Efficient Fitting of Bayesian Regression Models with Spatio-Temporally Varying Coefficients

Abstract

Bayesian regression models with spatio-temporally varying coefficients are gaining popularity among researchers who are looking to model the spatio-temporal processes that are ubiquitous in the environmental and physical sciences. The fitting of these highly overparameterised and non-stationary models is challenging and computationally expensive. By combining existing ideas of reparameterisation, marginalisation and interweaving we develop a number of hybrid fitting strategies. We use the MCMC output to compare these methods in terms of convergence rates and effective sample sizes per second and thus identify the most efficient fitting strategy for models of this type. Implementation of the optimal strategy achieves faster convergence rates and significant savings in computation time, illustrated here with a simulation example and also a real data example modelling daily ozone concentration data.