Mathematical Sciences: Statistical Theory for Classification

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Probability models can be used to distinguish naturally occurring clusters of observations even when these observations are intermixed and unlabelled. Established theory draws on mixture models, modal models, and, for evolutionary classification, generalized Markov models. This research introduces and investigates a new class of probability models: product partition models. These will have wide application in determining classifications and in predicting based on partial or complete classifications. Applications for these classification algorithms include the construction of evolutionary trees, recognition of change-points for modelled processes, image reconstruction, and failure prediction for complex cases like the space shuttle.