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B1472
**Title: **On normalizing constants of chordal graphical Gaussian models with group symmetry
**Authors: **Hideyuki Ishi - Osaka City University (Japan) **[presenting]**

**Abstract: **The graphical Gaussian models are statistical models of central multivariate Gaussian distributions with prescribed conditional independence given by simple graphs. It is known that, if the graph is chordal, then the model admits various explicit calculations. In particular, we have an analytic formula for the normalizing constant of the Wishart distribution of type II, that is, the Diaconis-Ylvisaker conjugate prior for the precision parameter. We consider the graphical Gaussian models invariant under the natural action of a subgroup of the automorphism group of the graph. If the graph is chordal, we obtain an explicit formula for the normalizing constant of the Wishart distributions of type II. In our calculation, some observation of an algebraic structure of a specific block decomposition of the precision matrices is crucial.