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

Castro-Camilo, D. , Mhalla, L. and Opitz, T. (2021) Bayesian space-time gap filling for inference on extreme hot-spots: an application to Red Sea surface temperatures. Extremes, 24(1), pp. 105-128. (doi: 10.1007/s10687-020-00394-z)

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.

• Item Type: Articles
• Status: Published
• Refereed: Yes
• Glasgow Author(s) Enlighten ID: Castro-Camilo, Dr Daniela
• Authors: Castro-Camilo, D., Mhalla, L., and Opitz, T.
• College/School: College of Science and Engineering > School of Mathematics and Statistics > Statistics
• Journal Name: Extremes
• Publisher: Springer
• ISSN: 1386-1999
• ISSN (Online): 1572-915X
• Published Online: 15 September 2020