Further Study of the Old Evidence Problem

SES 99-84005 - Carl G.瓦格纳（田纳西大学）“旧证据问题的进一步研究“几年前，理查德·杰弗里设计了一种概率修正方法，称为补偿，当发现H暗示先前已知的证据E时，它会增加假设H的概率。私家侦探随后，将这种方法推广到不确定的旧证据和概率性的新解释，确定了几个条件，足以保证在这个更一般的情况下H的确认。这种推广是基于基于解释性修正应保留某些贝叶斯因子的原则。一个合理的替代原则规定，基于解释和基于观察的修正应互换。这一原则的一个公式等价于贝叶斯因子的一致性，但另一个公式则不是。在这个项目中，PI。我将调查这些相互竞争的修订原则，以确定是否有一个上级主张来为赔偿的普遍化奠定基础（从而抓住杰弗里方法的本质），或者如果每一个可能适合于一个单独的类不确定的旧证据问题。这些原则的比较将基于对它们的属性的进一步数学分析，以及某些基准问题的发展，这些基准问题足够具体，使人们能够决定性地确定适用于解决这些问题的原则。问题的分类和诊断有一个正式的旧证据/新的解释结构，但更密切的联系相对频率比典型的判断概率的科学解释，似乎是有前途的候选人。在某种程度上，在科学解释领域的老证据问题，然后可以同化到一个或多个这些基准，洞察他们的解决方案可能是预期的。

SES 99-84005 - Carl G. Wagner (University of Tennessee) "Further Study of the Old Evidence Problem"Several years ago Richard Jeffrey devised a probability revision method, called reparation, that increases the probability of hypothesis H when it is discovered that H implies previously known evidence E. The P.I. subsequently generalized this method to apply to uncertain old evidence and probabilistic new explanation, identifying several conditions sufficient to guarantee the confirmation of H in this more general context. This generalization was based on the principle that explanation-based revisions should preserve certain Bayes factors.A plausible alternative principle dictates that explanation- and observation-based revisions should commute. One formulation of this principle is equivalent to the uniformity of Bayes factors, but another is not. In this project the P.I. will investigate these competing revision principles to determine if one has a superior claim to ground a generalization of reparation (and thus to capture the essence of Jeffrey's method), or if each might be appropriate to a separate class of uncertain old evidence problems.Comparison of these principles will be based both on further mathematical analysis of their properties, and on the development of certain benchmark problems sufficiently concrete to enable one to determine decisively the principle applicable to their solution. Problems of classification and diagnosis having a formal old evidence/new explanation structure, but a closer connection to relative frequencies than the typical judgmental probabilities of scientific explanation, appear to be promising candidates. To the extent that old evidence problems in the realm of scientific explanation can then be assimilated to one or more of these benchmarks, insight into their solution may be expected.