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Optimal experimental design: Formulations and computations

Part of: Design of experiments Communication, information Sequential methods Partial differential equations, initial value and time-dependent initial-boundary value problems Statistics Sufficiency and information

Published online by Cambridge University Press:  04 September 2024

Xun Huan ,
Jayanth Jagalur  and
Youssef Marzouk Open the ORCID record for Youssef Marzouk [Opens in a new window]
Xun Huan
Affiliation:
University of Michigan, 1231 Beal Ave, Ann Arbor, MI 48109, USA Email: [email protected]
Jayanth Jagalur
Affiliation:
Center for Applied Scientific Computing, Lawrence Livermore National Laboratory, 7000 East Ave, Livermore, CA 94550, USA Email: [email protected]
Youssef Marzouk
Affiliation:
Massachusetts Institute of Technology, 77 Massachusetts Ave, Cambridge, MA 02139, USA Email: [email protected]
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Abstract

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Questions of ‘how best to acquire data’ are essential to modelling and prediction in the natural and social sciences, engineering applications, and beyond. Optimal experimental design (OED) formalizes these questions and creates computational methods to answer them. This article presents a systematic survey of modern OED, from its foundations in classical design theory to current research involving OED for complex models. We begin by reviewing criteria used to formulate an OED problem and thus to encode the goal of performing an experiment. We emphasize the flexibility of the Bayesian and decision-theoretic approach, which encompasses information-based criteria that are well-suited to nonlinear and non-Gaussian statistical models. We then discuss methods for estimating or bounding the values of these design criteria; this endeavour can be quite challenging due to strong nonlinearities, high parameter dimension, large per-sample costs, or settings where the model is implicit. A complementary set of computational issues involves optimization methods used to find a design; we discuss such methods in the discrete (combinatorial) setting of observation selection and in settings where an exact design can be continuously parametrized. Finally we present emerging methods for sequential OED that build non-myopic design policies, rather than explicit designs; these methods naturally adapt to the outcomes of past experiments in proposing new experiments, while seeking coordination among all experiments to be performed. Throughout, we highlight important open questions and challenges.

MSC classification

Primary: 62-02: Research exposition (monographs, survey articles) 62B15: Theory of statistical experiments 62K05: Optimal designs
Secondary: 62L05: Sequential design 94A17: Measures of information, entropy 65M32: Inverse problems
Type
Research Article
Information
Acta Numerica , Volume 33 , July 2024 , pp. 715 - 840
Creative Commons
Creative Common License - CCCreative Common License - BY
This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted re-use, distribution, and reproduction in any medium, provided the original work is properly cited.
Copyright
© The Author(s), 2024. Published by Cambridge University Press

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