Mathematical Sciences: Statistical Theory for Classification

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The principal investigator will develop specific probability models for testing, evaluating and applying classifications. Classification is the method of constructing classes of similar objects. The established models for this purpose are mixture models, modal models, and for evolutionary classification, generalized Markov models. The investigator introduces a new class of probability models, product partition models, that have wide application in classification, both for evaluating and selecting classifications, and for using classifications in prediction. He also considers more specialized probability models for devising significance tests for the existence of clusters, and for reconstructing evolutionary trees.