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Extremes

, Volume 20, Issue 2, pp 239–263 | Cite as

A Poisson process reparameterisation for Bayesian inference for extremes

  • Paul SharkeyEmail author
  • Jonathan A. Tawn
Open Access
Article

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.

Keywords

Poisson processes Extreme value theory Bayesian inference Reparameterisation Covariate modelling 

AMS 2000 Subject Classifications

60G70 62F15 62P12 62G32 

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Copyright information

© The Author(s) 2016

Open AccessThis article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.

Authors and Affiliations

  1. 1.STOR-i Centre for Doctoral Training, Department of Mathematics and StatisticsLancaster UniversityLancasterUK

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