Dr. Fine is continuing his research into the development of lower probability based on models for frequentist phenomena and is continuing to explore the implications of such models, particularly as they contrast with analyses of such phenomena by conventional probability. His previous research allowed him to break a bond between convergence of relative frequencies and hypotheses of stationarity. An example of a stationarity hypothesis is the common assumption in analysis of frequentist phenomena of successive trials being independent and identically distributed. In this new research, Dr. Fine is examining some forms of evidence that would lead to the adoption of lower probability models; continuing to develop an ability to construct lower probability models to conform with the evidence; and strengthening the calculus by adoption and study of an appropriate notion of lower expectation. Lower expectation can provide entry to associated concepts of conditioning and independence and to the rudiments of statistical decision theory. It is hoped that this research will encourage the broadening of the scope of probabilistic reasoning by exploring alternatives to conventional probability with some of the vigor with which the various interpretations of probability have been discussed.
