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The design of an experiment can be always be considered at least implicitlyBayesian, with prior knowledge used informally to aid decisions such as thevariables to be studied and the choice of a plausible relationship between theexplanatory variables and measured responses. Bayesian methods allowuncertainty in these decisions to be incorporated into design selection throughprior distributions that encapsulate information available from scientificknowledge or previous experimentation. Further, a design may be explicitlytailored to the aim of the experiment through a decision-theoretic approachusing an appropriate loss function. We review the area of decision-theoreticBayesian design, with particular emphasis on recent advances in computationalmethods. For many problems arising in industry and science, experiments resultin a discrete response that is well described by a member of the class ofgeneralised linear models. We describe how Gaussian process emulation, commonlyused in computer experiments, can play an important role in facilitatingBayesian design for realistic problems. A main focus is the combination ofGaussian process regression to approximate the expected loss with cyclicdescent (coordinate exchange) optimisation algorithms to allow optimal designsto be found for previously infeasible problems. We also present the firstoptimal design results for statistical models formed from dimensional analysis,a methodology widely employed in the engineering and physical sciences toproduce parsimonious and interpretable models. Using the famous paperhelicopter experiment, we show the potential for the combination of Bayesiandesign, generalised linear models and dimensional analysis to produce small butinformative experiments.

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