JSM 2012 Home

## JSM 2012 Online Program

The views expressed here are those of the individual authors and not necessarily those of the JSM sponsors, their officers, or their staff.

Online Program Home

#### Abstract Details

 Activity Number: 373 Type: Invited Date/Time: Tuesday, July 31, 2012 : 2:00 PM to 3:50 PM Sponsor: Section on Bayesian Statistical Science Abstract - #303488 Title: Bayes Factors and the Geometry of Discrete Loglinear Models Author(s): Helene M Massam*+ and Gerard Letac Companies: York University and Universite Paul Sabatier Address: 4700 Keele Street, Toronto, ON, M4N2A8, Canada Keywords: discrete loglinear models ; Bayes factors ; geometry ; characteristic function ; faces of a polyhedron Abstract: We consider the class of hierarchical loglinear models for discrete data with multinomial sampling. We assume that the Diaconis-Ylvisaker conjugate prior is the prior distribution on the loglinear parameters. Under these conditions, the Bayes factor between two models is a function of their prior and posterior normalizing constants under each model. These constants are functions of the data and of the hyperparameters $(m,\alpha)$, which can be interpreted respectively as marginal counts and the total count of a fictive contingency table. Both constants are finite when $\alpha$ is positive and $m$ and the data are in the interior $C$ of the support of the multinomial distribution. We will always assume that $m$ which is a prior hyperparameter of our choice satisfies this condition and we study what happens when $\alpha\rightarrow 0$ and the data is on the boundary of $C$. We will see that the behaviour of the Bayes factor is dictated by the dimension of the face of $C$ to which the data belongs. We will also emphasize the role played by the characteristic function of $C$, a new object in the toolbox of exponential families.

The address information is for the authors that have a + after their name.
Authors who are presenting talks have a * after their name.

2012 JSM Online Program Home

For information, contact jsm@amstat.org or phone (888) 231-3473.