University of Washington - Statistics
This talk is concerned with approximate Bayesian model choice for singular models such as reduced rank regression or mixture models. Singular models do not obey the regularity conditions underlying the derivation of the usual Bayesian Information Criterion (BIC) and the penalty structure in BIC need not accurately reflect the frequentist large-sample behavior of their marginal likelihood. While large-sample theory for the marginal likelihood of singular models has been developed recently, the resulting approximations depend on the true parameter value and lead to a paradox of circular reasoning. I will discuss a resolution to this problem and suggest a practical extension of BIC to singular models.