Flexible covariate representations for extremes

Environmental extremes often show systematic variation with covariates. Three different non-parametric descriptions (penalised B-splines, Bayesian adaptive regression splines, and Voronoi partition) for the dependence of extreme value model parameters on covariates are considered. These descriptions take the generic form of a linear combination of basis functions on the covariate domain, but differ (a) in the way that basis functions are constructed and possibly modified, and potentially (b) by additional penalisation of the variability (e.g. variance or roughness) of basis coefficients, for a given sample, to improve inference. The three representations are used to characterise variation of parameters in a non-stationary generalised Pareto model for the magnitude of threshold exceedances with respect to covariates. Computationally-efficient schemes for Bayesian inference are used, including mMALA (Riemann manifold Metropolis-adjusted Langevin algorithm) and reversible jump. A simulation study assesses relative performance of the three descriptions in estimating the distribution of the T-year maximum event (for arbitrary T greater than the period of the sample) from a peaks over threshold extreme value analysis with respect to a single periodic covariate. The three descriptions are also used to estimate a directional tail model for peaks over threshold of storm peak significant wave height at a location in the northern North Sea.