Research on an Objective Ensemble-Oriented Theory of Lower Probability

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Conventional probability theory has, since the 17th century, been enormously successful in characterizing chance, uncertainty, and indeterminate phenomena. Its success has been so great that there has been little interest in developing alternatives to the conventional position. Professor Fine and his students are continuing their long-term study of the structure, interpretation and application of one alternative, the frequentist theory of lower probability, which they believe offers considerable advantages over the traditional approach. By "lower probability" they refer to a probability-like but superadditive nonnegative and unit formed set function, examples of which include the familiar countably and finitely additive probability measures, the widely discussed belief functions pioneered by Demster and Shafer, the lower envelopes studied by Kyburg, Levi, Suppes, Walley and others, and the class of undominated lower probabilities introduced by Professor Fine and his students. Under this renewal grant, they aim to develop lower probability- based reasoning about nondeterministic physical and natural phenomena and particularly the development and study of a theory of statistics that can coordinate time series data with the lower probability models that are provided by the statistical theory. They expect to exploit their recently developed definition of lower expectation as a basis for a theory of estimation and for learning from observations through conditioning. While the interpretations of lower probability offered by others have been of either subjective or epistemic varieties, their efforts will continue to concentrate on the possibilities of an objective frequentist-related interpretation. This research on an objective interpretation of lower probability should also enhance our understanding of such interpretations for conventional probability.