Priors for a Bayesian Analysis of Extreme Values

Sally A. Wood, Melbourne Business School, University of Melbourne
julian Wang, University of Western Sydney

Abstract

This article proposes a new prior specification for a Bayesian analysis of the k largest order statistics model. We show that using Jeffreys priors for the end-point and shape parameters of the k largest order statistics model leads to biased estimates of the shape parameter for small to medium sample sizes and to the posterior mode of the end-point being equal to the most extreme observed value. We propose a conjugate prior for the shape parameter and a prior for the end-point which removes the posterior mode at the most extreme observed value while remaining uninformative for values of the end-point away from this value. We show by simulation that the proposed priors perform well even when the sample sizes are small and/or when the shape parameter is less than one. We illustrate the performance of our method by comparing the tail distributions of female and male lifespans and by analysing the improvement in time of the men's 100m sprint from the 68 &72 Olympic games to the 1988 &1992 Olympics.