Conditional simulation of max-stable processes

By Clément Dombry, Fr'ed'eric 'Eyi-Minko, Mathieu Ribatet. 2012

93 citations recorded by the source corpus.

Since many environmental processes are spatial in extent, a single extreme event may affect several locations, and the spatial dependence must be taken into account in an appropriate way. This paper proposes a framework for conditional simulation of max-stable processes and gives closed forms for the regular conditional distributions of Brown--Resnick and Schlather processes. We test the method on simulated data and present applications to extreme rainfall around Zurich and extreme temperatures in Switzerland. The proposed framework provides accurate conditional simulations and can handle problems of realistic size. Copyright 2013, Oxford University Press.

Subfields: Environmental Engineering, Finance, Global and Planetary Change

View Paper: https://www.semanticscholar.org/paper/88a3302c868512c3916bd37acc8ad4cf7f9b7cd9

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Citations in the corpus

Modeling asymptotically independent spatial extremes based on Laplace random fields (2015, background): “ependence among maxima of components, for instance), and it would considerably underestimate joint risks at the subasymptotic level. Moreover, the limiting Pareto processes for threshold exceedances [Dombry et al., 2013, Ferreira and De Haan, 2014, Dombry and Ribatet, 2014, Thibaud and Opitz, 2015] ”
Extreme value copulas and max-stable processes (2013, methodology): “For each model and following the work of [4, 10], we consider the following trend surfaces”
Estimation of Hüsler–Reiss distributions and Brown–Resnick processes (2012, background): “Research on theoretical properties of Brown–Resnick processes is rapidly advancing at present (e.g. Engelke et al. (2011), Oesting et al. (2012) and Dombry et al. (2013)).”
Spatial extremes: Max-stable processes at work (2013, methodology): “Given Z(x) = z, it can be shown Dombry et al. (2013) that Φ can be decomposed into two independent point processes”
Regular conditional distributions of continuous max-infinitely divisible random fields (2013, methodology): “According to Equation (4.1) P[η(s) z | η(t) = y] = Pt(y, {f(s) z}) exp[−µ({f(s) 6 z, f(t) y})].”
Bridging asymptotic independence and dependence in spatial extremes using Gaussian scale mixtures (2016, methodology): “…new models to make inference based on a full likelihood with partial censoring and to eﬃciently perform conditional simulation, which is much more tricky when max-stable models are involved (Dombry et al., 2013). propose several new models able to transition from one asymptotic regime to the other.”
Threshold modeling of extreme spatial rainfall (2013, methodology): “[27] Another class of asymptotically independent models, related to the classical theory of geostatistics and kriging [Diggle and Ribeiro, 2007], corresponds to fitting a Gaussian copula to threshold exceedances, or equivalently to fitting a Gaussian process to transformed margins.”
Efficient inference and simulation for elliptical Pareto processes (2013, methodology): “These stations have elevations varying from 327 to 718 m. Similar data were used by Davison et al. (2012) for maxstable estimation and by Dombry et al. (2013) for conditional max-stable simulation.”
Graphical models for extremes (2018, background): “2=y 1); (y 1;y 2) 2E; (12) satises conditions (L1) and (L2) above and thus denes a valid exponent measure density. We call U1 2 the extremal function at coordinate 2, relative to coordinate 1 (cf., Dombry et al., 2013, 2016). Equivalently, we can write the density in terms of the extremal function U”