Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A conjugate prior for discrete hierarchical log-linear models   In Bayesian analysis of multi-way contingency tables, the selection of a
prior distribution for either the log-linear parameters or the cell
probabilities parameters is a major challenge. In this paper, we define a
flexible family of conjugate priors for the wide class of discrete hierarchical
log-linear models, which includes the class of graphical models. These priors
are defined as the Diaconis--Ylvisaker conjugate priors on the log-linear
parameters subject to "baseline constraints" under multinomial sampling. We
also derive the induced prior on the cell probabilities and show that the
induced prior is a generalization of the hyper Dirichlet prior. We show that
this prior has several desirable properties and illustrate its usefulness by
identifying the most probable decomposable, graphical and hierarchical
log-linear models for a six-way contingency table.

21
The categories of this paper are: adap-org
35
The categories of this paper are: mtrl-th
26
The categories of this paper are: bayes-an
25
The categories of this paper are: patt-sol
20
The categories of this paper are: acc-phys
6
The categories of this paper are: astro-ph
13
The categories of this paper are: quant-ph
1
The categories of this paper are: cs
14
The categories of this paper are: math-ph
5
The categories of this paper are: gr-qc
24
The categories of this paper are: dg-ga
9
The categories of this paper are: nlin
4
The categories of this paper are: cond-mat
19
The categories of this paper are: eess
18
The categories of this paper are: econ
32
The categories of this paper are: atom-ph