Orthogonal parallel MCMC methods for sampling and optimization

L. Martino*, V. Elvira, D. Luengo, J. Corander, F. Louzada

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract / Description of output

Monte Carlo (MC) methods are widely used for Bayesian inference and optimization in statistics, signal processing and machine learning. A well-known class of MC methods are Markov Chain Monte Carlo (MCMC) algorithms. In order to foster better exploration of the state space, specially in high-dimensional applications, several schemes employing multiple parallel MCMC chains have been recently introduced. In this work, we describe a novel parallel interacting MCMC scheme, called orthogonal MCMC (O-MCMC), where a set of “vertical” parallel MCMC chains share information using some “horizontal” MCMC techniques working on the entire population of current states. More specifically, the vertical chains are led by random-walk proposals, whereas the horizontal MCMC techniques employ independent proposals, thus allowing an efficient combination of global exploration and local approximation. The interaction is contained in these horizontal iterations. Within the analysis of different implementations of O-MCMC, novel schemes in order to reduce the overall computational cost of parallel Multiple Try Metropolis (MTM) chains are also presented. Furthermore, a modified version of O-MCMC for optimization is provided by considering parallel Simulated Annealing (SA) algorithms. Numerical results show the advantages of the proposed sampling scheme in terms of efficiency in the estimation, as well as robustness in terms of independence with respect to initial values and the choice of the parameters.

Original languageEnglish
Pages (from-to)64-84
Number of pages21
JournalDigital Signal Processing: A Review Journal
Early online date29 Jul 2016
Publication statusPublished - 1 Nov 2016

Keywords / Materials (for Non-textual outputs)

  • Bayesian inference
  • Block Independent Metropolis
  • Optimization
  • Parallel Markov Chain Monte Carlo
  • Parallel Multiple Try Metropolis
  • Parallel Simulated Annealing


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