Ensemble Markov Chain Monte Carlo with Teleporting Walkers

Michael Lindsey, Jonathan Weare, Anna Zhang

Research output: Contribution to journalArticlepeer-review

Abstract

We introduce an ensemble Markov chain Monte Carlo approach to sampling from a probability density with known likelihood. This method upgrades an underlying Markov chain by allowing an ensemble of such chains to interact via a process in which one chain’s state is cloned as another’s is deleted. This effective teleportation of states can overcome issues of metastability in the underlying chain, as the scheme enjoys rapid mixing once the modes of the target density have been populated. We derive a mean-field limit for the evolution of the ensemble. We analyze the global and local convergence of this mean-field limit, showing asymptotic convergence independent of the spectral gap of the underlying Markov chain, and moreover we interpret the limiting evolution as a gradient flow. We explain how interaction can be applied selectively to a subset of state variables in order to maintain advantage on very high-dimensional problems. Finally, we present the application of our methodology to Bayesian hyperparameter estimation for Gaussian process regression.

Original languageEnglish (US)
Pages (from-to)860-885
Number of pages26
JournalSIAM-ASA Journal on Uncertainty Quantification
Volume10
Issue number3
DOIs
StatePublished - 2022

Keywords

  • interacting particles
  • Markov chain Monte Carlo
  • mean-field limits

ASJC Scopus subject areas

  • Statistics and Probability
  • Modeling and Simulation
  • Statistics, Probability and Uncertainty
  • Discrete Mathematics and Combinatorics
  • Applied Mathematics

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