Research on a Frequentist Theory of Lower Probability

自17世纪以来，传统的概率论在刻画偶然性、不确定性和不确定性现象方面取得了巨大的成功。它的成功如此之大，以至于人们对开发传统地位的替代品几乎没有兴趣。然而，Fine教授令人信服地辩称，在之前NSF的支持下，他一直在研究的替代方法有相当大的优势。例如，传统的方法不适用于一些具体的案例，如自然语言研究、个人和群体信念的研究以及严重的测量误差。这种新的方法，他称之为频率较低概率理论，指的是一种类似概率但超可加性的集合函数。根据这笔拨款，Fine教授和他的学生将继续研究较低概率的结构和客观频率主义解释。结构性问题包括产生有可能模拟客观和主观不确定性现象的低概率族，以及适用于整个低概率类的期望的定义。这种对期望的定义对条件反射思想的发展具有很大的潜力。以前对较低概率的解释都是主观认识的变体。Fine教授发展了一种对频率变种的客观解释，有望对半导体和石英晶体振荡器中的闪烁/半导体/L/f噪声这一重要但鲜为人知的情况有重大应用。

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.