https://hal-univ-avignon.archives-ouvertes.fr/hal-02504783Allard, DenisDenisAllardBioSP - Biostatistique et Processus Spatiaux - INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’EnvironnementEmery, XavierXavierEmeryDepartment of Mining Engineering and Advanced Mining Technology Center - Department of Mining Engineering and Advanced Mining Technology Center - UCHILE - Universidad de Chile = University of Chile [Santiago]Lacaux, CélineCélineLacauxLMA - EA2151 Laboratoire de Mathématiques d'Avignon - AU - Avignon UniversitéLantuéjoul, ChristianChristianLantuéjoulGEOSCIENCES - Centre de Géosciences - MINES ParisTech - École nationale supérieure des mines de Paris - PSL - Université Paris sciences et lettresSimulating space-time random fields with nonseparable Gneiting-type covariance functionsHAL CCSD2020[MATH.MATH-PR] Mathematics [math]/Probability [math.PR][STAT] Statistics [stat]Lacaux, Céline2020-03-11 09:20:192022-02-22 11:36:042020-03-11 09:20:19enJournal articles10.1007/s11222-020-09956-41Two algorithms are proposed to simulate space-time Gaussian random fields with a covariance function belonging to an extended Gneiting class, the definition of which depends on a completely monotone function associated with the spatial structure and a conditionally negative definite function associated with the temporal structure. In both cases, the simulated random field is constructed as a weighted sum of cosine waves, with a Gaussian spatial frequency vector and a uniform phase. The difference lies in the way to handle the temporal component. The first algorithm relies on a spectral decomposition in order to simulate a temporal frequency conditional upon the spatial one, while in the second algorithm the temporal frequency is replaced by an intrinsic random field whose variogram is proportional to the conditionally negative definite function associated with the temporal structure. Both algorithms are scalable as their computational cost is proportional to the number of space-time locations, which may be unevenly spaced in space and/or in time. They are illustrated and validated through synthetic examples.