Developments of the total entropy utility function for the dual purpose of model discrimination and parameter estimation in Bayesian design

The total entropy utility function is considered for the dual purpose of model discrimination and parameter estimation in Bayesian design. A sequential design setting is considered where it is shown how to efficiently estimate the total entropy utility function in discrete data settings. Utility estimation relies on forming particle approximations to a number of intractable integrals which is afforded by the use of the sequential Monte Carlo algorithm for Bayesian inference. A number of motivating examples are considered for demonstrating the performance of total entropy in comparison to utilities for model discrimination and parameter estimation. The results suggest that the total entropy utility selects designs which are efficient under both experimental goals with little compromise in achieving either goal. As such, for the type of problems considered in this paper, the total entropy utility is advocated as a general utility for Bayesian design in the presence of model uncertainty.