Multivariate Output Analysis for Markov Chain Monte Carlo

• Activity Number: 502
• Type: Contributed
• Date/Time: Wednesday, August 12, 2015 : 8:30 AM to 10:20 AM
• Sponsor: Section on Statistical Computing
• Author(s): Dootika Vats* and Galin Jones and James M. Flegal
• Companies: University of Minnesota and University of Minnesota and UC Riverside
• Keywords: Markov chain Monte Carlo ; Batch Means ; Covariance matrix ; strong invariance principle ; monte carlo error

Abstract

Markov chain Monte Carlo (MCMC) methods produce a correlated sample in order to estimate several (many) unknown expectations of a target distribution with a vector of sample means. Ensuring that this procedure is reliable requires assessment of the Monte Carlo error. However, the multivariate nature of the estimation process has been ignored in the MCMC literature. We present multivariate estimators of the Monte Carlo error and its implementation in an R package. These estimators allow for joint confidence regions for parameters and additional graphical convergence diagnostics for MCMC. Finally, we investigate the use of classical multivariate methods in this setting of MCMC.