In statistical clustering, we usually devise probability models that begin by specifying joint distributions of data and possible classifications and end in reporting classifications that are probable given the data. Yet the art and practice of classification is more fundamental and prior to probabilistic analysis, and so it is worthwhile to ask how one might derive probabilities from classifications, rather than derive classifications from probabilities. In this scheme, a classifier is assumed able to express any knowledge as a classification consisting of a number of statements of the form x ∈ y, in words, x is a member of y. We specify an inductive probability distribution over all such classifications. Probabilities for future outcomes are determined by the probabilities of the classifications formed by the classifier corresponding to those outcomes. Particular examples studied are coin tossing, recognition, the globular cluster Messier 5, and the next president of the United States.
KeywordsGlobular Cluster Classifier Probability Proper Motion Cluster Member Soft Fact
Unable to display preview. Download preview PDF.
- BERNOULLI, JAMES (1713) Ars Conjectandi.Google Scholar
- DE FINETTI, B. (1973): Bayesianism: Its unifying role for both the foundations and the applications of Statistics. Bulletin of the International Statistical Institute, 39(4), 349–368Google Scholar
- HUME, DAVID(1758) An Enquiry concerning Human Understanding Google Scholar
- LOCKE, JOHN(1689) An Essay Concerning Human Understanding Google Scholar