Zwiernik, Piotr (2010) Asymptotic model selection and identifiability of directed tree models with hidden variables. Working Paper. University of Warwick. Centre for Research in Statistical Methodology, Coventry.

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Abstract

The standard Bayesian Information Criterion (BIC) is derived under some regularity conditions which are not always satisfied by the graphical models with hidden variables. In this paper we derive the BIC score for Bayesian networks in the case when the data is binary and the underlying graph is a rooted tree and all the inner nodes represent hidden variables. This provides a direct generalization of a similar formula given by Rusakov and Geiger in [10]. Geometric results obtained in this paper are complementary to the results in the previous paper [18] extending our understanding of this class of models. The main tool used in this paper is the connection between asymptotic approximation of Laplace integrals and the real log-canonical threshold.

Item Type:	Working or Discussion Paper (Working Paper)
Subjects:	Q Science > QA Mathematics
Divisions:	Faculty of Science > Statistics
Library of Congress Subject Headings (LCSH):	Bayesian statistical decision theory, Trees (Graph theory)
Series Name:	Working papers
Publisher:	University of Warwick. Centre for Research in Statistical Methodology
Place of Publication:	Coventry
Date:	2010
Volume:	Vol.2010
Number:	No.6
Number of Pages:	27
Status:	Not Peer Reviewed
Access rights to Published version:	Open Access
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URI:	http://wrap.warwick.ac.uk/id/eprint/35068

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