  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.
