Geostatistics of extremes

By A. C. Davison, Mehdi Mohammad Gholamrezaee. Proceedings of the Royal Society A, 2012

204 citations recorded by the source corpus.

We describe a prototype approach to flexible modelling for maxima observed at sites in a spatial domain, based on fitting of max-stable processes derived from underlying Gaussian random fields. The models we propose have generalized extreme-value marginal distributions throughout the spatial domain, consistent with statistical theory for maxima in simpler cases, and can incorporate both geostatistical correlation functions and random set components. Parameter estimation and fitting are performed through composite likelihood inference applied to observations from pairs of sites, with occurrence times of maxima taken into account if desired, and competing models are compared using appropriate information criteria. Diagnostics for lack of model fit are based on maxima from groups of sites. The approach is illustrated using annual maximum temperatures in Switzerland, with risk analysis proposed using simulations from the fitted max-stable model. Drawbacks and possible developments of the approach are discussed.

Subfields: Environmental Engineering, Finance, Global and Planetary Change

View Paper: https://www.semanticscholar.org/paper/ccc09f372d239545cd5050432e1e86a010de720a

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Citations in the corpus

Spatial modeling of extreme snow depth (2011, methodology): “Davison and Gholamrezaee (2010) have proposed extensions to allow independence in (8), and Kabluchko, Schlather and de Haan (2009) have extended both Smith’s and Schlather’s representations.”
Non-Stationary Dependence Structures for Spatial Extremes (2014, methodology): “In particular, when df = 1, (6) reduces to the Schlather (2002) model, which has been fitted in numerous applications (Davison and Gholamrezaee, 2012; Davison et al., 2012; Ribatet, 2013; Thibaud et al., 2013).”
Statistical Modeling of Spatial Extremes (2012, background): “Davison and Gholamrezaee (2012) fit models based on (22) and (23) to extreme temperature data.”
Functional peaks‐over‐threshold analysis (2020, methodology): “Model comparison can be performed using the Akaike or composite likelihood information criteria (Davison and Gholamrezaee, 2012), and formal comparison of nested models can be based on scoring rules (Dawid et al.”
Space–time modelling of extreme events (2012, methodology): “We considered a variant, CLICÅ, which is scaled to be comparable with AIC for independent data (Davison and Gholamrezaee, 2012).”
Composite likelihood estimation for the Brown–Resnick process (2013, methodology): “Likelihood inference for max-stable models is difficult, since only the bivariate marginal density functions are known in most cases, and pairwise marginal likelihood is typically used (Padoan et al., 2010; Davison & Gholamrezaee, 2012).”
Geostatistics of Dependent and Asymptotically Independent Extremes (2013, methodology): “The composite likelihood information criterion, CLIC, the analogue of the AIC for composite likelihoods, allows model comparison (Varin and Vidoni 2005; Davison and Gholamrezaee 2012).”
Evaluating environmental joint extremes for the offshore industry (2012, methodology): “Despite the fact that the full multivariate probability density function cannot be written in closed form, composite likelihood methods provide one approach to inference as illustrated e.g. by Padoan et al. (2010), Davison and Gholamrezaee (2012) and Davison et al. (2012).”
Likelihood estimators for multivariate extremes (2014, unknown): “A log-pairwise likelihood based on block maxima may be written as Max,Pair(ψ) = N∑ i=1 ∑ d1<d2 log { g ( mi,d1 , mi,d2; ψ )} , (24) where g(z1, z2; ψ) denotes the bivariate density stemming from G(z) (Padoan et al. 2010; Davison and Gholamrezaee 2012).”
AN OVERVIEW OF COMPOSITE LIKELIHOOD METHODS (2011, methodology): “Despite the attractive properties of these models, both classical and Bayesian inference are impractical because of the curse of dimensionality with the likelihood computation, see Davison and Gholamrezaee (2009). At the present time, only expressions for bivariate marginal densities have been deriv”