6 research outputs found
Fixed-width output analysis for Markov chain Monte Carlo
Markov chain Monte Carlo is a method of producing a correlated sample in
order to estimate features of a target distribution via ergodic averages. A
fundamental question is when should sampling stop? That is, when are the
ergodic averages good estimates of the desired quantities? We consider a method
that stops the simulation when the width of a confidence interval based on an
ergodic average is less than a user-specified value. Hence calculating a Monte
Carlo standard error is a critical step in assessing the simulation output. We
consider the regenerative simulation and batch means methods of estimating the
variance of the asymptotic normal distribution. We give sufficient conditions
for the strong consistency of both methods and investigate their finite sample
properties in a variety of examples
Markov Chain Monte Carlo Estimation of Quantiles
We consider quantile estimation using Markov chain Monte Carlo and establish conditions under which the sampling distribution of the Monte Carlo error is approximately Normal. Further, we investigate techniques to estimate the associated asymptotic variance, which enables construction of an asymptotically valid interval estimator. Finally, we explore the finite sample properties of these methods through examples and provide some recommendations to practitioners.