Bayesian Methods for Non-stationary Extreme Value Analysis

Abstract

Non-stationary models for extremes have attracted significant attention in recent years. These models require adapted estimation methods. Bayesian inference offers an attractive framework to estimate non-stationary models and, importantly, to quantify estimation and predictive uncertainties. This chapter therefore focuses on the application of Bayesian inference to non-stationary extreme models. It is organized as a step-by-step building of non-stationary models of increasing generality. The principles of Bayesian inference are introduced using the simple case of a univariate and stationary distribution. The construction of at-site non-stationary models, using regression functions linking parameter values with time-varying covariates, is then presented. The difficulty of identifying non-stationary components based on the sole use of at-site data is also discussed, and motivates the construction of regional non-stationary models. Such models are based on the concept of “regional parameters”, i.e. parameters being assumed identical for all sites within a homogeneous region. The inference of regional models poses an additional difficulty compared to the at-site approach: the existence of spatial dependences makes the derivation of the inference equations challenging. A practical solution, based on the use of spatial copulas, is briefly presented. Lastly, a generalization of the “regional parameter” paradigm, based on Bayesian hierarchical modeling, is discussed.