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Optimizing threshold-schedules for sequential approximate Bayesian computation: applications to molecular systems

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Title: Optimizing threshold-schedules for sequential approximate Bayesian computation: applications to molecular systems
Authors: Silk, D
Filippi, S
Stumpf, MPH
Item Type: Journal Article
Abstract: The likelihood–free sequential Approximate Bayesian Computation (ABC) algorithms are increasingly popular inference tools for complex biological models. Such algorithms proceed by constructing a succession of probability distributions over the parameter space conditional upon the simulated data lying in an ε–ball around the observed data, for decreasing values of the threshold ε. While in theory, the distributions (starting from a suitably defined prior) will converge towards the unknown posterior as ε tends to zero, the exact sequence of thresholds can impact upon the computational efficiency and success of a particular application. In particular, we show here that the current preferred method of choosing thresholds as a pre-determined quantile of the distances between simulated and observed data from the previous population, can lead to the inferred posterior distribution being very different to the true posterior. Threshold selection thus remains an important challenge. Here we propose that the threshold–acceptance rate curve may be used to determine threshold schedules that avoid local optima, while balancing the need to minimise the threshold with computational efficiency. Furthermore, we provide an algorithm based upon the unscented transform, that enables the threshold–acceptance rate curve to be efficiently predicted in the case of deterministic and stochastic state space models.
Issue Date: 7-Sep-2013
Date of Acceptance: 1-Jul-2013
URI: http://hdl.handle.net/10044/1/44691
DOI: https://dx.doi.org/10.1515/sagmb-2012-0043
ISSN: 2194-6302
Publisher: De Gruyter
Start Page: 603
End Page: 618
Journal / Book Title: Statistical Applications in Genetics and Molecular Biology
Volume: 12
Issue: 5
Copyright Statement: © 2013 De Gruyter.
Keywords: stat.CO
Publication Status: Published
Appears in Collections:School of Public Health