Bayesian Information Criteria and Problems of Parameter Identifiability

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This project is concerned with statistical model selection by means of optimization of information criteria. Specifically, the investigator develops a generalization of the Bayesian information criterion for irregular model selection problems, such as determining the number of components in mixture models or the number of factors in latent factor models. The main difficulty in these irregular model selection problems is a lack of parameter identifiability. The investigator studies identifiability properties of widely used statistical models to provide the mathematical foundation for application of the new information criterion.Virtually every scientific data analysis brings about a problem of statistical model choice, where the different statistical models capture different scientific hypotheses. In many applications, the hypotheses involve latent variables that cannot or were not observed. Such latent variables could be, for instance, notions of intelligence in a psychological study or variables describing a patient's genetic composition in a medical study. Statistical models that are formulated using such latent variables typically lack the regularity properties that underlie the justification of standard statistical procedures. This project develops new statistical techniques for model selection that are theoretically justified and allow for an improved assessment of model uncertainty in a wide array of applications in which influential unobserved variables are at play.