A1186
Title: Efficient Bayesian filtering and inference for integro-difference equation models
Authors: Evan Tate Paterson Hughes - Durham University (United Kingdom) [presenting]
Abstract: Integro Difference Equation (IDE) models are a class of dynamic spatio-temporal models which use a convolution kernel to describe the dependence of a spatial process on its previous time point, usually to model advection and diffusion of some random field over time. This work addresses the computational challenges involved in Bayesian inference and posterior distribution estimation of these models. First, in inference for these models, Kalman filtering and smoothing are often used either to compute marginal likelihoods or to sample from the hidden process conditional on the rest of the parameters of the model. There are many variations of the Kalman filter and smoother with varying performance profiles and stability, and these forms are briefly analysed in the context of IDEs, considering computation speed and stability. Second, there are two main methods of inference used for the kind of dynamical system that IDEs can be reduced to: marginal and joint inference. Either the marginal data likelihood computed directly from filtering is used to estimate the posterior densities directly with MCMC, or the full joint distribution of the unobserved process and observed state is analysed using a block Gibbs sampler. These two approaches are compared in terms of computational efficiency and practical performance in the IDE setting using a simulation study with varying observation and hidden state dimensions, and the methods are illustrated with a challenging case study.
