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Asymptotic model selection and identifiability of directed tree models with hidden variables
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Zwiernik, Piotr (2010) Asymptotic model selection and identifiability of directed tree models with hidden variables. Working Paper. Coventry: University of Warwick. Centre for Research in Statistical Methodology. Working papers, Vol.2010 (No.6).

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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 logcanonical 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  
Official Date:  2010  
Dates: 


Volume:  Vol.2010  
Number:  No.6  
Number of Pages:  27  
Status:  Not Peer Reviewed  
Access rights to Published version:  Open Access  
References:  [1] V. Arnold, S. GuseinZade, and A. Varchenko, Singularities of differentiable maps, 

URI:  http://wrap.warwick.ac.uk/id/eprint/35068 
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