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跨极端依赖类别的统一建模AI 解读

Summary Different dependence scenarios can arise in multivariate extremes, entailing careful selection of an appropriate class of models. In bivariate extremes, the variables are either asymptotically dependent or are asymptotically independent. Most available statistical models suit one or other of these cases, but not both, resulting in a stage in the inference that is unaccounted for but can substantially impact subsequent extrapolation. Existing modelling solutions to…

与对数高斯随机函数相关的空间极值过程的高效推断AI 解读

Max-stable processes arise as the only possible nontrivial limits for maxima of affinely normalized identically distributed stochastic processes, and thus form an important class of models for the extreme values of spatial processes. Until recently, inference for max-stable processes has been restricted to the use of pairwise composite likelihoods, due to intractability of higher-dimensional distributions. In this work we consider random fields that are in the domain of…

空间极值的依赖建模AI 解读

Current dependence models for spatial extremes are based upon max-stable processes. Within this class, there are few inferentially viable models available, and we propose one further model. More problematic are the restrictive assumptions that must be made when using max-stable processes to model dependence for spatial extremes: it must be assumed that the dependence structure of the observed extremes is compatible with a limiting model that holds for all events more extreme…

极值建模中阈值诊断与不确定性的似然方法AI 解读

Summary For extreme value modelling based on threshold techniques, a well-documented issue is the sensitivity of inference from the model to the choice of threshold. The threshold above which we assume a non-homogeneous Poisson process, or equivalently generalized Pareto representation, to be a reasonable approximation to the distribution is traditionally selected before analysis and subsequently treated as fixed and known. In doing so, the analyst cannot account for the…