A Study of Conditionalization

条件化研究

• 批准号: 8921269
• 负责人: Carl Wagner
• 金额: $ 2万
• 依托单位: University of Tennessee Knoxville
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1990
• 资助国家: 美国
• 起止时间: 1990-06-01 至 1992-05-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=8921269&HistoricalAwards=false
• 关键词: Study; Conditionalization

Within probability theory, one must be concerned with what one thinks before new conditions are presented (i.e. the "priors" or prior probabilities). Richard Jeffrey presented a generalization of ordinary conditionalization to update a "prior" in the light of new evidence that dictates a reassessment of the probabilities of members of some partition of a sample space. Dr. Wagner is studying a generalization of Jeffrey's conditionalization in which new evidence bounds the possible revisions of a prior below by a type of lower probability first studied by Dempster, and later abstractly characterized and termed a belief function by Shafer. As an anticipated philosophical consequence of this study, Dr. Wagner hopes to show the superiority of Jeffrey-type approaches to updating over mechanical updating methods such as maxent (and to establish that it is simple a fluke that the results of Jeffrey's rule coincide with those of maxent,since this is not the case for the natural generalization of Jeffrey's rule which he proposes). An additional aim is to establish a clear distinction between conditionalization and symmetric combination techniques such as Dempster's rule. Finally, he hopes to show that Dempster's construction of lower probabilities provides a fully satisfactory response to Carnap's demand for a reasoned construction of the new probabilities on a Jeffrey partition.

在概率论中，人们必须在新的条件出现之前关心自己的想法(即“先验”或先验概率)。理查德·杰弗里根据要求重新评估样本空间某一部分的概率的新证据，对普通条件化进行了推广，以更新“先验”。瓦格纳博士正在研究杰弗里条件化的一个推广，在这个推广中，新的证据以一种较低的概率限制了对下面先验的可能修正，这种较低的概率首先由邓普斯特研究，后来由谢弗抽象地描述并命名为信念函数。作为这项研究的一个预期的哲学结果，瓦格纳博士希望展示杰弗里类型的方法在更新方面的优越性，而不是像MAXENT这样的机械更新方法(并确定杰弗里规则的结果与MAXENT规则的结果一致只是一种侥幸，因为这不是他提出的杰弗里规则的自然推广的情况)。另一个目标是在条件化和对称组合技术(如邓普斯特法则)之间建立明确的区别。最后，他希望证明Dempster的低概率构造提供了一个完全令人满意的响应，以满足Carnap关于在Jeffrey划分上合理构造新概率的要求。