Bayesian space-time gap filling for inference on extreme hot-spots: an application to Red Sea surface temperatures

Daniela Castro-Camilo, Linda Mhalla, Thomas Opitz

Research output: Contribution to journalArticlepeer-review

5 Scopus citations

Abstract

We develop a method for probabilistic prediction of extreme value hot-spots in a spatio-temporal framework, tailored to big datasets containing important gaps. In this setting, direct calculation of summaries from data, such as the minimum over a space-time domain, is not possible. To obtain predictive distributions for such cluster summaries, we propose a two-step approach. We first model marginal distributions with a focus on accurate modeling of the right tail and then, after transforming the data to a standard Gaussian scale, we estimate a Gaussian space-time dependence model defined locally in the time domain for the space-time subregions where we want to predict. In the first step, we detrend the mean and standard deviation of the data and fit a spatially resolved generalized Pareto distribution to apply a correction of the upper tail. To ensure spatial smoothness of the estimated trends, we either pool data using nearest-neighbor techniques, or apply generalized additive regression modeling. To cope with high space-time resolution of data, the local Gaussian models use a Markov representation of the Matérn correlation function based on the stochastic partial differential equations (SPDE) approach. In the second step, they are fitted in a Bayesian framework through the integrated nested Laplace approximation implemented in R-INLA. Finally, posterior samples are generated to provide statistical inferences through Monte-Carlo estimation. Motivated by the 2019 Extreme Value Analysis data challenge, we illustrate our approach to predict the distribution of local space-time minima in anomalies of Red Sea surface temperatures, using a gridded dataset (11315 days, 16703 pixels) with artificially generated gaps. In particular, we show the improved performance of our two-step approach over a purely Gaussian model without tail transformations.
Original languageEnglish (US)
Pages (from-to)105-128
Number of pages24
JournalExtremes
Volume24
Issue number1
DOIs
StatePublished - Sep 15 2020
Externally publishedYes

Bibliographical note

KAUST Repository Item: Exported on 2022-06-14
Acknowledgements: This work started when Daniela Castro-Camilo was a postdoctoral fellow at King Abdullah University of Science and Technology (KAUST). Support from the KAUST Supercomputing Laboratory and access to Shaheen is therefore gratefully acknowledged. Linda Mhalla acknowledges the financial support of the Swiss National Science Foundation.
This publication acknowledges KAUST support, but has no KAUST affiliated authors.

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