Hierarchical experiments and likelihood approximations

The project will develop new statistical methods for statistical design, modelling and inference using systems and approximations available on at least two hierarchical scales.

Understanding and exploiting hierarchical differences in the accuracy and cost of systems and approximations across different (physical, computational) scales is an important topic in many areas of statistical research. In general, accuracy and cost will be inversely related, with economically or computationally expensive "evaluations" (physical observations or computational approximations) giving highly accurate results. However, project budgets will generally be insufficient to allow statistical modelling and inference to rely solely on results from these evaluations. Instead, use must be made of lower cost, but lower accuracy, evaluations, which will be available in much greater quantities.

This unique project would allow a student to make contributions to both design of experiments and likelihood-based inference by developing generic methods to best combine data and approximations from different scales. Example problems include designing experiments across lab, pilot and manufacturing scales to understand and predict manufactured product performance in the pharmaceutical industry, and constructing likelihood approximations for nonlinear regression models combining analytic (e.g. Laplace) with computational (e.g. Monte Carlo) approximations to obtain statistically valid and efficient inferences.