A new prior for discrete DAG models with a restricted set of directions

Helene Massam , Jacek Wesołowski

Abstract

In this paper, we first develop a new family of conjugate prior distributions for the cell probability parameters of discrete graphical models Markov with respect to a set P of moral directed acyclic graphs with skeleton a given decomposable graph G. This family, which we call the P-Dirichlet, is a generalization of the hyper Dirichlet given in [Ann. Statist. 21 (1993) 1272– 1317]: it keeps the directed strong hyper Markov property for every DAG in P but increases the flexibility in the choice of its parameters, that is, the hyper parameters. Our second contribution is a characterization of the P-Dirichlet, which yields, as a corollary, a characterization of the hyper Dirichlet and a characterization of the Dirichlet also. Like the characterization of the Dirichlet given in [Ann. Statist. 25 (1997) 1344–1369], our characterization of the P-Dirichlet is based on local and global independence of the probability parameters and also a separability property explicitly defined here but implicitly used in that paper through the choice of two particular DAGs. Another advantage of our approach is that we need not make the assumption of the existence of a positive density function. We use the method of moments for our proofs.
Author Helene Massam
Helene Massam,,
-
, Jacek Wesołowski ZRPSM
Jacek Wesołowski,,
- Department of Probability and Mathematical Statistics
Journal seriesAnnals of Statistics, ISSN 0090-5364
Issue year2016
Vol44
No3
Pages1010-1037
Publication size in sheets1.35
Keywords in EnglishBayesian learning, directed strong hyper Markov, conjugate priors, hyper Dirichlet distribution, characterization, local and global independence
Abstract in PolishW pracy wprowadzono nowy rozkład a priori w dyskretnych bayesowskich modelach graficznych uogólniając standardowo stosowany rozkład hiper-Dirichleta. Ta nowa rodzina rozkładów P-Dirichleta pozwala na lepszy dobór parametrów modelu, zachowując przy tym wszystkie użyteczne własności rozkładu hiper-Dirichleta. Udowodniono również charakteryzację obu rodzin rozkładów wykorzystującą tzw. globalną i lokalną niezależność parametrów w bayesowskich modelach graficznych znacznie uogólniając klasyczną charakteryzację Geigera i Heckermana z 1997 roku.
DOIDOI:10.1214/15-AOS1396
URL http://massamh.info.yorku.ca/files/2016/04/2016-AOS1396-weso.pdf
Languageen angielski
Score (nominal)45
ScoreMinisterial score [Punktacja MNiSW] = 45.0, 28-11-2017, ArticleFromJournal
Ministerial score (2013-2016) [Punktacja MNiSW (2013-2016)] = 45.0, 28-11-2017, ArticleFromJournal
Publication indicators WoS Impact Factor [Impact Factor WoS]: 2016 = 3.023 (2) - 2016=4.258 (5)
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