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On optimality of kernels for approximate Bayesian computation using sequential Monte Carlo

Filippi, S; Barnes, C; Cornebise, J; Stumpf, MPH; (2011) On optimality of kernels for approximate Bayesian computation using sequential Monte Carlo. Statistical Applications in Genetics and Molecular Biology , 12 (1) pp. 87-107. 10.1515/sagmb-2012-0069. Green open access

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Abstract

Approximate Bayesian computation (ABC) has gained popularity over the past few years for the analysis of complex models arising in population genetics, epidemiology and system biology. Sequential Monte Carlo (SMC) approaches have become work-horses in ABC. Here we discuss how to construct the perturbation kernels that are required in ABC SMC approaches, in order to construct a sequence of distributions that start out from a suitably defined prior and converge towards the unknown posterior. We derive optimality criteria for different kernels, which are based on the Kullback-Leibler divergence between a distribution and the distribution of the perturbed particles. We will show that for many complicated posterior distributions, locally adapted kernels tend to show the best performance. We find that the added moderate cost of adapting kernel functions is easily regained in terms of the higher acceptance rate. We demonstrate the computational efficiency gains in a range of toy examples which illustrate some of the challenges faced in real-world applications of ABC, before turning to two demanding parameter inference problems in molecular biology, which highlight the huge increases in efficiency that can be gained from choice of optimal kernels. We conclude with a general discussion of the rational choice of perturbation kernels in ABC SMC settings.

Type:Article
Title:On optimality of kernels for approximate Bayesian computation using sequential Monte Carlo
Open access status:An open access version is available from UCL Discovery
DOI:10.1515/sagmb-2012-0069
Publisher version:http://dx.doi.org/10.1515/sagmb-2012-0069
Language:English
Keywords:Dynamical systems; Bayesian parameter inference; sequential Monte Carlo; adaptive kernels; Likelihood-free; Kullback-Leibler
UCL classification:UCL > School of Life and Medical Sciences > Faculty of Life Sciences > Biosciences (Division of) > Cell and Developmental Biology
UCL > School of BEAMS > Faculty of Maths and Physical Sciences > Statistical Science

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