Research on a Frequentist 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 has, however, argued persuasively that there are considerable advantages to an alternative approach which he has been investigating under previous NSF support. The conventional approach, for example, has not worked for a number of specific cases such as natural language studies, studies of individual and group beliefs, and gross measurement errors. This new approach which he calls the frequentist theory of lower probability refers to a probability-like but superadditive set function. Under this grant, Professor Fine and his students will continue research on the structure and the objective frequentist interpretation of lower probability. Structural issues include the generation of families of lower probabilities that have potential for modeling objective and subjective nondeterministic phenomena and a definition of expectation applicable to the whole class of lower probabilities. This definition of expectation has great potential for development of ideas of conditioning. Previous interpretations of lower probability have been of the subjective epistemic varieties. Professor Fine's development of an objective interpretation of a frequentist variety promises to have significant application to the important but little understood case of flicker/semiconductor/l/f noise in semiconductors and in quartz crystal oscillators.