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Activity Number: 502
Type: Contributed
Date/Time: Wednesday, August 12, 2015 : 8:30 AM to 10:20 AM
Sponsor: Section on Statistical Computing
Abstract #315795
Title: A Practical Sequential Stopping Rule for High-Dimensional Markov Chain Monte Carlo
Author(s): Lei Gong* and James M. Flegal
Companies: UC Riverside and UC Riverside
Keywords: Bayesian computation ; Markov chain Monte Carlo ; sequential stopping rules ; effective sample size ; batch means
Abstract:

A current challenge for many Bayesian analyses is determining when to terminate high-dimensional Markov chain Monte Carlo simulations. To this end, we propose using an automated sequential stopping procedure that terminates the simulation when the computational uncertainty is small relative to the posterior uncertainty. Further, we show this stopping rule is equivalent to stopping when the effective sample size is sufficiently large. Such a stopping rule has previously been shown to work well in settings with posteriors of moderate dimension. In this paper, we illustrate its utility in high-dimensional simulations while overcoming some current computational issues. As examples, we consider two complex Bayesian analyses on spatially and temporally correlated datasets. The first involves a dynamic space-time model on weather station data and the second a spatial variable selection model on fMRI brain imaging data. Our results show the sequential stopping rule is easy to implement, provides uncertainty estimates, and performs well in high-dimensional settings.


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