ResearchStats: Gianluca Mazzarella & Dave Woods

Gianluca Mazzarella Combining Jump and Kink Ratio Estimators in Regression Discontinuity Design Dave Woods (University of Southampton) Design of Experiments for Bayesian Model Discrimination 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. This talk will describe a new decision-theoretic criterion for design selection when the aim of the experiment is discrimination between rival statistical models. Motivated by an experiment from materials science, we consider the problem of early stage screening experimentation to choose an appropriate linear model, potentially including interactions, to describe the dependence of a response on a set of factors. We adopt an expected loss for model selection which is a weighted sum of posterior model probabilities and introduce the Penalised Model Discrepancy (PMD) criterion for design selection. The use of this criterion is explored through a variety of issues pertinent to screening experiments, including the choice of initial and follow-up designs and the robustness of design performance to prior information. Designs from the PMD criterion are compared with those from existing approaches through examples. We also investigate reducing the computational burden of the method for experiments with a large number of contending models, through both the use of informative prior distributions and the approximation of the PMD objective function. Some directions of current and future research will also be discussed.