Spatial Bayesian Model for Maximum Temperature

A three-stage Bayesian spatial model is fitted to temperature extremes covering Tasmania. In the first stage, the data in each grid cell are assumed to follow a GEV distribution with particular parameters. In the second stage, each GEV parameter is assumed to follow a Normal distribution with mean structure comprising a fixed and random effect component. A usual regression model with covariates longitude, latitude and elevation is employed for
the fixed effect component, and a conditional auto regressive (CAR) model is used for the random effect. The estimation of the posterior parameters was conducted by Monte Carlo method using a hybrid MCMC of Metropolis and Gibbs sampler algorithm. We found the spatial random effect successfully smoothed the shape parameters, so that credible intervals of return levels were well behaved.