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We develop a method for probabilistic prediction of extreme value hot-spotsin a spatio-temporal framework, tailored to big datasets containing importantgaps. In this setting, direct calculation of summaries from data, such as theminimum over a space-time domain, is not possible. To obtain predictivedistributions for such cluster summaries, we propose a two-step approach. Wefirst model marginal distributions with a focus on accurate modeling of theright tail and then, after transforming the data to a standard Gaussian scale,we estimate a Gaussian space-time dependence model defined locally in the timedomain for the space-time subregions where we want to predict. In the firststep, we detrend the mean and standard deviation of the data and fit aspatially resolved generalized Pareto distribution to apply a correction of theupper tail. To ensure spatial smoothness of the estimated trends, we eitherpool data using nearest-neighbor techniques, or apply generalized additiveregression modeling. To cope with high space-time resolution of data, the localGaussian models use a Markov representation of the Mat\'ern correlationfunction based on the stochastic partial differential equations (SPDE)approach. In the second step, they are fitted in a Bayesian framework throughthe integrated nested Laplace approximation implemented in R-INLA. Finally,posterior samples are generated to provide statistical inferences throughMonte-Carlo estimation. Motivated by the 2019 Extreme Value Analysis datachallenge, we illustrate our approach to predict the distribution of localspace-time minima in anomalies of Red Sea surface temperatures, using a griddeddataset (11315 days, 16703 pixels) with artificially generated gaps. Inparticular, we show the improved performance of our two-step approach over apurely Gaussian model without tail transformations.

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