Model assessment for Bayesian spatio-temporal epidemic models for complex data sets using hybrid computational methods

Abstract

This project investigates the use of model assessment techniques for stochastic spatiotemporal models, with a focus on embedding classical style tests within the Bayesian framework and applying them to study real-world systems. Techniques will be investigated within the context of epidemic models. These models model the spread of a disease, for example, citrus canker, over a spatial region. We will focus on methods of choosing between different transmission kernels. The transmission kernel is a component in the model which determines how the disease spreads over space and time, and is important in choosing the right strategy for the disease, for example, culling of infected individual. The methods for model selection within this context are challenging to develop and implement. Building on recent work within the group which has focused on tests applied to residual processes, we will investigate how likelihood-based tests might be applied to latent processes in order to formulate methods that avoid the sensitivity to parameter priors suffered by purely Bayesian approaches to model comparison. In addition, we extend existing latent residual tests to detect the presence of anisotropic spatial kernels. The power of these tests will be calculated and their advantages and disadvantages investigated, both from a computational and a practical perspective as well from a theoretical perspective. These investigations will be carried out using computational statistical methods performed on simulated and real-world data sets, including the DEFRA data-set for the foot-and-mouth outbreak of 2001. Our investigations show that the likelihood-based methods are able to detect misspecification of spatial kernel, sometimes exceeding the power of existing latent residual tests. Our directional infection link residual test is shown to be able detect anisotropy in simulated data. Using hybrid computational programming techniques, our tests have been shown to scale to big data sets of 188,361 individuals, and detect mis-specification of kernel in an existing analysis of the data.