A Bayesian hierarchical model for spatial extremes with multiple durations

Bayesian spatial modeling of extreme values has become increasingly popular due to its ability to obtain relevant uncertainty measures for the estimates. This has implications for the problem of limited data on the study of extreme climatological events. Noticing the abundance of non-daily environmental records, 1-h and 6-h records in particular, we propose a Bayesian hierarchical model that can address multiple durations, in addition to the spatial effects, within a set of extreme records with multiple durations. The generalized Pareto distribution for threshold exceedances and the binomial distribution for exceedance frequencies are adopted for the top-most characterization of extreme data. The duration effect on spatial extremes is characterized by pooling the extremes with different durations and merging the duration into a latent spatial process structure as one of the covariates. Statistical inference is performed using Markov Chain Monte Carlo (MCMC) methods, for which an adaptive tuning algorithm is proposed. The methodology is applied to simulated datasets and real precipitation data for a region around Hong Kong.