A Poisson process reparameterisation for Bayesian inference for extremes

作者：Sharkey Paul^*; Tawn Jonathan A

来源：Extremes, 2017, 20(2): 239-263.

DOI：10.1007/s10687-016-0280-2

• Poisson processes
• Extreme value theory
• Bayesian inference
• Reparameterisation
• Covariate modelling

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.

• 出版日期2017-6