An approach for finding fully Bayesian optimal designs using normal-based approximations to loss functions

Overstall, A. M., McGree, J. M. and Drovandi, C. C. (2018) An approach for finding fully Bayesian optimal designs using normal-based approximations to loss functions. Statistics and Computing, 28(2), pp. 343-358. (doi: 10.1007/s11222-017-9734-x)

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The generation of decision-theoretic Bayesian optimal designs is complicated by the significant computational challenge of minimising an analytically intractable expected loss function over a, potentially, high-dimensional design space. A new general approach for approximately finding Bayesian optimal designs is proposed which uses computationally efficient normal-based approximations to posterior summaries to aid in approximating the expected loss. This new approach is demonstrated on illustrative, yet challenging, examples including hierarchical models for blocked experiments, and experimental aims of parameter estimation and model discrimination. Where possible, the results of the proposed methodology are compared, both in terms of performance and computing time, to results from using computationally more expensive, but potentially more accurate, Monte Carlo approximations. Moreover, the methodology is also applied to problems where the use of Monte Carlo approximations is computationally infeasible.

Item Type:Articles
Additional Information:A.M. Overstall was supported by a Research Incentive Grant (70424) from the Carnegie Trust for the Universities of Scotland. C.C. Drovandi was supported by an Australian Research Council’s Discovery Early Career Researcher Award funding scheme (DE160100741).
Glasgow Author(s) Enlighten ID:Overstall, Dr Antony
Authors: Overstall, A. M., McGree, J. M., and Drovandi, C. C.
College/School:College of Science and Engineering > School of Mathematics and Statistics
Journal Name:Statistics and Computing
ISSN (Online):1573-1375
Published Online:20 February 2017
Copyright Holders:Copyright © 2017 The Authors
First Published:First published in Statistics and Computing 28(2): 343-358
Publisher Policy:Reproduced under a Creative Commons License

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Project CodeAward NoProject NamePrincipal InvestigatorFunder's NameFunder RefLead Dept
732421Expectation propagation to accelerate Bayesian optimal design of experimentsAntony OverstallThe Carnegie Trust for the Universities of Scotland (CARNEGTR)70424M&S - STATISTICS