2020/04/01 by Daniela Castro‐Camilo, Linda Mhalla, Castro-Camilo, Daniela +3
Economics, Econometrics and Finance · Environmental Science · Mathematics · #Climate variability and models #FOS: Computer and information sciences #Methodology (stat.ME) #Spatial and Panel Data Analysis #Statistical Methods and Inference
paper · pdf · doi:10.48550/arxiv.2004.00386
openalex publication_date 2020/04/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We develop a method for probabilistic prediction of extreme value hot-spots\nin a spatio-temporal framework, tailored to big datasets containing important\ngaps. In this setting, direct calculation of summaries from data, such as the\nminimum over a space-time domain, is not possible. To obtain predictive\ndistributions for such cluster summaries, we propose a two-step approach. We\nfirst model marginal distributions with a focus on accurate modeling of the\nright tail and then, after transforming the data to a standard Gaussian scale,\nwe estimate a Gaussian space-time dependence model defined locally in the time\ndomain for the space-time subregions where we want to predict. In the first\nstep, we detrend the mean and standard deviation of the data and fit a\nspatially resolved generalized Pareto distribution to apply a correction of the\nupper tail. To ensure spatial smoothness of the estimated trends, we either\npool data using nearest-neighbor techniques, or apply generalized additive\nregression modeling. To cope with high space-time resolution of data, the local\nGaussian models use a Markov representation of the Mat 'ern correlation\nfunction based on the stochastic partial differential equations (SPDE)\napproach. In the second step, they are fitted in a Bayesian framework through\nthe integrated nested Laplace approximation implemented in R-INLA. Finally,\nposterior samples are generated to provide statistical inferences through\nMonte-Carlo estimation. Motivated by the 2019 Extreme Value Analysis data\nchallenge, we illustrate our approach to predict the distribution of local\nspace-time minima in anomalies of Red Sea surface temperatures, using a gridded\ndataset (11315 days, 16703 pixels) with artificially generated gaps. In\nparticular, we show the improved performance of our two-step approach over a\npurely Gaussian model without tail transformations.\n