Publications

A methodology is proposed to derive Bayesian experimental designs for discriminating between rival epidemiological models with computationally intractable likelihoods. Methods from approximate Bayesian computation are used to facilitate inference in this setting, and an efficient implementation of this inference framework for approximating the expectation of utility functions is proposed. Three utility functions for model discrimination are considered, and the performance each utility is explored in designing experiments for discriminating between three epidemiological models; the death model, the Susceptible–Infected model, and the Susceptible–Exposed–Infected model. The challenge of efficiently locating optimal designs is addressed by an adaptation of the coordinate exchange algorithm which exploits parallel computational architectures.

Complex models used to describe biological processes in epidemiology and ecology often have computationally intractable or expensive likelihoods. This poses significant challenges in terms of Bayesian inference but more significantly in the design of experiments. Bayesian designs are found by maximising the expectation of a utility function over a design space, and typically this requires sampling from or approximating a large number of posterior distributions. This renders approaches adopted in inference computationally infeasible to implement in design. Consequently, optimal design in such fields has been limited to a small number of dimensions or a restricted range of utility functions. To overcome such limitations, we propose a synthetic likelihood-based Laplace approximation for approximating utility functions for models with intractable likelihoods. As will be seen, the proposed approximation is flexible in that a wide range of utility functions can be considered, and remains computationally efficient in high dimensions. To explore the validity of this approximation, an illustrative example from epidemiology is considered. Then, our approach is used to design experiments with a relatively large number of observations in two motivating applications from epidemiology and ecology.

Foot and mouth disease (FMD) is a highly contagious infectious disease which has frequently plagued livestock across many different countries worldwide. Currently, the spread of the disease is not well understood, and thus experiments are needed such that targeted disease detection, prevention and control measures can be developed. However, developing such experiments is challenging as typically the likelihood of models for such infectious diseases is computationally intractable. This poses challenges in quantifying the usefulness of different experiments through a utility function. For this purpose, a novel synthetic likelihood approach is considered which allows experiments for infectious diseases to be developed through the consideration of a dual-purpose utility function for parameter estimation and model discrimination. The new methodology is validated on an illustrative example before being applied to experiments for FMD which motivate this work. Across both examples, the results suggest that the derived dual purpose designs perform similarly well in achieving each experimental goal when compared to the designs optimised for each individual goal. Further, the results from the motivating example suggest that new knowledge about how FMD spreads throughout a population could be discovered if our approaches are adopted in future experimentation.