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Name: Manuel Hentschel 

Talk Title: Statistical inference for decomposable Hüsler-Reiss graphical models

Abstract: \documentclass[a4paper, 12pt]{article}\begin{document} \section*{Abstract} In \cite{engelkeHitz2020}, the authors introduce extremal graphical models for multivariate Pareto distributions. They define an analogue to the classical Markov property and show a Hammersley-Clifford theorem for the class of connected, decomposable graphs. Furthermore, they introduce methods for statistical inference on block graphs, a subclass of the much more general class of decomposable graphs. In this work, we study properties of H\"usler-Reiss graphical models on general decomposable graphs. In particular, we prove a matrix completion theorem that shows that it is sufficient to specify the distribution on the lower-dimensional cliques of the graph and explicitly construct the unique completion of its variogram matrix. We further show how this can be translated into effective statistical inference. This is joint work with Sebastian Engelke. \begin{thebibliography}{} \bibitem[Engelke and Hitz, 2020 {engelkeHitz2020} Engelke, S. and Hitz, A.~S. (2020).\newblock Graphical models for extremes. \newblock {\em Journal of the Royal Statistical Society: Series B (Statistical Methodology)}, 82(4):871--932. \end{thebibliography}\end{document}

This talk is a contributed talk at EVA 2021. View the programme here.