Default priors based on pseudo-likelihoods for the poisson-GPD model

Abstract

Extreme values are usually modeled with the peaks over the threshold approach by means of the Poisson-Generalized Pareto Distribution (Poisson-GPD). This model is governed by three parameters: the Poisson rate, the scale and the shape of the GPD. The quantity of interest, in many applications, is the mean return level which is a function of Poisson-GPD parameters. Moreover, the shape parameter of GPD is itself of interest in order to gain more insights on the underlying extremal process. For a suitable orthogonal parametrization, we derive matching priors for shape, scale and Poisson rate parameters based on an approximate conditional pseudo-likelihood. The formal rule, used here to obtain such priors, in some cases leads to the same priors obtained with Jeffreys’ and Reference procedures. Moreover, we can provide a formal proof that each marginal prior for shape and scale parameters, respectively, are second order matching priors. We estimate the coverages of the corresponding posterior credible intervals and apply our approach to an example from hydrology.