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arXiv · 1605.03508

A Poisson process reparameterisation for Bayesian inference for extremes

Paul Sharkey·Jonathan A. Tawn
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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.

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Paul Sharkey, Jonathan A. Tawn. 2016-12-08. A Poisson process reparameterisation for Bayesian inference for extremes. https://arxiv.org/abs/1605.03508

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