Comparing Different Objective Priors for Extremes
摘要
The Generalized Extreme Value (GEV) distribution plays a crucial role in modeling block maxima due to the Fisher-Tippet-Gnedenko theorem. In this framework, one is typically interested in estimating return levels. It is well known that the use of maximum likelihood estimation (MLE) introduces bias in their estimation, and Bayesian inference offers a potential remedy. However, from a Bayesian perspective, there is no general consensus on which prior to use for this type of model in situations with limited or no prior information. The Jeffreys prior is a popular objective tool but, for the GEV distribution, it always yields an improper posterior. Recently, a new type of objective prior has been proposed. A simple form of this family is the multivariate Lomax distribution. Motivated by the availability of these results, we conduct a comparison between the multivariate Lomax prior and other objective priors for the inference on the GEV parameters. In particular, a truncated maximal data information density and the flat prior are considered. The comparison is made through a simulation study with particular emphasis to reliability analysis of return levels.