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 good estimates of the desired quantities? I will introduce a method that stops the MCMC sampling when the width of a confidence interval 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-width 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.