidence regions. I will then
compare these methods from both theoretical and practical perspectives.
The main results will be illustrated in several examples.
This talk is based on joint work with Brian Caffo of Johns Hopkins,
Murali Haran of Penn State and Ronald Neath of Minnesota.