Conditional independence in extremes | Vidéo | Carmin.tv

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Conditional independence in extremes

De Kirstin Strokorb

Apparaît dans la collection : Adaptive and High-Dimensional Spatio-Temporal Methods for Forecasting / Méthodes spatio-temporelles adaptatives et en grande dimension pour la prédiction

Statistical modelling of complex dependencies in extreme events requires meaningful sparsity structures in multivariate extremes. In this context two perspectives on conditional independence and graphical models have recently emerged: One that focuses on threshold exceedances and multivariate pareto distributions, and another that focuses on max-linear models and directed acyclic graphs. What connects these notions is the exponent measure that lies at the heart of each approach. In this work we develop a notion of conditional independence defined directly on the exponent measure (and even more generally on measures that explode at the origin) that extends recent work of Engelke and Hitz (2019), who had been confined to homogeneous measures with density. We prove easier checkable equivalent conditions to verify this new conditional independence in terms of a reduction to simple test classes, probability kernels and density factorizations. This provides a pathsway to graphical modelling among general multivariate (max-)infinitely distributions. Structural max-linear models turn out to form a Bayesian network with respect to our new form of conditional independence.

Informations sur la vidéo

Date de captation 26/09/2022
Date de publication 10/10/2022
Institut CIRM
Licence CC BY NC ND
Langue Anglais
Audience Chercheurs, Doctorants
Réalisateur(s) Luca Recanzone
Format MP4

Données de citation

DOI 10.24350/CIRM.V.19961703
Citer cette vidéo Strokorb, Kirstin (26/09/2022). Conditional independence in extremes. CIRM. Audiovisual resource. DOI: 10.24350/CIRM.V.19961703
URL https://dx.doi.org/10.24350/CIRM.V.19961703

Domaine(s)

Probabilités

Bibliographie

AMÉNDOLA, Carlos, KLÜPPELBERG, Claudia, LAURITZEN, Steffen, et al. Conditional independence in max-linear Bayesian networks. The Annals of Applied Probability, 2022, vol. 32, no 1, p. 1-45. - http://dx.doi.org/10.1214/21-AAP1670
ENGELKE, Sebastian et HITZ, Adrien S. Graphical models for extremes. Journal of the Royal Statistical Society: Series B (Statistical Methodology), 2020, vol. 82, no 4, p. 871-932. - https://doi.org/10.1111/rssb.12355
LAURITZEN, Steffen L. Graphical models. Clarendon Press, 1996. -

Codes MSC

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