Global consensus Monte Carlo

Lewis J. Rendell*, Adam M. Johansen, Anthony Lee, Nick Whiteley

*Corresponding author for this work

Research output: Contribution to journalArticle (Academic Journal)peer-review

18 Citations (Scopus)
94 Downloads (Pure)

Abstract

To conduct Bayesian inference with large data sets, it is often convenient or necessary to distribute the data across multiple machines. We consider a likelihood function expressed as a product of terms, each associated with a subset of the data. Inspired by global variable consensus optimisation, we introduce an instrumental hierarchical model associating auxiliary statistical parameters with each term, which are conditionally independent given the top-level parameters. One of these top-level parameters controls the unconditional strength of association between the auxiliary parameters. This model leads to a distributed MCMC algorithm on an extended state space yielding approximations of posterior expectations. A trade-off between computational tractability and fidelity to the original model can be controlled by changing the association strength in the instrumental model. We further propose the use of a SMC sampler with a sequence of association strengths, allowing both the automatic determination of appropriate strengths and for a bias correction technique to be applied. In contrast to similar distributed Monte Carlo algorithms, this approach requires few distributional assumptions. The performance of the algorithms is illustrated with a number of simulated examples.
Original languageEnglish
Number of pages12
JournalJournal of Computational and Graphical Statistics
DOIs
Publication statusPublished - 16 Oct 2020

Keywords

  • Bayesian inference
  • Distributed inference
  • Markov chain Monte Carlo
  • Sequential Monte Carlo

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