Relative Fixed-Width Stopping Rule and Its Application to Spatial Bayesian Models on fMRI Time-Series Data

• Activity Number: 221
• Type: Topic Contributed
• Date/Time: Monday, August 4, 2014 : 2:00 PM to 3:50 PM
• Sponsor: Section on Bayesian Statistical Science
• Author(s): Lei Gong*+ and James Flegal
• Companies: University of California, Riverside and University of California, Riverside
• Keywords: Bayesian computation ; Markov chain Monte Carlo ; sequential stopping rules ; batch means ; spatial-temporal models

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. 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. Further, we investigate the relationship between the stopping rule and effective sample size. As an example, we consider a spatial Bayesian 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.