Geostatistics of Dependent and Asymptotically Independent Extremes

By A. C. Davison, Raphaël Huser, Emeric Thibaud. Mathematical Geosciences, 2013

123 citations recorded by the source corpus.

Spatial modeling of rare events has obvious applications in the environmental sciences and is crucial when assessing the effects of catastrophic events (such as heatwaves or widespread flooding) on food security and on the sustainability of societal infrastructure. Although classical geostatistics is largely based on Gaussian processes and distributions, these are not appropriate for extremes, for which max-stable and related processes provide more suitable models. This paper provides a brief overview of current work on the statistics of spatial extremes, with an emphasis on the consequences of the assumption of max-stability. Applications to winter minimum temperatures and daily rainfall are described.

Subfields: Environmental Engineering, Finance, Global and Planetary Change

View Paper: https://www.semanticscholar.org/paper/e995a8423b80cc8ead8c0c1ddd639ef3df0f9ab3

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Citations in the corpus

Efficient inference and simulation for elliptical Pareto processes (2013, methodology): “More realistic models such as the extremal Gaussian model (Schlather, 2002) or the Brown–Resnick-type models (Brown & Resnick, 1977; Kabluchko et al., 2009) have proven to be well-suited for modelling extremal dependence of environmental data (Davison et al., 2012, 2013; Thibaud et al., 2013).”
Space–time modelling of extreme events (2012, background): “However, it is common in practice to observe two distinct events becoming increasingly less dependent as their rarity increases, in particular when rainfall data are considered (Davison et al., 2013).”
Modeling Spatial Processes with Unknown Extremal Dependence Class (2017, background): “Mistakenly identifying this asymptotically-vanishing dependence as genuine asymptotic dependence, and fitting a max-stable or generalized Pareto model, will lead to incorrect extrapolation into the joint upper tail (Davison et al., 2013). Appropriately capturing the rate of tail decay in threshold e”
Bridging asymptotic independence and dependence in spatial extremes using Gaussian scale mixtures (2016, background): “However, as far as the modeling of extremes is concerned, they have been heavily criticized (Davison et al., 2013) as being unable to capture asymptotic dependence; Gaussian processes are asymptotically independent, meaning that the dependence strength between events observed at two distinct…”
Non-Stationary Dependence Structures for Spatial Extremes (2014, background): “One possibility would be to “invert” the non-stationary max-stable models proposed above (see Wadsworth and Tawn, 2012; Davison et al., 2013).”
Factor Copula Models for Replicated Spatial Data (2015, methodology): “ting extreme-value copula in the exponential factor model (Example 2) corresponds to the Hu¨sler and Reiss (1989) distribution, which has been widely used as a ﬂexible family to model extreme events (Davison et al., 2013, 2012; Huser and Davison, 2013; Thibaud et al., 2013). The proof of this result”
Modeling asymptotically independent spatial extremes based on Laplace random fields (2015, background): “For many processes like wind gust speed or heavy rainfall such behavior seems plausible owing to physical limits, and it is corroborated by empirical findings (Davison et al., 2013; Thibaud et al., 2013; Opitz et al., 2015).”