Group Importance Sampling for particle filtering and MCMC

Luca Martino*, Víctor Elvira, Gustau Camps-Valls

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

Bayesian methods and their implementations by means of sophisticated Monte Carlo techniques have become very popular in signal processing over the last years. Importance Sampling (IS) is a well-known Monte Carlo technique that approximates integrals involving a posterior distribution by means of weighted samples. In this work, we study the assignation of a single weighted sample which compresses the information contained in a population of weighted samples. Part of the theory that we present as Group Importance Sampling (GIS) has been employed implicitly in different works in the literature. The provided analysis yields several theoretical and practical consequences. For instance, we discuss the application of GIS into the Sequential Importance Resampling framework and show that Independent Multiple Try Metropolis schemes can be interpreted as a standard Metropolis–Hastings algorithm, following the GIS approach. We also introduce two novel Markov Chain Monte Carlo (MCMC) techniques based on GIS. The first one, named Group Metropolis Sampling method, produces a Markov chain of sets of weighted samples. All these sets are then employed for obtaining a unique global estimator. The second one is the Distributed Particle Metropolis–Hastings technique, where different parallel particle filters are jointly used to drive an MCMC algorithm. Different resampled trajectories are compared and then tested with a proper acceptance probability. The novel schemes are tested in different numerical experiments such as learning the hyperparameters of Gaussian Processes, two localization problems in a wireless sensor network (with synthetic and real data) and the tracking of vegetation parameters given satellite observations, where they are compared with several benchmark Monte Carlo techniques. Three illustrative Matlab demos are also provided.

Original languageEnglish
Pages (from-to)133-151
Number of pages19
JournalDigital Signal Processing: A Review Journal
Volume82
Early online date7 Aug 2018
DOIs
Publication statusPublished - 1 Nov 2018

Keywords

  • Bayesian inference
  • Importance Sampling
  • Markov Chain Monte Carlo (MCMC)
  • Multiple Try Metropolis
  • Particle filtering
  • Particle Metropolis–Hastings

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