Bayesian sequential design for Copula models

Abstract

Bayesian design requires determining the value of controllable variables in an experiment to maximise the information that will be obtained for subsequently collected data, with the majority of research in this field being focused on experiments that yield a univariate response. In this paper, a robust and computationally efficient Bayesian design approach is proposed to derive designs for experiments which yield bivariate discrete and mixed responses. To construct the joint distribution of responses, Copula models are considered, and a sequential Monte Carlo algorithm is adopted to reduce the computational effort required in deriving sequential designs. The total entropy utility function is considered to derive designs for the dual experimental goals of parameter estimation and model discrimination for Copula models. The results show that designs constructed within our framework are able to precisely estimate model parameters and that it is possible to discriminate between different competing Copula models. However, for experiments which yield binary and continuous data, it appears as though discriminating between Copula models can require a large number of data points, which may limit the general applicability of our methods and/or the range of experimental objectives that can be considered in experiments that yield multiple responses.