On Estimation and Prediction of Simple Model and Spatial Hierarchical Model for Temperature Extremes

A simple independent generalized extreme value (GEV) model and a three-stage hierarchical model were applied to regional climate model outputs for temperature extremes over Tasmania, Australia. The parameters of each model were estimated using a maximum likelihood and a hybrid Markov chain Monte Carlo (MCMC) approach respectively. The two models were compared based on how well the models could predict extremes for 50 randomly selected locations that were withheld from fitting, using root mean squared prediction error (RMSPE), ten times. The RMSPEs of the two models show that the three-stage hierarchical model outperformed the simple model. We showed that the spatial hierarchical model has successfully smoothed the shape parameters. The high values tend to be pulled down, the low values to be pushed up.