Bayesian optimal design for ordinary differential equation models with application in biological science

Overstall, Antony M., Woods, David C. and Parker, Ben M. (2019) Bayesian optimal design for ordinary differential equation models with application in biological science. Journal of the American Statistical Association, 115 (530). pp. 583-598. ISSN 0162-1459

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Bayesian optimal design is considered for experiments where the response distribution depends on the solution to a system of non-linear ordinary differential equations. The motivation is an experiment to estimate parameters in the equations governing the transport of amino acids through cell membranes in human placentas. Decisiontheoretic Bayesian design of experiments for such nonlinear models is conceptually very attractive, allowing the formal incorporation of prior knowledge to overcome the parameter dependence of frequentist design and being less reliant on asymptotic approximations. However, the necessary approximation and maximization of the, typically analytically intractable, expected utility results in a computationally challenging problem. These issues are further exacerbated if the solution to the differential equations is not available in closed-form. This paper proposes a new combination of a probabilistic solution to the equations embedded within a Monte Carlo approximation to the expected utility with cyclic descent of a smooth approximation to find the optimal design. A novel precomputation algorithm reduces the computational burden, making the search for an optimal design feasible for bigger problems. The methods are demonstrated by finding new designs for a number of common models derived from differential equations, and by providing optimal designs for the placenta experiment.

Item Type: Article
Identifier: 10.1080/01621459.2019.1617154
Additional Information: © 2019 The Author(s). Published with license by Taylor & Francis Group, LLC.This is an Open Access article distributed under the terms of the Creative Commons Attribution License (, which permits unrestricted use, distribution,and reproduction in any medium, provided the original work is properly cited
Keywords: Approximate coordinate exchange algorithm, Decision-theoretic design, Gaussian process emulation, Nonlinear design
Subjects: Statistics
Depositing User: Ben Parker
Date Deposited: 15 Jul 2019 10:11
Last Modified: 06 Feb 2024 16:00


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