Monitoring Joint Convergence of MCMC Samplers

Published

Journal Article

© 2017, In the public domain. We present a diagnostic for monitoring convergence of a Markov chain Monte Carlo (MCMC) sampler to its target distribution. In contrast to popular existing methods, we monitor convergence to the joint target distribution directly rather than a select scalar projection. The method uses a simple nonparametric posterior approximation based on a state-space partition obtained by clustering the 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, and generalizes directly to non-Euclidean state spaces. Our method also provides approximate high-posterior-density regions, and a characterization of differences between nonconverged chains, all with little additional computational burden. We demonstrate this approach on applications to sampling posterior distributions over Rp, graphs, and partitions. Supplementary materials for this article are available online.

Full Text

Duke Authors

Cited Authors

  • VanDerwerken, D; Schmidler, SC

Published Date

  • July 3, 2017

Published In

Volume / Issue

  • 26 / 3

Start / End Page

  • 558 - 568

Electronic International Standard Serial Number (EISSN)

  • 1537-2715

International Standard Serial Number (ISSN)

  • 1061-8600

Digital Object Identifier (DOI)

  • 10.1080/10618600.2017.1297240

Citation Source

  • Scopus