On Riesz and Wishart distributions associated with decomposable undirected graphs

Steen A. Andersson and Thomas Klein

Journal of Multivariate Analysis, 2010, vol. 101, issue 4, 789-810

Abstract: Classical Wishart distributions on the open convex cone 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 and Wojnar (2004) [4] and [8]. This work also extends the Wishart distributions of type I in Letac and Massam (2007) [7] and, more importantly, presents an alternative point of view on the latter paper.

Keywords: Decomposable; undirected; graphs; Exponential; families; Graphical; models; Riesz; distribution; Siegel; integral; Wishart; distribution (search for similar items in EconPapers)
Date: 2010
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Citations: View citations in EconPapers (7)

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