The Statistics Seminar speaker for Wednesday, April 20, is Mathias Drton, a statistics professor at the University of Washington.

Via his website: "My current interests revolve around graphical models, algebraic statistics, and problems of model selection. A graphical model is a multivariate statistical model that is associated to a graph whose nodes correspond to variables of interest. The edges of the graph reflect a pattern of allowed (conditional) dependences among the variables. Graphical models often have algebraic structure and many statistical problems pertaining to graphical models benefit from application of techniques from computational algebraic geometry."

**Title**: A Bayesian Information Criterion for Singular Models

**Abstract**: We consider approximate Bayesian model choice for model selection problems that involve models whose Fisher-information matrices may fail to be invertible along other competing submodels. Such singular models do not obey the regularity conditions underlying the derivation of Schwarz's Bayesian information criterion (BIC) and the penalty structure in BIC generally does not 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. Guided by examples such as determining the number of components of mixture models, the number of factors in latent factor models or the rank in reduced-rank regression, we propose a resolution to this paradox and give a practical extension of BIC for singular model selection problems.