Statistical Modeling of Spatial Extremes

By A. C. Davison, Simone A. Padoan, Mathieu Ribatet. 2012

591 citations recorded by the source corpus.

The areal modeling of the extremes of a natural process such as rainfall or temperature is important in environmental statistics; for example, understanding extreme areal rainfall is crucial in flood protection. This article reviews recent progress in the statistical modeling of spatial extremes, starting with sketches of the necessary elements of extreme value statistics and geostatistics. The main types of statistical models thus far proposed, based on latent variables, on copulas and on spatial max-stable processes, are described and then are compared by application to a data set on rainfall in Switzerland. Whereas latent variable modeling allows a better fit to marginal distributions, it fits the joint distributions of extremes poorly, so appropriately-chosen copula or max-stable models seem essential for successful spatial modeling of extremes.

Subfields: Environmental Engineering, Finance, Global and Planetary Change

View Paper: https://www.semanticscholar.org/paper/253736c139bdaa46f3c9cd142eff4f06e6fe0f50

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Citations in the corpus

Exploiting Multi-Core Architectures for Reduced-Variance Estimation with Intractable Likelihoods (2014, methodology): “An early attempt to circumvent this difficulty is the pseudo-likelihood approach of Besag (1972), which in turn has been generalised to composite likelihood approximations, see for example Davison et al. (2012).”
Evaluating environmental joint extremes for the offshore industry (2012, methodology): “(2010), Davison and Gholamrezaee (2012) and Davison et al. (2012). Censored”
Random Fields Simplified: Preserving Marginal Distributions, Correlations, and Intermittency, With Applications From Rainfall to Humidity (2020, background): “…extremes, extreme value theory also provides other options such as max‐stable processes and corresponding random fields (e.g., Blanchet & Davison, 2011; Cooley et al., 2006; Davison et al., 2012; Davison & Gholamrezaee, 2012; Robert, 2013; Martin Schlather, 2002; Tyralis & Langousis, 2019).”
Spatial extremes: Max-stable processes at work (2013, methodology): “Similarly to the case study given in Davison et al. (2012), it might indicate difficulties in estimating the upper bound of the extremal coefficient function.”
Modelling spatial extreme events with environmental applications (2018, methodology): “This Gaussian assumption may appear to be a very strong assumption but it is the assumed process for all Brown-Resnick max-stable processes (Davison et al., 2012), for the type of processes given in Engelke et al. (2015) and in a conditional form for Pareto processes (Ferreira and de Haan, 2014). Th”
Modeling the spatial dependence of floods using the Fisher copula (2019, methodology): “…with their main catchment characteristics and an abbreviation that will be used in the sequel of this paper to refer to the individual stations For each of the measurement stations, an hourly runoff time series spanning 30 to 40 years was available from the Federal Ofﬁce for the Environment”
Flexible semiparametric generalized Pareto modeling of the entire range of rainfall amount (2019, unknown): “It would be of interest to adapt our model to make a regional analysis that will spatially share spatial information, marginally and in a multivariate way (see, e.g. Cooley et al. , 2007; Davison et al. , 2012; Carreau et al. , 2017).”
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).”
Bayesian estimation of rainfall intensity-duration-frequency relationships (2015, background): “Recent advances in Bayesian modelling of spatial extremes are reviewed in Davison et al. (2012).”
Geostatistics of Dependent and Asymptotically Independent Extremes (2013, background): “Other reviews, also involving comparisons with other approaches, include Davison et al. (2012) and Cooley et al. (2012a).”
Extended generalised Pareto models for tail estimation (2011, background): “ce of pooling parameters and more specically of the tail index in the extreme value modelling framework can be found in various applications including Coles and Tawn (1990); Cooley et al. (2007) and Davison et al. (2011) to name but a few. A A A A A A A A A A A A A A A A A A A A -0.6 -0.5 -0.4 -0.3 ”
Composite likelihood estimation for the Brown–Resnick process (2013, methodology): “The Smith model can be obtained by taking a Brown–Resnick process with variogram 2γ (h) = hT −1h for some covariance matrix , which corresponds to taking α = 2 after an affine transformation; on the other hand, Davison et al. (2012) found that 1/2 < α < 1 for the rainfall data they examined.”
Modeling Spatial Processes with Unknown Extremal Dependence Class (2017, background): “…P [X1 ≤ F−1X {1 − (tx1)−1} , . . . , Xd ≤ F−1X { 1 − (txd )−1 }]) , which describes the joint dependence of the associated maxstable or generalized Pareto process, see Davison, Padoan, and Ribatet (2012), Cooley et al. (2012), Segers (2012), or Davison and Huser (2015) for recent reviews on…”
Threshold modeling of extreme spatial rainfall (2013, methodology): “[3] Max-stable processes [de Haan, 1984; de Haan and Ferreira, 2006; Davison et al., 2012] extend the generalized extreme-value (GEV) distribution, which is widely used to describe univariate maxima, to the spatial setting, and thus provide consistent multivariate distributions for maxima in…”
Extreme value copulas and max-stable processes (2013, background): “It is not difficult to show [29, 5] that, for all z1, .”