Modelling of Spatial Extreme Values with Random Field and Copula Function

In this article a spatial model is presented for extreme values with marginal generalized extreme value (GEV) distribution. The spatial model would be able to capture the multi-scale spatial dependencies. The small scale dependencies in this model is modeled by means of copula function and then in a hierarchical manner a random field is related to location parameters of marginal GEV distributions in order to account for large scale dependencies. Bayesian inference of presented model is accomplished by offered Markov chain Monte Carlo (MCMC) design، which consisted of Gibbs sampler، random walk Metropolis-Hastings and adaptive independence sampler algorithms. In proposed MCMC design the vector of location parameters is updated simultaneously based on devised multivariate proposal distribution. Also، we attain Bayesian spatial prediction by approximation of the predictive distribution. Finally، the estimation of model parameters and possibilities for capturing and separation of multi-scale spatial dependencies are investigated in a simulation example and analysis of wind speed extremes.