On Riesz and Wishart distributions associated with decomposable undirected graphs

  • Classical Wishart distributions on the open convex cones of positive definite matrices and their fundamental features are extended to generalized Riesz and Wishart distributions associated with decomposable undirected graphs using the basic theory of exponential families. The families of these distributions are parameterized by their expectations/natural parameter and multivariate shape parameter and have a non-trivial overlap with the generalized Wishart distributions defined in Andersson & WOjnar (2004a,b). This work also extends the Wishart distributions of type I in Letac & Massam (2007) and, more importantly, presents an alternative point of view on the latter paper.

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Metadaten
Author:Steen A. Andersson, Thomas Klein
URN:urn:nbn:de:bvb:384-opus4-4966
Frontdoor URLhttps://opus.bibliothek.uni-augsburg.de/opus4/626
Series (Serial Number):Preprints des Instituts für Mathematik der Universität Augsburg (2008-06)
Type:Preprint
Language:English
Publishing Institution:Universität Augsburg
Release Date:2008/02/06
Tag:Decomposable undirected graph; exponential families; graphical models; Riesz distribution; Siegel integral; Wishart distribution
GND-Keyword:Wahrscheinlichkeitsverteilung; Exponentialfamilie; Graphisches Modell; Ungerichteter Graph
Institutes:Mathematisch-Naturwissenschaftlich-Technische Fakultät
Mathematisch-Naturwissenschaftlich-Technische Fakultät / Institut für Mathematik
Dewey Decimal Classification:5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik

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