On the performance of the Bayesian composite likelihood estimation of max-stable processes

ABSTRACT

The max-stable process is a natural approach for modelling extrenal dependence in spatial data. However, the estimation is difficult due to the intractability of the full likelihoods. One approach that can be used to estimate the posterior distribution of the parameters of the max-stable process is to employ composite likelihoods in the Markov chain Monte Carlo (MCMC) samplers, possibly with adjustment of the credible intervals. In this paper, we investigate the performance of the composite likelihood-based MCMC samplers under various settings of the Gaussian extreme value process and the Brown–Resnick process. Based on our findings, some suggestions are made to facilitate the application of this estimator in real data.

KEYWORDS:

• Max-stable processes
• Gaussian extreme value process
• Brown–Resnick process
• composite likelihoods
• Markov chain Monte Carlo
• estimation performance

MATHEMATICS SUBJECT CLASSIFCATIONS:

• 62H99
• 62F15
• 62P12

Disclosure statement

No potential conflict of interest was reported by the authors.