Title: Practical left-tail correction for the GEV model
Authors: Daniela Castro-Camilo - University of Glasgow (United Kingdom) [presenting]
Abstract: The generalized extreme value distribution (GEV) is a three parameters family that describes the asymptotic behaviour of properly normalized maxima of a sequence of independent and identically distributed random variables. If the shape parameter $\xi$ is equal to zero, the GEV has infinite support, whereas if $\xi>0$, the limiting distribution has a power-law decay with infinite upper endpoint but finite lower endpoint. In practical applications, we assume that the GEV is a reasonable approximation for the distribution of maxima over blocks and we fit it accordingly. This implies that GEV properties, such as finite lower endpoint in the case $\xi>0$, are inherited by the original distribution of block maxima, which might not have bounded support. This issue is particularly problematic in the presence of covariates. We propose the blended GEV distribution with infinite support to tackle this usually overlooked issue. Using a Bayesian framework, we reparametrize the GEV to offer a more natural interpretation of the (possible covariate-dependent) model parameters. Independent priors over the new location and spread parameters produce a joint prior distribution for the original location and scale parameters, while a property-preserving penalized complexity prior approach is used for the shape parameter to avoid inconsistencies in the existence of first and second moments.