Wilkinson, R.D. orcid.org/0000-0001-7729-7023 (2013) Approximate Bayesian computation (ABC) gives exact results under the assumption of model error. Statistical Applications in Genetics and Molecular Biology, 12 (2). pp. 129-141. ISSN 2194-6302
Abstract
Approximate Bayesian computation (ABC) or likelihood-free inference algorithms are used to find approximations to posterior distributions without making explicit use of the likelihood function, depending instead on simulation of sample data sets from the model. In this paper we show that under the assumption of the existence of a uniform additive model error term, ABC algorithms give exact results when sufficient summaries are used. This interpretation allows the approximation made in many previous application papers to be understood, and should guide the choice of metric and tolerance in future work. ABC algorithms can be generalized by replacing the 0–1 cut-off with an acceptance probability that varies with the distance of the simulated data from the observed data. The acceptance density gives the distribution of the error term, enabling the uniform error usually used to be replaced by a general distribution. This generalization can also be applied to approximate Markov chain Monte Carlo algorithms. In light of this work, ABC algorithms can be seen as calibration techniques for implicit stochastic models, inferring parameter values in light of the computer model, data, prior beliefs about the parameter values, and any measurement or model errors.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © 2013 De Gruyter. This is an author produced version of a paper subsequently published in Statistical Applications in Genetics and Molecular Biology. Uploaded in accordance with the publisher's self-archiving policy. |
Keywords: | Approximate Bayesian computation; calibration; likelihood-free inference; implicit inference; Monte Carlo |
Dates: |
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Institution: | The University of Sheffield |
Academic Units: | The University of Sheffield > Faculty of Science (Sheffield) > School of Mathematics and Statistics (Sheffield) |
Depositing User: | Symplectic Sheffield |
Date Deposited: | 12 May 2016 10:20 |
Last Modified: | 13 May 2016 16:53 |
Published Version: | http://dx.doi.org/10.1515/sagmb-2013-0010 |
Status: | Published |
Publisher: | De Gruyter |
Refereed: | Yes |
Identification Number: | 10.1515/sagmb-2013-0010 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:99543 |