An adaptive sequential Monte Carlo method for approximate Bayesian computation

Authors:
Pierre Moral;Arnaud Doucet;Ajay Jasra
Affiliations:
Centre INRIA Bordeaux Sud-Ouest & Institut de Mathéématiques, Université Bordeaux I, Talence cedex, France 33405;Department of Statistics, University of Oxford, Oxford, UK OX1 3TG;Department of Statistics and Applied Probability, National University of Singapore, Singapore, Singapore 117546
Venue:
Statistics and Computing
Year:
2012

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Abstract

Approximate Bayesian computation (ABC) is a popular approach to address inference problems where the likelihood function is intractable, or expensive to calculate. To improve over Markov chain Monte Carlo (MCMC) implementations of ABC, the use of sequential Monte Carlo (SMC) methods has recently been suggested. Most effective SMC algorithms that are currently available for ABC have a computational complexity that is quadratic in the number of Monte Carlo samples (Beaumont et al., Biometrika 86:983---990, 2009; Peters et al., Technical report, 2008; Toni et al., J. Roy. Soc. Interface 6:187---202, 2009) and require the careful choice of simulation parameters. In this article an adaptive SMC algorithm is proposed which admits a computational complexity that is linear in the number of samples and adaptively determines the simulation parameters. We demonstrate our algorithm on a toy example and on a birth-death-mutation model arising in epidemiology.