Sparse Log Gaussian Processes via MCMC for Spatial Epidemiology

Log Gaussian processes are an attractive manner to construct intensity surfaces for the purposes of spatial epidemiology. The intensity surfaces are naturally smoothed by placing a Gaussian process (GP) prior over the relative log Poisson rate, and the spatial correlations between areas can be included in an explicit and natural way into the model via a correlation function. The drawback with using a Gaussian process is the computational burden of the covariance matrix calculations. To overcome the computational limitations a number of approximations for Gaussian process have been suggested in the literature. In this work a fully independent training conditional sparse approximation is used to speed up the computations. The posterior inference is conducted using Markov chain Monte Carlo simulations and the sampling of the latent values is sped up by a transformation taking into account their posterior covariance. The sparse approximation is compared to a full GP with two sets of mortality data.