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

By Thomas Opitz, Raphaël Huser, H. Bakka, Håvard Rue. Extremes, 2018

106 citations recorded by the source corpus.

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%\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$99.8\%$\end{document} 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.

Subfields: Global and Planetary Change, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/dc69f8183d83033f7c9589afdae6b066be9420f5

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Citations in the corpus

Spatiotemporal wildfire modeling through point processes with moderate and extreme marks (2021, methodology): “Following Opitz et al. (2018), we use a log-link function for the median µGPDit of the GPD.”
Spatial modelling with R-INLA: A review (2018, background): “, 2018) and predicting extreme rainfall events in space and time (Opitz et al., 2018).”
Space-time landslide predictive modelling (2019, background): “The general framework of INLA is that of Bayesian latent Gaussian models, which has found widespread interest in a diverse range of applications (Lombardo et al., 2018a; Opitz et al., 2018; Krainski et al., 2018; Moraga, 2019).”
Geostatistical Modeling to Capture Seismic‐Shaking Patterns From Earthquake‐Induced Landslides (2018, background): “The INLA methodology is very general and has also found a wide range of applications beyond the spatial modeling of landslides (Illian et al., 2013; Opitz et al., 2018).”