The Annals of Applied Statistics

Extremes on river networks

Abstract

Max-stable processes are the natural extension of the classical extreme-value distributions to the functional setting, and they are increasingly widely used to estimate probabilities of complex extreme events. In this paper we broaden them from the usual situation in which dependence varies according to functions of Euclidean distance to situations in which extreme river discharges at two locations on a river network may be dependent because the locations are flow-connected or because of common meteorological events. In the former case dependence depends on river distance, and in the second it depends on the hydrological distance between the locations, either of which may be very different from their Euclidean distance. Inference for the model parameters is performed using a multivariate threshold likelihood, which is shown by simulation to work well. The ideas are illustrated with data from the upper Danube basin.

Article information

Source
Ann. Appl. Stat., Volume 9, Number 4 (2015), 2023-2050.

Dates
Revised: July 2015
First available in Project Euclid: 28 January 2016

https://projecteuclid.org/euclid.aoas/1453994189

Digital Object Identifier
doi:10.1214/15-AOAS863

Mathematical Reviews number (MathSciNet)
MR3456363

Zentralblatt MATH identifier
06560819

Citation

Asadi, Peiman; Davison, Anthony C.; Engelke, Sebastian. Extremes on river networks. Ann. Appl. Stat. 9 (2015), no. 4, 2023--2050. doi:10.1214/15-AOAS863. https://projecteuclid.org/euclid.aoas/1453994189

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Supplemental materials

• Supplement to “Extremes on river networks”. The supplementary material contains the following: a PDF document containing the derivation of the new likelihood representation mentioned in Section 4.3.2, results of the simulation study mentioned in Section 4.3.3, and additional details germane to Section 5.3; and R code and data files to reproduce the data analysis and figures.