Generalized Pareto processes for simulating space-time extreme events

Fátima Palacios-Rodríguez , Gwladys Toulemonde , Julie Carreau (1) , Thomas Opitz (2)

1 HSM - Hydrosciences Montpellier
2 BioSP - Biostatistique et Processus Spatiaux

To better manage the risks of destructive natural disasters, impact models can be fed with simulations of extreme scenarios to study sensitivity to temporal and spatial variability. We propose semi-parametric stochastic simulation of realistic spatio-temporal extreme fields using a moderate number of observed extreme space-time episodes to generate an unlimited number of extreme scenarios of any magnitude. Our framework draws sound theoretical justification from extreme value theory, building on generalized Pareto limit processes. For illustration on hourly gridded precipitation data in Mediterranean France, we calculate risk measures using extreme event simulations for yet unobserved magnitudes.

Mots clés: extreme-value theory; precipitation; space-time Pareto processes; stochastic simula- tion

Domaines: Théorie [stat.TH]; Méthodologie [stat.ME]; Calcul [stat.CO]; Applications [stat.AP]

Fátima Palacios-Rodríguez, Gwladys Toulemonde, Julie Carreau, Thomas Opitz. Generalized Pareto processes for simulating space-time extreme events. 2019. ⟨hal-02136681v1⟩