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

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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.

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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.

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Authors and Affiliations

  1. School of Mathematics and Statistics, University of Glasgow, Glasgow, UK

    Daniela Castro-Camilo

  2. Department of Decision Sciences, HEC Montréal, Montréal, Canada

    Linda Mhalla

  3. Biostatistics and Spatial Processes, INRAE, Avignon, France

    Thomas Opitz

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  1. Daniela Castro-Camilo
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  2. Linda Mhalla
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  3. Thomas Opitz
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Correspondence to Linda Mhalla.

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Castro-Camilo, D., Mhalla, L. & Opitz, T. Bayesian space-time gap filling for inference on extreme hot-spots: an application to Red Sea surface temperatures. Extremes 24, 105–128 (2021). https://doi.org/10.1007/s10687-020-00394-z

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