Bayesian threshold selection for extremal models using measures of surprise

TL;DR

This paper introduces a Bayesian method using surprise measures to select thresholds in extremal models, applicable to both univariate and multivariate data, addressing a gap in existing threshold selection techniques.

Contribution

It proposes a novel Bayesian threshold selection approach based on surprise measures, suitable for multivariate extremal models where existing methods are limited.

Findings

Effective threshold determination in multivariate extremes

Applicable to both univariate and multivariate models

No need for alternative model specification

Abstract

Statistical extreme value theory is concerned with the use of asymptotically motivated models to describe the extreme values of a process. A number of commonly used models are valid for observed data that exceed some high threshold. However, in practice a suitable threshold is unknown and must be determined for each analysis. While there are many threshold selection methods for univariate extremes, there are relatively few that can be applied in the multivariate setting. In addition, there are only a few Bayesian-based methods, which are naturally attractive in the modelling of extremes due to data scarcity. The use of Bayesian measures of surprise to determine suitable thresholds for extreme value models is proposed. Such measures quantify the level of support for the proposed extremal model and threshold, without the need to specify any model alternatives. This approach is easily implemented for both univariate and multivariate extremes.