Reparameterization of extreme value framework for improved Bayesian workflow

TL;DR

This paper introduces an orthogonal reparameterization for Bayesian extreme value analysis, enhancing MCMC convergence and prior derivation, demonstrated through Garonne flow data analysis.

Contribution

It proposes a novel orthogonal parameterization for Bayesian extreme value models, improving computational efficiency and prior formulation.

Findings

Enhanced MCMC convergence with orthogonal parameters

Facilitated derivation of Jeffreys and penalized complexity priors

Applied framework to real Garonne flow data

Abstract

Using Bayesian methods for extreme value analysis offers an alternative to frequentist ones, with several advantages such as easily dealing with parametric uncertainty or studying irregular models. However, computations can be challenging and the efficiency of algorithms can be altered by poor parametrization choices. The focus is on the Poisson process characterization of univariate extremes and outline two key benefits of an orthogonal parameterization. First, Markov chain Monte Carlo convergence is improved when applied on orthogonal parameters. This analysis relies on convergence diagnostics computed on several simulations. Second, orthogonalization also helps deriving Jeffreys and penalized complexity priors, and establishing posterior propriety thereof. The proposed framework is applied to return level estimation of Garonne flow data (France).