WASSERSTEIN-BASED METHODS FOR CONVERGENCE COMPLEXITY ANALYSIS OF MCMC WITH APPLICATIONS

Qian Qin, James P. Hobert

Research output: Contribution to journalArticlepeer-review

1 Scopus citations

Abstract

Over the last 25 years, techniques based on drift and minorization (d&m) have been mainstays in the convergence analysis of MCMC algorithms. However, results presented herein suggest that d&m may be less useful in the emerging area of convergence complexity analysis, which is the study of how the convergence behavior of Monte Carlo Markov chains scales with sample size, n, and/or number of covariates, p. The problem appears to be that minorization can become a serious liability as dimension increases. Alternative methods of constructing convergence rate bounds (with respect to total variation distance) that do not require minorization are investigated. Based on Wasserstein distances and random mappings, these methods can produce bounds that are substantially more robust to increasing dimension than those based on d&m. The Wasserstein-based bounds are used to develop strong convergence complexity results for MCMC algorithms used in Bayesian probit regression and random effects models in the challenging asymptotic regime where n and p are both large.

Original languageEnglish (US)
Pages (from-to)124-166
Number of pages43
JournalAnnals of Applied Probability
Volume32
Issue number1
DOIs
StatePublished - Feb 2022

Bibliographical note

Funding Information:
The second author was supported by NSF Grant DMS-15-11945.

Publisher Copyright:
© Institute of Mathematical Statistics, 2022

Keywords

  • Coupling
  • drift condition
  • geometric ergodicity
  • high dimensional inference
  • minorization condition
  • random mapping

Fingerprint

Dive into the research topics of 'WASSERSTEIN-BASED METHODS FOR CONVERGENCE COMPLEXITY ANALYSIS OF MCMC WITH APPLICATIONS'. Together they form a unique fingerprint.

Cite this