Spatio-temporal dependence modelling of extreme rainfall in South Africa: A Bayesian integrated nested Laplace approximation technique

Abstract The spatial and spatio-temporal dependence modeling to extreme value distributions have been used to analyze the extremes of daily maximum rainfall data across selected weather stations in South Africa combining generalized Pareto distribution (GPD) with the flexible Bayesian Latent Gaussian Model (LGM). The paper demonstrated the spatio-temporal GPD model for applications in extreme rainfall data that capture systematic variation through spatial and spatio-temporal modeling framework, in which the temporal constitutes the week and month as random separately. The paper uses the Bayesian integrated Nested Laplace approximation (INLA) algorithm to estimate marginal posterior means of the parameters and hyper-parameters for Bayesian spatio-temporal models. The Bayesian inferences using INLA technique were applied to obtain prediction of the return levels at each station, which incorporate uncertainty due to model estimation, as well as the randomness that is inherent in the processes.