Asymptotic Model Selection and Identifiability of Directed Tree Models with Hidden Variables
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 . Geometric results obtained in this paper are complementary to the results in the previous paper  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.