On Sequential Monte Carlo, Partial Rejection Control and Approximate Bayesian Computation

Probability Surveys, ISSN: 1549-5787 (2008)

24 Pages Posted: 5 Jun 2017

See all articles by Gareth Peters

Gareth Peters

Department of Actuarial Mathematics and Statistics, Heriot-Watt University; University College London - Department of Statistical Science; University of Oxford - Oxford-Man Institute of Quantitative Finance; London School of Economics & Political Science (LSE) - Systemic Risk Centre; University of New South Wales (UNSW) - Faculty of Science

Y. Fan

University of New South Wales (UNSW) - School of Mathematics and Statistics

Scott Sisson

University of New South Wales (UNSW) - School of Mathematics and Statistics

Date Written: 2008

Abstract

We present a sequential Monte Carlo sampler variant of the partial rejection control algorithm introduced by Liu (2001), termed SMC sampler PRC, and show that this variant can be considered under the same framework of the sequential Monte Carlo sampler of Del Moral et al. (2006). We make connections with existing algorithms and theoretical results, and extend some theoretical results to the SMC sampler PRC setting. We examine the properties of the SMC sampler PRC and give recommendations for user specified quantities. We also study the special case of SMC sampler PRC in the “likelihood free” approximate Bayesian computation framework, as introduced by Sisson et al. (2007).

Keywords: Asymptotic analysis, Convergence, Interacting particle systems, Sequential Monte Carlo samplers

Suggested Citation

Peters, Gareth and Fan, Y. and Sisson, Scott, On Sequential Monte Carlo, Partial Rejection Control and Approximate Bayesian Computation (2008). Probability Surveys, ISSN: 1549-5787 (2008), Available at SSRN: https://ssrn.com/abstract=2980448

Gareth Peters (Contact Author)

Department of Actuarial Mathematics and Statistics, Heriot-Watt University ( email )

Edinburgh Campus
Edinburgh, EH14 4AS
United Kingdom

HOME PAGE: http://garethpeters78.wixsite.com/garethwpeters

University College London - Department of Statistical Science ( email )

1-19 Torrington Place
London, WC1 7HB
United Kingdom

University of Oxford - Oxford-Man Institute of Quantitative Finance ( email )

University of Oxford Eagle House
Walton Well Road
Oxford, OX2 6ED
United Kingdom

London School of Economics & Political Science (LSE) - Systemic Risk Centre ( email )

Houghton St
London
United Kingdom

University of New South Wales (UNSW) - Faculty of Science ( email )

Australia

Y. Fan

University of New South Wales (UNSW) - School of Mathematics and Statistics ( email )

Sydney, 2052
Australia

Scott Sisson

University of New South Wales (UNSW) - School of Mathematics and Statistics ( email )

Sydney, 2052
Australia

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