Bayesian design of experiments for generalised linear models and dimensional analysis with industrial and scientific application

TL;DR

This paper reviews Bayesian design of experiments, emphasizing computational advances, and demonstrates its application to generalized linear models and dimensional analysis in scientific and industrial contexts.

Contribution

It introduces a novel combination of Gaussian process emulation and cyclic descent algorithms for Bayesian design in complex models, including the first optimal designs for dimensional analysis models.

Findings

Gaussian process emulation facilitates Bayesian design for complex problems.

Cyclic descent algorithms enable optimal design computation for previously infeasible models.

Application to the helicopter experiment shows efficient, informative experimental designs.

Abstract

The design of an experiment can be always be considered at least implicitly Bayesian, with prior knowledge used informally to aid decisions such as the variables to be studied and the choice of a plausible relationship between the explanatory variables and measured responses. Bayesian methods allow uncertainty in these decisions to be incorporated into design selection through prior distributions that encapsulate information available from scientific knowledge or previous experimentation. Further, a design may be explicitly tailored to the aim of the experiment through a decision-theoretic approach using an appropriate loss function. We review the area of decision-theoretic Bayesian design, with particular emphasis on recent advances in computational methods. For many problems arising in industry and science, experiments result in a discrete response that is well described by a member of the class of generalised linear models. We describe how Gaussian process emulation, commonly used in computer experiments, can play an important role in facilitating Bayesian design for realistic problems. A main focus is the combination of Gaussian process regression to approximate the expected loss with cyclic descent (coordinate exchange) optimisation algorithms to allow optimal designs to be found for previously infeasible problems. We also present the first optimal design results for statistical models formed from dimensional analysis, a methodology widely employed in the engineering and physical sciences to produce parsimonious and interpretable models. Using the famous paper helicopter experiment, we show the potential for the combination of Bayesian design, generalised linear models and dimensional analysis to produce small but informative experiments.