Monitoring Joint Convergence of MCMC Samplers Using Cluster-Based Partitions

• Activity Number: 433
• Type: Contributed
• Date/Time: Tuesday, August 6, 2013 : 2:00 PM to 3:50 PM
• Sponsor: Section on Bayesian Statistical Science
• Author(s): Douglas VanDerwerken*+ and Scott C. Schmidler
• Companies: Duke University and Duke University
• Keywords: MCMC ; convergence diagnostics ; clustering ; total variation distance

Abstract

We present a diagnostic for monitoring convergence of MCMC samplers to the target distribution. In contrast to popular existing methods, we monitor convergence of the joint target distribution directly instead of via select scalar projections. The method uses a simple nonparametric posterior approximation based on a state-space partition obtained by clustering pooled draws from multiple chains, and convergence is determined when the estimated posterior probabilities of partition elements under each chain are sufficiently similar. This framework applies to a wide variety of problems, requiring only that the posterior density be available (up to normalization) and that a metric on the elements of the sample space be provided. In particular, the approach generalizes directly to non-Euclidean state spaces. The proposed method also provides the user with approximate HPD regions and a characterization how non-converged chains differ, all with little additional computational burden. We call this approach the PAUSE diagnostic, short for: Partition-based Approximation Used for Stationarity Evaluation.