Singular Bayesian Information Criterion

• Singular Bayesian Information Criterion is a generalization of classical BIC that adjusts for model singularities via algebraic-geometric invariants.
• It employs invariants from algebraic geometry to capture non-standard asymptotic behavior in models with latent variables and degenerate Fisher information.
• The framework, based on Watanabe's singular learning theory, enables more robust model selection in non-regular statistical settings.

The Singular Bayesian Information Criterion (sBIC) generalizes the classical Bayesian Information Criterion (BIC) to statistical models exhibiting singularities, including non-identifiabilities, degenerate Fisher information, or latent variable structures. sBIC replaces the classical BIC penalty, which depends solely on the parametric dimension, with penalty terms arising from algebraic-geometric invariants that characterize the rate of concentration of the marginal likelihood in singular models. Its theoretical foundations rest on Watanabe's singular learning theory, which formalizes the asymptotic behavior of the Bayesian evidence for a wide class of non-regular, singular statistical models (Drton et al., 2013, Liu et al., 2024).