Bayesian Design of Experiments for Intractable Likelihood Models Using Coupled Auxiliary Models and Multivariate Emulation
A Bayesian design is given by maximising the expected utility over the design space. The utility is chosen to represent the aim of the experiment and its expectation is taken with respect to all unknowns: responses, parameters and/or models. Although straightforward in principle, there are several challenges to finding Bayesian designs in practice. Firstly, the expected utility is rarely available in closed form and requires approximation. Secondly, the expected utility needs to be maximised over a, potentially, high-dimensional design space. In the case of intractable likelihood models, these problems are compounded by the fact that the likelihood function, whose evaluation is required to approximate the expected utility, is not available in closed form. A strategy is proposed to find Bayesian designs for intractable likelihood models. It relies on the development of new methodology involving auxiliary modelling to approximate the expected utility, under an intractable likelihood model, applied with the latest approaches to maximising approximated expected utilities.