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Inference with uncertain evidence.

机译：用不确定的证据推断。

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摘要

The subjectivist view of interpretation of Probability Theory considers probability to be the universal measure of uncertainty, and Bayes Theorem the principal rule for learning from evidence. In recent decades, alternative theories of uncertainty, including Possibility Theory and Evidence Theory, have been developed which seek to provide solutions for problems of evidential reasoning to which Bayes Theorem allegedly fails to apply. These problems can largely be characterized as cases of evidence uncertainty.; Evidence uncertainty occurs when the evidential meaning of observations is not well-defined. Possible causes include vagueness or ambiguity in descriptions of reality, lack of observational capabilities, and lack of definition of the representation of reality in which reasoning takes place.; This dissertation demonstrates that a probabilistic treatment of evidence uncertainty is possible. The solution method is based on a formalized notion of uncertain interpretation, which represents an observer's uncertainty about what can be concluded from an observation. Dependencies in the interpretations of multiple observations are treated by constructing joint interpretations, or alternatively by introducing assumptions on which interpretations are based as uncertain variables into the problem.; Inference takes place using a probabilistic rule of combination, which includes Bayes Theorem as a special case. This rule has the property that it performs simultaneous belief revision for the uncertain variables of interest and the assumptions on which interpretations are based. Observations are reinterpreted whenever new evidence is obtained.; It is concluded that the probabilistic treatment of uncertain evidence provides significant advantages over Bayes Theorem, particularly in terms of representing the evidential meaning of observations, and has behavioral characteristics that are intuitively appealing. It is further concluded that the rule of inference should be preferred over Evidence Theory and Possibility Theory, because of the solid conceptual background provided by Probability Theory.
机译：概率论解释的主观观点认为，概率是不确定性的普遍度量，贝叶斯定理是从证据中学习的主要规则。在最近的几十年中，已经开发了包括可能性理论和证据理论在内的不确定性的替代理论，旨在为贝叶斯定理据称未能适用的证据推理问题提供解决方案。这些问题在很大程度上可以归结为证据不确定的情况。当观察的证据含义不明确时，就会出现证据不确定性。可能的原因包括在对现实的描述中含糊不清或含糊不清，缺乏观察力以及缺乏对进行推理的现实表示的定义。本文证明了概率不确定性证据处理是可能的。解决方案方法基于不确定性解释的形式化概念，该概念表示观察者不确定可以从观察中得出的结论。通过构造联合解释，或者通过引入假设作为解释的不确定变量，来处理对多个观测结果的解释的依赖性。推论使用概率组合规则进行，其中包括贝叶斯定理作为特例。该规则具有对感兴趣的不确定变量和解释所基于的假设执行同步置信修订的特性。每当获得新证据时，都会重新解释观察结果。结论是，不确定证据的概率处理相对于贝叶斯定理具有明显的优势，特别是在表示观察的证据含义方面，并且具有直观上吸引人的行为特征。进一步得出结论，由于概率理论提供了扎实的概念背景，因此推理规则应优先于证据理论和可能性理论。

著录项

  • 作者

    Groen, Franciscus Johannes.;

  • 作者单位

    University of Maryland College Park.;

  • 授予单位 University of Maryland College Park.;
  • 学科 Statistics.; Engineering General.
  • 学位 Ph.D.
  • 年度 2000
  • 页码 289 p.
  • 总页数 289
  • 原文格式 PDF
  • 正文语种 eng
  • 中图分类 统计学;工程基础科学;
  • 关键词

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