Related papers: X-Vine Models for Multivariate Extremes

In a wide variety of situations, anomalies in the behaviour of a complex system, whose health is monitored through the observation of a random vector X = (X1,. .. , X d) valued in R d , correspond to the simultaneous occurrence of extreme…

Extreme values modeling has attracting the attention of researchers in diverse areas such as the environment, engineering, or finance. Multivariate extreme value distributions are particularly suitable to model the tails of multidimensional…

In multivariate extreme value analysis, the nature of the extremal dependence between variables should be considered when selecting appropriate statistical models. Interest often lies with determining which subsets of variables can take…

We propose a new variational Bayes estimator for high-dimensional copulas with discrete, or a combination of discrete and continuous, margins. The method is based on a variational approximation to a tractable augmented posterior, and is…

When passing from the univariate to the multivariate setting, modelling extremes becomes much more intricate. In this introductory exposition, classical multivariate extreme value theory is presented from the point of view of multivariate…

We propose a novel structure selection method for high dimensional (d > 100) sparse vine copulas. Current sequential greedy approaches for structure selection require calculating spanning trees in hundreds of dimensions and fitting the pair…

Vine copulas are pair-copula constructions enabling multivariate dependence modeling in terms of bivariate building blocks. One of the main tasks of fitting a vine copula is the selection of a suitable tree structure. For this the prevalent…

The classical multivariate extreme-value theory concerns the modeling of extremes in a multivariate random sample, suggesting the use of max-stable distributions. In this work, the classical theory is extended to the case where aggregated…

We introduce an extension of R-vine copula models for the purpose of spatial dependency modeling and model based prediction at unobserved locations. The newly derived spatial R-vine model combines the flexibility of vine copulas with the…

Vine copulas are flexible dependence models using bivariate copulas as building blocks. If the parameters of the bivariate copulas in the vine copula depend on covariates, one obtains a conditional vine copula. We propose an extension for…

Vine copula models have become highly popular and practical tools for modelling multivariate probability distributions due to their flexibility in modelling different kinds of dependences between the random variables involved. However,…

Modern technology often generates data with complex structures in which both response and explanatory variables are matrix-valued. Existing methods in the literature are able to tackle matrix-valued predictors but are rather limited for…

The time-varying Vine Copula model has become a new direction in the Vine Copula class of models due to its time-varying structural parameters. We have observed that the Vine structures of the time-varying Vine Copula model currently used…

Vine copulas allow to build flexible dependence models for an arbitrary number of variables using only bivariate building blocks. The number of parameters in a vine copula model increases quadratically with the dimension, which poses new…

Leveraging the recently emerging geometric approach to multivariate extremes and the flexibility of normalising flows on the hypersphere, we propose a principled deep-learning-based methodology that enables accurate joint tail extrapolation…

Multivariate rapid variation describes decay rates of joint light tails of a multivariate distribution. We impose a local uniformity condition to control decay variation of distribution tails along different directions, and using…

Extreme value statistics provides accurate estimates for the small occurrence probabilities of rare events. While theory and statistical tools for univariate extremes are well-developed, methods for high-dimensional and complex data sets…

Vine pair-copula constructions exist for a mix of continuous and ordinal variables. In some steps, this can involve estimating a bivariate copula for a pair of mixed continuous-ordinal variables. To assess the adequacy of copula fits for…

In situations where both extreme and non-extreme data are of interest, modelling the whole data set accurately is important. In a univariate framework, modelling the bulk and tail of a distribution has been extensively studied before.…

Despite the major progress of deep models as learning machines, uncertainty estimation remains a major challenge. Existing solutions rely on modified loss functions or architectural changes. We propose to compensate for the lack of built-in…