A Skewed and Heavy-Tailed Latent Random Field Model for Spatial Extremes

ABSTRACT

This article develops Bayesian inference of spatial models with a flexible skew latent structure. Using the multivariate skew-normal distribution of Sahu et al., a valid random field model with stochastic skewing structure is proposed to take into account non-Gaussian features. The skewed spatial model is further improved via scale mixing to accommodate more extreme observations. Finally, the skewed and heavy-tailed random field model is used to describe the parameters of extreme value distributions. Bayesian prediction is done with a well-known Gibbs sampling algorithm, including slice sampling and adaptive simulation techniques. The model performance—as far as the identifiability of the parameters is concerned—is assessed by a simulation study and an analysis of extreme wind speeds across Iran. We conclude that our model provides more satisfactory results according to Bayesian model selection and predictive-based criteria. R code to implement the methods used is available as online supplementary material.

KEYWORDS:

• Bayesian prediction
• Extreme wind speeds
• Multivariate skew-normal distribution
• Skewed random field model

Acknowledgments

The author thanks the associate Editor and two anonymous referees for many helpful comments and suggestions that greatly improved this article.