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

Bizjajeva, Svetlana LU and Olsson, Jimmy (2016) In Annals of the Institute of Statistical Mathematics 68(5). p.1025-1053
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... (More)

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.

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author
organization
publishing date
type
Contribution to journal
publication status
published
subject
keywords
Antithetic sampling, Central limit theorem, Optimal filtering, Optimal kernel, Particle filter, State-space models
in
Annals of the Institute of Statistical Mathematics
volume
68
issue
5
pages
29 pages
publisher
Springer
external identifiers
  • Scopus:84983331324
  • WOS:000382007400005
ISSN
0020-3157
DOI
10.1007/s10463-015-0524-y
language
English
LU publication?
yes
id
3d96d4c7-69a0-4959-bd15-4cb96e8f730a
date added to LUP
2016-10-17 08:58:57
date last changed
2017-01-01 08:36:58
@article{3d96d4c7-69a0-4959-bd15-4cb96e8f730a,
  abstract     = {<p>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.</p>},
  author       = {Bizjajeva, Svetlana and Olsson, Jimmy},
  issn         = {0020-3157},
  keyword      = {Antithetic sampling,Central limit theorem,Optimal filtering,Optimal kernel,Particle filter,State-space models},
  language     = {eng},
  month        = {10},
  number       = {5},
  pages        = {1025--1053},
  publisher    = {Springer},
  series       = {Annals of the Institute of Statistical Mathematics},
  title        = {Antithetic sampling for sequential Monte Carlo methods with application to state-space models},
  url          = {http://dx.doi.org/10.1007/s10463-015-0524-y},
  volume       = {68},
  year         = {2016},
}