Dmitry Rusakov, Dan Geiger.
Year: 2005, Volume: 6, Issue: 1, Pages: 1−35
We develop a closed form asymptotic formula to compute the marginal likelihood of data given a naive Bayesian network model with two hidden states and binary features. This formula deviates from the standard BIC score. Our work provides a concrete example that the BIC score is generally incorrect for statistical models that belong to stratified exponential families. This claim stands in contrast to linear and curved exponential families, where the BIC score has been proven to provide a correct asymptotic approximation for the marginal likelihood.