TY - JOUR

T1 - Flexible covariate representations for extremes

AU - Zanini, Elena

AU - Eastoe, Emma

AU - Jones, Matthew

AU - Randell, David

AU - Jonathan, Philip

N1 - This is the peer reviewed version of the following article: Zanini, E, Eastoe, E, Jones, MJ, Randell, D, Jonathan, P. Flexible covariate representations for extremes. Environmetrics. 2020;e2624. https://doi.org/10.1002/env.2624 which has been published in final form at https://onlinelibrary.wiley.com/doi/abs/10.1002/env.2624 This article may be used for non-commercial purposes in accordance With Wiley Terms and Conditions for self-archiving.

PY - 2020/8/1

Y1 - 2020/8/1

N2 - Environmental extremes often show systematic variation with covariates. Three different nonparametric descriptions (penalized 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 (i) in the way that basis functions are constructed and possibly modified, and potentially (ii) by additional penalization of the variability (e.g., variance or roughness) of basis coefficients, for a given sample, to improve inference. The three representations are used to characterize variation of parameters in a nonstationary generalized Pareto model for the magnitude of threshold exceedances with respect to covariates. Computationally efficient schemes for Bayesian inference are used, including 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.

AB - Environmental extremes often show systematic variation with covariates. Three different nonparametric descriptions (penalized 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 (i) in the way that basis functions are constructed and possibly modified, and potentially (ii) by additional penalization of the variability (e.g., variance or roughness) of basis coefficients, for a given sample, to improve inference. The three representations are used to characterize variation of parameters in a nonstationary generalized Pareto model for the magnitude of threshold exceedances with respect to covariates. Computationally efficient schemes for Bayesian inference are used, including 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.

U2 - 10.1002/env.2624

DO - 10.1002/env.2624

M3 - Journal article

VL - 31

JO - Environmetrics

JF - Environmetrics

SN - 1180-4009

IS - 5

M1 - e2624

ER -