A Poisson process reparameterisation for Bayesian inference for extremes

TL;DR

This paper introduces a novel Bayesian estimation method for extreme value models using a reparameterisation with a tuning parameter m, improving convergence and sampling efficiency in Poisson process models for extremes.

Contribution

It proposes a reparameterisation technique with an optimal m that orthogonalises parameters, enhancing Bayesian inference for Poisson process models of extremes.

Findings

Improved convergence speed in MCMC sampling.

More efficient joint posterior sampling.

Validated on extreme rainfall data in Cumbria, UK.

Abstract

A common approach to modelling extreme values is to consider the excesses above a high threshold as realisations of a non-homogeneous Poisson process. While this method offers the advantage of modelling using threshold-invariant extreme value parameters, the dependence between these parameters makes estimation more difficult. We present a novel approach for Bayesian estimation of the Poisson process model parameters by reparameterising in terms of a tuning parameter $m$. This paper presents a method for choosing the optimal value of m that near-orthogonalises the parameters, which is achieved by minimising the correlation between the asymptotic posterior distribution of the parameters. This choice of m ensures more rapid convergence and efficient sampling from the joint posterior distribution using Markov Chain Monte Carlo methods. Samples from the parameterisation of interest are then obtained by a simple transform. Results are presented in the cases of identically and non-identically distributed models for extreme rainfall in Cumbria, UK.