Bayesian optimal experimental design for the study of natural phenomena

Mavrogonatou, Lida (2021) Bayesian optimal experimental design for the study of natural phenomena. PhD thesis, University of Glasgow.

Abstract

Modern science has been progressively moving towards the study of increasingly complex structures, investigating not only their individual components but also their interactions, dependencies and co-existence as a whole. This thesis is concerned with optimal experimental design methodology for the study of such phenomena.

A decision-theoretic framework for optimal experimental design is adopted in this thesis. The employed methods operate based on an optimality criterion, quantifying the benefit incurred from each alternative experimental design - commonly known as the expected utility. An analytical expression is, in most studies of interest, not available for this quantity and so estimation techniques are typically required for its evaluation.

Currently, existing estimation methods fail to adequately address issues arising in optimal design problems within a modern scientific framework. This is predominantly attributed to the considerable computational cost incurred by consideration of mathematical models sophisticated enough to adequately capture the complexity of the studied structures. In face of this restriction, researchers often resort to consideration of rather simplistic models, hindering the progress towards a more realistic representation and better understanding of such systems.

Efficient methodology for evaluation of the expected utility constitutes the first main contribution of this thesis. The presented approach adopts a flexible, non-parametric framework combined with variational approximation techniques that translate the initial evaluation problem to an alternative, more tractable problem, solution of which is achieved through more efficient and computationally inexpensive procedures. A problem shift is thus achieved under which, estimation of the expected utility is accomplished through its corresponding dual problem. This alternative representation is shown to incur considerable computational gains compared to traditionally adopted approaches without compromising the quality of the produced estimates.

The proposed estimator paves the way to an autonomous, comprehensive framework for the optimal study of complex phenomena within a realistic time frame, currently posing an ongoing challenge. Establishment of such a setup composes the second main contribution of this thesis. The proposed framework attempts to emulate a typical research scheme of closed-loop data collection, knowledge update and optimal decision making which, combined with instrument control software, facilitates modern scientific studies under minimal human input. The class of Bayesian optimisation algorithms is finally considered, allowing for truly optimal decision making during the established procedure. This class of algorithms, although particularly well-suited to optimal experimental design problems, has been given little consideration in the relevant literature. Their integration to the proposed framework, thus, constitutes an additional contribution of this thesis.

Application of the adopted experimental design framework is examined in three increasingly challenging case studies, addressing a broad range of issues typically encountered in optimal design problems. The first study explores the optimal experimental design for a model discrimination problem adopting a set of simpler, polynomial models. An initial assessment of the proposed estimator and a comparison with the currently adopted methodology is performed, under a setup where application of the latter is not hindered by the incurred computational complexity. The subsequent two cases represent real-life problems of optimal experimental design for model inference in Systems Biology and Spectroscopy, employing models under which, traditionally adopted methods can become from highly inefficient to intractable and thus alternative approaches are needed for the study of such phenomena.

• Item Type: Thesis (PhD)
• Qualification Level: Doctoral
• Keywords: Bayesian optimal design, experimental design, variational approximation.
• Subjects: H Social Sciences > HA Statistics; Q Science > QA Mathematics
• Colleges/Schools: College of Science and Engineering > School of Mathematics and Statistics > Statistics
• Supervisor's Name: Vyshemirsky, Dr. Vladislav and Evers, Dr. Ludger
• Date of Award: 2021
• Depositing User: Lida Mavrogonatou
• Unique ID: glathesis:2021-81987
• Copyright: Copyright of this thesis is held by the author.
• Date Deposited: 09 Feb 2021 17:17
• Last Modified: 09 Feb 2021 17:44
• Thesis DOI: 10.5525/gla.thesis.81987
• URI: https://theses.gla.ac.uk/id/eprint/81987