Information Geometry with Application to Model Selection

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Information Geometry with Application to Model SelectionAbstract of Proposed ResearchJun Zhang, Ovidiu Calin and Hiroshi MatsuzoeThis research is to further develop the mathematical foundations of information geometry and to apply it to the problem of model selection in social and behavioral science. Information geometry is a differential geometric approach to statistics in which models are represented as a set of points forming a manifold with properties invariant against specific parametrizations. We are particularly interested in investigating the use of the volume element of a manifold as a measure of model complexity.The core of many problems in the social and behavioral sciences often centers on making good selections between competing quantitative models. This project will investigate the use of various geometrical ideas for criteria of model selection.