Conditional independence in extremes | Vidéo | Carmin.tv

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Conditional independence in extremes

By Kirstin Strokorb

Appears in 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.

Information about the video

Date of recording 26/09/2022
Date of publication 10/10/2022
Institution CIRM
Licence CC BY NC ND
Language English
Audience Researchers, Graduate Students
Director(s) Luca Recanzone
Format MP4

Citation data

DOI 10.24350/CIRM.V.19961703
Cite this video 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

Domain(s)

Probability

Bibliography

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. -

MSC codes

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