  The standard Bayesian Information Criterion (BIC) is derived under 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 of binary data and when 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 for naive Bayes models. The
main tool used in this paper is a connection between asymptotic approximation
of Laplace integrals and the real log-canonical threshold.
