Likelihood-Based Inference for Max-Stable Processes

By Simone A. Padoan, Mathieu Ribatet, Scott Anthony Sisson. 2009

449 citations recorded by the source corpus.

The last decade has seen max-stable processes emerge as a common tool for the statistical modeling of spatial extremes. However, their application is complicated due to the unavailability of the multivariate density function, and so likelihood-based methods remain far from providing a complete and flexible framework for inference. In this article we develop inferentially practical, likelihood-based methods for fitting max-stable processes derived from a composite-likelihood approach. The procedure is sufficiently reliable and versatile to permit the simultaneous modeling of marginal and dependence parameters in the spatial context at a moderate computational cost. The utility of this methodology is examined via simulation, and illustrated by the analysis of United States precipitation extremes.

Subfields: Demography, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/5ba76e4aa795141cba879763fddcf5f428665239

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Citations in the corpus

Threshold modeling of extreme spatial rainfall (2013, methodology): “The marginal and dependence parameters are estimated simultaneously, as suggested by Padoan et al. [2010]. [35] Under essentially the same regularity conditions as those needed for the limiting normality of the standard maximum likelihood estimator, the maximum pairwise likelihood estimator ŵ has a ”
Bayesian Inference from Composite Likelihoods, with an Application to Spatial Extremes (2009, methodology): “Padoan et al. [2010] and Gholamrezaee [2010] propose the use of composite likelihood based on marginal events to ﬁt max-stable processes, and Rue and Tjelmeland [2002] have used composite likelihoods based on omitting components of the full likelihood in approximating Gaussian random ﬁelds.”
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 extremes (2012, methodology): “A (2012) Pauli & Coles (2001), Chavez-Demoulin & Davison (2005) and Padoan & Wand (2008) describe approaches to more flexible modelling, applied by Ramesh & Davison (2002) and Butler et al. (2007).”
Bridging asymptotic independence and dependence in spatial extremes using Gaussian scale mixtures (2016, methodology): “Full likelihoods can only be calculated in small dimensions, which led to the use of less efficient inference techniques, such as composite likelihoods (Padoan et al., 2010; Huser and Davison, 2013; Castruccio et al., 2016).”
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).”
Statistical inference for max‐stable processes in space and time (2012, methodology): “For max-stable random fields with replicates, which are independent in time, Padoan et al. (2009) showed consistency and asymptotic normality for the pairwise likelihood estimates.”
A Hierarchical Model for Serially-Dependent Extremes: A Study of Heat Waves in the Western US (2014, methodology): “Furthermore, when performing inference the hierarchical construction of the process allows the likelihood to be evaluated at all threshold exceedances, and pairwise likelihood methods (Padoan, Ribatet, and Sisson 2010) are not needed.”
Spatial Bayesian hierarchical modeling of precipitation extremes over a large domain (2015, background): “Max-stable processes [Schlather, 2002; Cooley et al., 2006; Shang et al., 2011; Ribatet et al., 2012; Padoan et al., 2010; Sang, 2015] refer to the specification of a joint distribution that is specifically formulated for spatial extreme data.”
Extreme value copulas and max-stable processes (2013, background): “, consistency and asymptotic normality, but yields to a loss in efficiency [26].”
A Bayesian hierarchical approach to regional frequency analysis (2011, methodology): “Including multivariate extreme models recently proposed in the literature [e.g., Keef et al., 2009; Padoan et al., 2010] would also constitute an improvement.”
AN OVERVIEW OF COMPOSITE LIKELIHOOD METHODS (2011, methodology): “Thus, pairwise likelihood inference is naturally considered as a surrogate for impossible ordinary likelihood analysis in Davison and Gholamrezaee (2009) and Padoan et al. (2009). In both of those papers, computations are carried out with the R (R Development Core Team, 2009) package SpatialExtremes”
Space–time modelling of extreme events (2012, methodology): “This result shows that the standard asymptotic normality result for composite likelihoods (Hjort and Varin, 2008; Lindsay, 1988; Godambe and Heyde, 1987; Varin, 2008; Varin and Vidoni, 2005; Cox and Reid, 2004; Padoan et al., 2010) still holds under mild conditions for moderately temporally dependen”
Statistical Modelling of Spatial Extremes (2012, background): “A more promising approach has been suggested in as-yet unpublished work of Reich and Shaby (2011), who develop a finite latent process approximation to the Smith process in a Bayesian framework, and are thus able to approximate this model closely using Markov chain Monte Carlo methods.”