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2022-03-07
摘要翻译:
一个理性的代理人根据新的证据改变她对某些命题/假设的信念的方式是贝叶斯推理的核心。正如范·弗拉森的反射原理([1984])所概括的那样,基本的自然假设是,在没有新证据的情况下,信念不应改变。然而,有一些例子声称违反了这一假设。这些例子所呈现的明显悖论,如果不解决,将表明贝叶斯方法的不一致性和/或不完整性,如果不消除这种不一致性,这种方法就不能被视为科学的。睡美人问题就是这样一个例子。现有的解决这一问题的尝试分为三类。前两者都认为缺乏新的证据,但在睡美人是否应该改变信仰以及为什么改变信仰的结论上存在分歧。第三类的特点是这样一种观点,即毕竟涉及到新的证据(尽管从最初的观点来看是隐藏的)。我的解决方案是完全不同的,不属于这两个类别中的任何一个。我通过论证睡美人问题中提出的两种不同程度的信念实际上是两种不同命题中的信念,即不需要解释信念的(不)变化,来淡化这一悖论。
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英文标题:
《The end of Sleeping Beauty's nightmare》
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作者:
Berry Groisman
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最新提交年份:
2008
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分类信息:

一级分类:Computer Science        计算机科学
二级分类:Artificial Intelligence        人工智能
分类描述:Covers all areas of AI except Vision, Robotics, Machine Learning, Multiagent Systems, and Computation and Language (Natural Language Processing), which have separate subject areas. In particular, includes Expert Systems, Theorem Proving (although this may overlap with Logic in Computer Science), Knowledge Representation, Planning, and Uncertainty in AI. Roughly includes material in ACM Subject Classes I.2.0, I.2.1, I.2.3, I.2.4, I.2.8, and I.2.11.
涵盖了人工智能的所有领域,除了视觉、机器人、机器学习、多智能体系统以及计算和语言(自然语言处理),这些领域有独立的学科领域。特别地,包括专家系统,定理证明(尽管这可能与计算机科学中的逻辑重叠),知识表示,规划,和人工智能中的不确定性。大致包括ACM学科类I.2.0、I.2.1、I.2.3、I.2.4、I.2.8和I.2.11中的材料。
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一级分类:Mathematics        数学
二级分类:Probability        概率
分类描述:Theory and applications of probability and stochastic processes: e.g. central limit theorems, large deviations, stochastic differential equations, models from statistical mechanics, queuing theory
概率论与随机过程的理论与应用:例如中心极限定理,大偏差,随机微分方程,统计力学模型,排队论
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英文摘要:
  The way a rational agent changes her belief in certain propositions/hypotheses in the light of new evidence lies at the heart of Bayesian inference. The basic natural assumption, as summarized in van Fraassen's Reflection Principle ([1984]), would be that in the absence of new evidence the belief should not change. Yet, there are examples that are claimed to violate this assumption. The apparent paradox presented by such examples, if not settled, would demonstrate the inconsistency and/or incompleteness of the Bayesian approach and without eliminating this inconsistency, the approach cannot be regarded as scientific.   The Sleeping Beauty Problem is just such an example. The existing attempts to solve the problem fall into three categories. The first two share the view that new evidence is absent, but differ about the conclusion of whether Sleeping Beauty should change her belief or not, and why. The third category is characterized by the view that, after all, new evidence (although hidden from the initial view) is involved.   My solution is radically different and does not fall in either of these categories. I deflate the paradox by arguing that the two different degrees of belief presented in the Sleeping Beauty Problem are in fact beliefs in two different propositions, i.e. there is no need to explain the (un)change of belief.
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PDF链接:
https://arxiv.org/pdf/0806.1316
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