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Considerate approaches to achieving sufficiency for ABC model selection

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Title: Considerate approaches to achieving sufficiency for ABC model selection
Authors: Barnes, C
Filippi, S
Stumpf, MPH
Thorne, T
Item Type: Journal Article
Abstract: For nearly any challenging scientific problem evaluation of the likelihood is problematic if not impossible. Approximate Bayesian computation (ABC) allows us to employ the whole Bayesian formalism to problems where we can use simulations from a model, but cannot evaluate the likelihood directly. When summary statistics of real and simulated data are compared—rather than the data directly—information is lost, unless the summary statistics are sufficient. Sufficient statistics are, however, not common but without them statistical inference in ABC inferences are to be considered with caution. Previously other authors have attempted to combine different statistics in order to construct (approximately) sufficient statistics using search and information heuristics. Here we employ an informationtheoretical framework that can be used to construct appropriate (approximately sufficient) statistics by combining different statistics until the loss of information is minimized. We start from a potentially large number of different statistics and choose the smallest set that captures (nearly) the same information as the complete set. We then demonstrate that such sets of statistics can be constructed for both parameter estimation and model selection problems, and we apply our approach to a range of illustrative and real-world model selection problems.
Issue Date: 9-Jun-2012
Date of Acceptance: 10-May-2012
URI: http://hdl.handle.net/10044/1/47892
DOI: https://dx.doi.org/10.1007/s11222-012-9335-7
ISSN: 0960-3174
Publisher: Springer Verlag
Start Page: 1181
End Page: 1197
Journal / Book Title: Statistics and Computing
Volume: 22
Issue: 6
Copyright Statement: © Springer-Verlag 2012. The final publication is available at Springer via https://dx.doi.org/10.1007/s11222-012-9335-7
Keywords: stat.CO
Statistics & Probability
0104 Statistics
0802 Computation Theory And Mathematics
Appears in Collections:School of Public Health