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A common approach to modelling extreme values is to consider the excessesabove a high threshold as realisations of a non-homogeneous Poisson process.While this method offers the advantage of modelling using threshold-invariantextreme value parameters, the dependence between these parameters makesestimation more difficult. We present a novel approach for Bayesian estimationof the Poisson process model parameters by reparameterising in terms of atuning parameter $m$. This paper presents a method for choosing the optimalvalue of m that near-orthogonalises the parameters, which is achieved byminimising the correlation between the asymptotic posterior distribution of theparameters. This choice of m ensures more rapid convergence and efficientsampling from the joint posterior distribution using Markov Chain Monte Carlomethods. Samples from the parameterisation of interest are then obtained by asimple transform. Results are presented in the cases of identically andnon-identically distributed models for extreme rainfall in Cumbria, UK.

A Poisson process reparameterisation for Bayesian inference for extremes