INLA goes extreme: Bayesian tail regression for the estimation of high spatio-temporal quantiles

Type
Article

Authors
Opitz, Thomas
Huser, Raphaël
Bakka, Haakon
Rue, Haavard

KAUST Department
Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
Statistics Program

KAUST Grant Number
OSR-CRG2017-3434

Preprint Posting Date
2018-02-04

Online Publication Date
2018-05-25

Print Publication Date
2018-09

Date
2018-05-25

Abstract
This work is motivated by the challenge organized for the 10th International Conference on Extreme-Value Analysis (EVA2017) to predict daily precipitation quantiles at the 99.8% level for each month at observed and unobserved locations. Our approach is based on a Bayesian generalized additive modeling framework that is designed to estimate complex trends in marginal extremes over space and time. First, we estimate a high non-stationary threshold using a gamma distribution for precipitation intensities that incorporates spatial and temporal random effects. Then, we use the Bernoulli and generalized Pareto (GP) distributions to model the rate and size of threshold exceedances, respectively, which we also assume to vary in space and time. The latent random effects are modeled additively using Gaussian process priors, which provide high flexibility and interpretability. We develop a penalized complexity (PC) prior specification for the tail index that shrinks the GP model towards the exponential distribution, thus preventing unrealistically heavy tails. Fast and accurate estimation of the posterior distributions is performed thanks to the integrated nested Laplace approximation (INLA). We illustrate this methodology by modeling the daily precipitation data provided by the EVA2017 challenge, which consist of observations from 40 stations in the Netherlands recorded during the period 1972–2016. Capitalizing on INLA’s fast computational capacity and powerful distributed computing resources, we conduct an extensive cross-validation study to select the model parameters that govern the smoothness of trends. Our results clearly outperform simple benchmarks and are comparable to the best-scoring approaches of the other teams.

Citation
Opitz T, Huser R, Bakka H, Rue H (2018) INLA goes extreme: Bayesian tail regression for the estimation of high spatio-temporal quantiles. Extremes. Available: http://dx.doi.org/10.1007/s10687-018-0324-x.

Acknowledgements
We thank Olivier Wintenberger for organizing the competition for the 10th International Conference on Extreme-Value Analysis. This publication is based upon work supported by the King Abdullah University of Science and Technology (KAUST) Office of Sponsored Research (OSR) under Award No. OSR-CRG2017-3434. Support from the KAUST Supercomputing Laboratory and access to Shaheen II is gratefully acknowledged.

Publisher
Springer Nature

Journal
Extremes

DOI
10.1007/s10687-018-0324-x

arXiv
1802.01085

Additional Links
https://link.springer.com/article/10.1007%2Fs10687-018-0324-x

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