Bayesian Decision-Theoretic Design of Experiments Under an Alternative Model

Traditionally Bayesian decision-theoretic design of experiments proceeds by choosing a design to minimize expectation of a loss function over the space of all designs. The loss represents the aim of the experiment and expectation is taken with respect to the joint distribution of all unknown quantities implied by the statistical model that will be fitted to observed responses. An extended framework is proposed whereby expectation of the loss is taken with respect to a joint distribution implied by an alternative statistical model. The framework can be employed to promote robustness, to ensure computational feasibility or to allow realistic prior specification. An asymptotic approximation to the resulting expected loss is developed to aid in exploring the framework and, in particular, on the implications of the choice of loss function. The framework is demonstrated on a linear regression versus full-treatment model scenario, and on estimating parameters of a non-linear model under differing model discrepancies.