Further Study of the Old Evidence Problem

“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“修复”，当发现H暗示了先前已知的证据e时，它会增加假设H的概率。随后，P.I.推广了这种方法，将其应用于不确定的旧证据和概率新解释。确定了几个足以保证在这种更一般的情况下确认H的条件。这种概括是基于基于解释的修正应该保留某些贝叶斯因素的原则。另一个貌似合理的原则是，基于解释和基于观察的修正应该相互交换。该原理的一种表述等价于贝叶斯因子的均匀性，而另一种则不然。在这个项目中，私家侦探将调查这些相互竞争的修订原则，以确定是否有一个更优越的主张来建立一个概括的赔偿（从而抓住杰弗里的方法的本质），或者是否每个都可能适合于一个单独的不确定的旧证据问题。对这些原理的比较将基于对其性质的进一步数学分析，以及对某些足够具体的基准问题的发展，使人们能够果断地确定适用于其解决方案的原理。分类和诊断问题具有正式的旧证据/新解释结构，但与科学解释的典型判断概率相比，与相对频率的联系更紧密，似乎是有希望的候选者。在某种程度上，科学解释领域的旧证据问题可以被同化到这些基准中的一个或多个，对它们的解决方案的洞察可能是预期的。

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.