Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Bayes factors and the geometry of discrete hierarchical loglinear models   A standard tool for model selection in a Bayesian framework is the Bayes
factor which compares the marginal likelihood of the data under two given
different models. In this paper, we consider the class of hierarchical
loglinear models for discrete data given under the form of a contingency table
with multinomial sampling. We assume that the Diaconis-Ylvisaker conjugate
prior is the prior distribution on the loglinear parameters and the uniform is
the prior distribution on the space of models. Under these conditions, the
Bayes factor between two models is a function of their prior and posterior
normalizing constants. These constants are functions of the hyperparameters
$(m,\alpha)$ which can be interpreted respectively as marginal counts and the
total count of a fictive contingency table.
  We study the behaviour of the Bayes factor when $\alpha$ tends to zero. In
this study two mathematical objects play a most important role. They are,
first, the interior $C$ of the convex hull $\bar{C}$ of the support of the
multinomial distribution for a given hierarchical loglinear model together with
its faces and second, the characteristic function $\mathbb{J}_C$ of this convex
set $C$.
  We show that, when $\alpha$ tends to 0, if the data lies on a face $F_i$ of
$\bar{C_i},i=1,2$ of dimension $k_i$, the Bayes factor behaves like
$\alpha^{k_1-k_2}$. This implies in particular that when the data is in $C_1$
and in $C_2$, i.e. when $k_i$ equals the dimension of model $J_i$, the sparser
model is favored, thus confirming the idea of Bayesian regularization.

5
The categories of this paper are: gr-qc
9
The categories of this paper are: nlin
35
The categories of this paper are: mtrl-th
8
The categories of this paper are: hep-ex
28
The categories of this paper are: alg-geom
14
The categories of this paper are: math-ph
7
The categories of this paper are: hep-th
33
The categories of this paper are: plasm-ph
37
The categories of this paper are: supr-con
0
The categories of this paper are: hep-ph
1
The categories of this paper are: cs
21
The categories of this paper are: adap-org
4
The categories of this paper are: cond-mat
12
The categories of this paper are: nucl-th
29
The categories of this paper are: funct-an
36
The categories of this paper are: cmp-lg