A1224
Title: Tuning-free objective Bayesian inference for extremes
Authors: Paolo Onorati - University of Padova (Italy) [presenting]
Isadora Antoniano-Villalobos - Ca Foscari University of Venice (Italy)
Antonio Canale - University of Padua (Italy)
Abstract: The generalized extreme value (GEV) distribution is widely used for modeling extreme events. Despite its frequent application, there is no consensus on the choice of prior distributions for the parameters in the Bayesian framework. The aim is to propose the usage of an objective prior based on a scoring rule, leading to a multivariate Lomax distribution for positive parameters and a double multivariate Lomax distribution for the general case. However, despite being well motivated by theoretical arguments, this choice introduces computational challenges, as the full conditional distributions do not have a closed form. Practical solutions are provided to these issues by exploiting a generalized elliptical slice sampling (GESS), which yields a self-contained algorithm that does not require tuning parameters and is rejection-free, ensuring that consecutive values in the chain are distinct. This method is quite general and can be extended to many other parametric families. The approach utilizes a new version of the multivariate logistic distribution, represented as a scale mixture of Gaussian distributions. It is shown how to compute its density and sample from the full conditional of the mixing density. The algorithm's performance is evaluated through simulation studies and empirical analysis.
