1. Hierarchical Space-Time Modeling of Asymptotically Independent Exceedances With an Application to Precipitation Data
- Author
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Gwladys Toulemonde, Carlo Gaetan, Jean-Noël Bacro, Thomas Opitz, Institut Montpelliérain Alexander Grothendieck (IMAG), Université de Montpellier (UM)-Centre National de la Recherche Scientifique (CNRS), Dipartimento di Scienze Ambientali, Informatica e Statistica [Venezia] (DAIS), University of Ca’ Foscari [Venice, Italy], Biostatistique et Processus Spatiaux (BIOSP), Institut National de la Recherche Agronomique (INRA), Littoral, Environnement : Méthodes et Outils Numériques (LEMON), Inria Sophia Antipolis - Méditerranée (CRISAM), Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), Université de Montpellier (UM), Centre National de la Recherche Scientifique (CNRS), Biostatistique et Processus Spatiaux (BioSP), Littoral, Environment: MOdels and Numerics (LEMON), Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Institut Montpelliérain Alexander Grothendieck (IMAG), Université de Montpellier (UM)-Centre National de la Recherche Scientifique (CNRS)-Université de Montpellier (UM)-Centre National de la Recherche Scientifique (CNRS)-Hydrosciences Montpellier (HSM), Institut de Recherche pour le Développement (IRD)-Institut national des sciences de l'Univers (INSU - CNRS)-Université de Montpellier (UM)-Centre National de la Recherche Scientifique (CNRS)-Institut de Recherche pour le Développement (IRD)-Institut national des sciences de l'Univers (INSU - CNRS)-Centre National de la Recherche Scientifique (CNRS), French National Programme LEFE/INSU, LabEx NUMEV, financial support from Ca’ Foscari University, Italy, and Centre National de la Recherche Scientifique (CNRS)-Université de Montpellier (UM)
- Subjects
Statistics and Probability ,Quasi-maximum likelihood ,Computer science ,01 natural sciences ,Composite likelihood ,010104 statistics & probability ,Asymptotic independence ,Gamma random fields ,Hourly precipitation ,Space-time convolution ,Space-time extremes ,[MATH.MATH-ST]Mathematics [math]/Statistics [math.ST] ,0502 economics and business ,Precipitation ,Statistical physics ,0101 mathematics ,050205 econometrics ,[STAT.AP]Statistics [stat]/Applications [stat.AP] ,Symptotic independence ,Space time ,05 social sciences ,Statistical model ,[STAT.TH]Statistics [stat]/Statistics Theory [stat.TH] ,[STAT]Statistics [stat] ,Event data ,Key (cryptography) ,Statistics, Probability and Uncertainty ,Settore SECS-S/01 - Statistica - Abstract
International audience; The statistical modeling of space-time extremes in environmental applications is key to understanding complex dependence structures in original event data and to generating realistic scenarios for impact models. In this context of high-dimensional data, we propose a novel hierarchical model for high threshold exceedances defined over continuous space and time by embedding a space-time Gamma process convolution for the rate of an exponential variable, leading to asymptotic independence inspace and time. Its physically motivated anisotropic dependence structure is based on geometric objects moving through space-time according to a velocity vector. We demonstrate that inference based on weighted pairwise likelihood is fast and accurate. The usefulness of our model is illustrated by an application to hourly precipitation data from a study region in Southern France, where it clearly improves on an alternative censored Gaussian space-time random field model. While classical limit models based on threshold-stability fail to appropriately capture relatively fast joint tail decay rates between asymptotic dependence and classical independence, strong empirical evidence from our application and other recent case studies motivates the use of more realistic asymptotic independence models such as ours.
- Published
- 2019
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