Antithetic sampling for sequential Monte Carlo methods with application to state-space models

Research output: Contribution to journalArticle

Abstract

In this paper, we cast the idea of antithetic sampling, widely used in standard Monte Carlo simulation, into the framework of sequential Monte Carlo methods. We propose a version of the standard auxiliary particle filter where the particles are mutated blockwise in such a way that all particles within each block are, first, offspring of a common ancestor and, second, negatively correlated conditionally on this ancestor. By deriving and examining the weak limit of a central limit theorem describing the convergence of the algorithm, we conclude that the asymptotic variance of the produced Monte Carlo estimates can be straightforwardly decreased by means of antithetic techniques when the particle filter is close to fully adapted, which involves approximation of the so-called optimal proposal kernel. As an illustration, we apply the method to optimal filtering in state-space models.

Details

Authors
  • Svetlana Bizjajeva
  • Jimmy Olsson
Organisations
External organisations
  • KTH Royal Institute of Technology
Research areas and keywords

Subject classification (UKÄ) – MANDATORY

  • Probability Theory and Statistics

Keywords

  • Antithetic sampling, Central limit theorem, Optimal filtering, Optimal kernel, Particle filter, State-space models
Original languageEnglish
Pages (from-to)1025-1053
Number of pages29
JournalAnnals of the Institute of Statistical Mathematics
Volume68
Issue number5
StatePublished - 2016 Oct 1
Peer-reviewedYes