Mathematical Sciences: Statistical Theory for Classification

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The proposal develops classification based approaches to prediction and statistical inference. Examples of statistical problems considered are change point problems, histograms, mode identification, reticulate evolution, and quantization of probability ditributions. A particular classification problem studied is the problem of types, the family of classes that most succinctly describes a primitive given family of classes. One way of predicting the future is by recognising circumstances that are similar to circumstances already experienced, that is, by placing the present circumstances in some established class of circumstances, from which we can infer other aspects of th future. Our method of classifying experience will determine how we predict the future. Thus we need to study classification to study prediction. We can't simply seize on some scheme of classification and use it permanently; we must develop new classifications adapting to the success or failure of predictions. Thus classification is needed for practical probability judgments, and practical probability judgments are needed for classification.