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arXiv 1207.4111cs.AI
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符号概率的决策

Decision Making for Symbolic Probability

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Phan H. Giang, Sathyakama Sandilya

摘要:

本文提出了概率论(SP)的符号推广的决策理论。Darwiche和Ginsberg [2,3]提出了SP,以放松对不确定性使用数字的要求,同时保留贝叶斯推理的理想模式。SP用符号支持表示不确定性,符号支持是部分排序的,而不是像标准概率那样完全排序的。我们表明,偏好关系的行为,满足一些直观的假设是由一个效用函数,其域是一组对支持。我们认为,一个主观的解释是有用的和适当的SP,因为它是数值概率。它是有用的,因为主观解释提供了一个基础,不确定性的启发。这是适当的,因为我们可以提供一个决策理论,解释如何偏好的行为是基于支持比较。

英文摘要:

This paper proposes a decision theory for a symbolic generalization of probability theory (SP). Darwiche and Ginsberg [2,3] proposed SP to relax the requirement of using numbers for uncertainty while preserving desirable patterns of Bayesian reasoning. SP represents uncertainty by symbolic supports that are ordered partially rather than completely as in the case of standard probability. We show that a preference relation on acts that satisfies a number of intuitive postulates is represented by a utility function whose domain is a set of pairs of supports. We argue that a subjective interpretation is as useful and appropriate for SP as it is for numerical probability. It is useful because the subjective interpretation provides a basis for uncertainty elicitation. It is appropriate because we can provide a decision theory that explains how preference on acts is based on support comparison.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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