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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 DiaconisYlvisaker 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.

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