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)

Abstract

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).
• Status: Published
• Refereed: Yes
• 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
• Publisher: Springer
• ISSN: 0960-3174
• 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

Project Code	Award No	Project Name	Principal Investigator	Funder's Name	Funder Ref	Lead Dept
73242	1	Expectation propagation to accelerate Bayesian optimal design of experiments	Antony Overstall	The Carnegie Trust for the Universities of Scotland (CARNEGTR)	70424	M&S - STATISTICS