Title: Efficient adaptive covariate modelling for extremes
Authors: Philip Jonathan - Lancaster University / Shell Research Limited (United Kingdom) [presenting]
David Randell - Shell (Netherlands)
Elena Zanini - Lancaster University (United Kingdom)
Emma Ross - Shell (Netherlands)
Matthew Jones - Shell (Netherlands)
Abstract: The characteristics of extreme values are usually dependent on covariates. For example, the severity of the ocean environment in a storm typically depends on a number of covariates, including the direction of storm propagation and the season of storm occurrence. Reliable practical application of extreme value methods therefore needs to accommodate the effects of covariates in a statistically- and computationally- efficient manner, and to quantify uncertainties in inferences carefully. Penalised spline representations for the variation of extreme value parameters with multi-dimensional covariates have been demonstrated to be useful and flexible; inference however becomes computationally unwieldy as the dimensionality of the covariate space and the complexity of covariate effects increase. For this reason, we explore alternative representations for covariate effects in extreme value models which yield more efficient, scalable inference without loss of (too much) flexibility. Specifically, for 2-dimensional covariates, we consider (a) Bayesian adaptive regression spline (BARS) parameterisations, and (b) Bayesian piecewise constant representations (motivated by previous work and Voronoi partitions of the covariate domain) of covariate effects in non-stationary extreme value models, and compare the performance of these models with those based on (c) Bayesian penalised B-spline representations.