A Bayesian information criterion for singular models

摘要: Summary We consider approximate Bayesian model choice for selection problems that involve models whose Fisher information matrices may fail to be invertible along other competing submodels. Such singular do not obey the regularity conditions underlying derivation of Schwarz's criterion BIC and penalty structure in generally does reflect frequentist large sample behaviour marginal likelihood. Although theory likelihood has been developed recently, resulting approximations depend on true parameter value lead a paradox circular reasoning. Guided by examples such as determining number components mixture models, factors latent factor or rank reduced regression, we propose resolution this give practical extension problems.