TITLE:  Bayesian design of experiments via Gaussian process emulation

ABSTRACT:

The design of any experiment is implicitly Bayesian, with prior knowledge being used informally to aid decisions such as which factors to vary and the choice of plausible causal relationships between the factors 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 with an appropriate loss function.

When designing experiments for nonlinear parametric models, finding a Bayesian optimal design is typically analytically intractable and often computational infeasible. The expected loss usually involves an intractable and high dimensional integral. We will present methodology for mitigating the computational expense of design through combining an application of Gaussian Process (GP) regression models with a cyclic descent (coordinate exchange) optimisation algorithm. We adopt methodology from the field of computer experiments and build a GP emulator for the expected loss. The methods allow optimal designs to be found for previously infeasible problems. We will describe the methodology and demonstrate it on a variety of examples.

Bio: Dave Woods is a Professor of Statistics at the University of Southampton with research interests in the design of experiments and the modelling of the resultant data. He holds a five-year research fellowship from the UK Engineering and Physical Sciences Research Council to develop new Bayesian design of experiments methods for nonparametric and mechanistic models. He gained his PhD from Southampton in 2003, and since then he has developed research programmes in design for nonlinear models, especially for discrete data and generalised linear models, screening experiments, and computer experiments and uncertainty quantification. He works extensively with industry and government, particularly in chemical development with the pharmaceutical industry, and he is an Associate Editor for Technometrics. He was the co-founder of the DEMA series of conferences in design of experiments, the most recent of which was held in Sydney, Australia, in December 2015.