An asymptotic approximation of the marginal likelihood for general\n Markov models

2010/12/03 by Piotr Zwiernik, Zwiernik, Piotr
Computer Science · Mathematics · #62E15 (Primary) 60K99 #62F99 (Secondary) #62H05 #Bayesian Methods and Mixture Models #Bayesian Modeling and Causal Inference #FOS: Mathematics #Statistical Methods and Bayesian Inference #Statistical Methods and Inference #Statistics Theory (math.ST)

paper · pdf · doi:10.48550/arxiv.1012.0753

openalex publication_date 2010/12/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The standard Bayesian Information Criterion (BIC) is derived under regularity\nconditions which are not always satisfied by the graphical models with hidden\nvariables. In this paper we derive the BIC score for Bayesian networks in the\ncase of binary data and when the underlying graph is a rooted tree and all the\ninner nodes represent hidden variables. This provides a direct generalization\nof a similar formula given by Rusakov and Geiger for naive Bayes models. The\nmain tool used in this paper is a connection between asymptotic approximation\nof Laplace integrals and the real log-canonical threshold.\n

Citations

• On real log canonical thresholds
• Asymptotic Equivalence of Bayes Cross Validation and Widely Applicable Information Criterion in Singular Learning Theory

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