Space–time modelling of extreme events

By Raphaël Huser, A. C. Davison. 2012

238 citations recorded by the source corpus.

Max‐stable processes are the natural analogues of the generalized extreme value distribution when modelling extreme events in space and time. Under suitable conditions, these processes are asymptotically justified models for maxima of independent replications of random fields, and they are also suitable for the modelling of extreme measurements over high thresholds. The paper shows how a pairwise censored likelihood can be used for consistent estimation of the extremes of space–time data under mild mixing conditions and illustrates this by fitting an extension of a model due to Schlather to hourly rainfall data. A block bootstrap procedure is used for uncertainty assessment. Estimator efficiency is considered and the choice of pairs to be included in the pairwise likelihood is discussed. The model proposed fits the data better than some natural competitors.

Subfields: Finance, Global and Planetary Change, Soil Science

View Paper: https://www.semanticscholar.org/paper/a7012735fb1c7d475404898e5a74e688eadb88da

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Citations in the corpus

A continuous updating weighted least squares estimator of tail dependence in high dimensions (2016, background): “Again as in Huser et al. (2016, Section 4.2), we take dimension d ∈ {2, 5, 10, 15, 20, 25, 30} and parameter θ ∈ {0.3, 0.6, 0.9, 0.95}. Note that in the likelihood setting, this is a very demanding experiment, and three of the ten likelihood-based estimators considered in Huser et al. (2016) are onl”
Threshold modeling of extreme spatial rainfall (2013, methodology): “Taking ¼ 2 is equivalent to using the Smith model with a symmetric covariance matrix R [Huser and Davison, 2013a].”
Likelihood estimators for multivariate extremes (2014, methodology): “The simulated data are positive, with a positive mass at zero, and heavytailed, which are common features of rainfall data for examp le (Huser and Davison , 2014). The distribution ( 30) is known to be in the max-domain of attraction of the logistic model with GEV margins ( 3) with shape parameters ”
A Hierarchical Model for Serially-Dependent Extremes: A Study of Heat Waves in the Western US (2014, background): “Also, both Huser and Davison (2013) and Jeon and Smith (2013) employ max-stable processes to spatially model threshold exceedances using pairwise like- lihood methods.”
Estimation of Hüsler–Reiss distributions and Brown–Resnick processes (2012, methodology): “However, in the recent simulation study of Huser and Davison (2014) in a framework similar to ours, the univariate normalization has only a moderate effect on the overall error.”
An M‐estimator of spatial tail dependence (2014, methodology): “In Huser and Davison (2014), a pairwise censored likelihood is used to analyze space-time extremes.”
INLA goes extreme: Bayesian tail regression for the estimation of high spatio-temporal quantiles (2018, background): “…numerous applications of threshold-based approaches to environmental extremes observed over space and/or time have since been published; see, e.g., Huser and Davison (2014), Thibaud and Opitz (2015) and Bacro et al. (2017) for recent applications to precipitation data, Chavez-Demoulin and Davison…”
Geostatistics of Dependent and Asymptotically Independent Extremes (2013, methodology): “For each dataset, we used a censored pairwise threshold-based approach (Huser and Davison, 2012) to fit three models to the exceedances over u98:”
Extremes on river networks (2015, methodology): “the use of Euclidean distance has become standard in spatial extremes (e.g., Davison and Gholamrezaee, 2012; Huser and Davison, 2014; Engelke et al., 2015).”
Bridging asymptotic independence and dependence in spatial extremes using Gaussian scale mixtures (2016, methodology): “Modeling of non-stationarity (Huser and Genton, 2016) and space-time dependence (Huser and Davison, 2014) is an important aspect in statistics of extremes; it would be interesting to investigate useful extensions of Gaussian scale mixture models in further research.”
Factor Copula Models for Replicated Spatial Data (2015, background): “s that the underlying spatial process (1) is not ergodic, which entails large-scale dependence. One remedy might be to consider mixtures of truncated processes constructed using a compact random set (Huser and Davison, 2014). This construction would also allow to capture independence at large distan”
Non-Stationary Dependence Structures for Spatial Extremes (2014, methodology): “To get around this computational bottleneck, the use of pairwise likelihoods is now a common practice (see, e.g., Padoan et al., 2010; Huser and Davison, 2014).”