Research on a Frequentist Theory of Lower Probability

频率论低概率理论研究

• 批准号: 8620055
• 负责人: Terrence Fine
• 金额: $ 3.8万
• 依托单位: Cornell University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1987
• 资助国家: 美国
• 起止时间: 1987-06-01 至 1988-11-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=8620055&HistoricalAwards=false
• 关键词: Research; Frequentist; Theory; Lower; Probability

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.

自 17 世纪以来，传统概率论在描述偶然性、不确定性和不确定现象方面取得了巨大成功。 它的成功如此之大，以至于人们对开发传统位置的替代方案兴趣不大。 然而，法恩教授令人信服地指出，他在之前的国家科学基金会支持下研究的替代方法具有相当大的优势。 例如，传统方法不适用于许多特定案例，例如自然语言研究、个人和群体信仰研究以及严重测量误差。 他将这种新方法称为较低概率频率论，它指的是类似概率但超可加的集合函数。 在这笔资助下，Fine教授和他的学生将继续研究较低概率的结构和客观的频率论解释。 结构性问题包括生成具有对客观和主观非确定性现象进行建模的潜力的较低概率族，以及适用于整个较低概率类别的期望定义。 这种期望的定义对于条件反射思想的发展具有巨大的潜力。 先前对较低概率的解释是主观认知变体。 Fine 教授对频率论变种的客观解释的发展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要的应用。