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
good 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
This talk is based on joint work with Brian Caffo of Johns Hopkins, Murali Haran of Penn State and Ronald Neath of Minnesota.
Meet the speaker in Room 212 Cockins Hall at 4:30 p.m. Refreshments will be served.