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A Poisson process reparameterisation for Bayesian inference for extremes

Research output: Contribution to journalJournal article

Published
<mark>Journal publication date</mark>06/2017
<mark>Journal</mark>Extremes
Issue number2
Volume20
Number of pages25
Pages (from-to)239-263
<mark>State</mark>Published
Early online date17/12/16
<mark>Original language</mark>English

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 dicult. 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 ecient 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.