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摘要翻译：
当处理统计学习中的不完全数据或概率推理中的不完全观察时，人们需要区分观察到某一事件的事实和观察到的事件已经发生的事实。由于保持这种适当的区别所带来的建模和计算复杂性通常是令人望而却步的，人们要求在什么条件下可以安全地忽略它。这些条件是由随机缺失(mar)和随机粗化(car)假设给出的。在本文中，我们对与MAR/CAR假设有关的几个问题进行了深入的分析。我们研究的主要目的是提供一个标准，以评估一个car假设是否合理的特定数据收集或观察过程。这个问题由于存在几个不同版本的MAR/CAR假设而变得复杂。因此，我们首先概述了这些不同的版本，其中我们强调了分布和粗化变量诱导版本之间的区别。我们表明，分布式版本的限制较少，对大多数应用程序来说都足够了。然后，我们从两个不同的角度来解决MAR/CAR假设何时成立的问题。首先，我们用完全数据和不完全观测联合概率分布的支撑结构给出了car假设的可容许性的静态分析。这里我们得到了一个等价刻划，改进和推广了Grunwald和Halpern最近的一个结果。然后我们转向一个过程分析，它根据实际数据（或观测）生成过程的过程模型来表征car假设的可容许性。该分析的主要结果是，完全随机粗化(ccar)条件是最合理的假设，因为它仅对应于满足自然鲁棒性的数据粗化过程。
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英文标题：
《Ignorability in Statistical and Probabilistic Inference》
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作者：
M. Jaeger
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最新提交年份：
2011
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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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英文摘要：
When dealing with incomplete data in statistical learning, or incomplete observations in probabilistic inference, one needs to distinguish the fact that a certain event is observed from the fact that the observed event has happened. Since the modeling and computational complexities entailed by maintaining this proper distinction are often prohibitive, one asks for conditions under which it can be safely ignored. Such conditions are given by the missing at random (mar) and coarsened at random (car) assumptions. In this paper we provide an in-depth analysis of several questions relating to mar/car assumptions. Main purpose of our study is to provide criteria by which one may evaluate whether a car assumption is reasonable for a particular data collecting or observational process. This question is complicated by the fact that several distinct versions of mar/car assumptions exist. We therefore first provide an overview over these different versions, in which we highlight the distinction between distributional and coarsening variable induced versions. We show that distributional versions are less restrictive and sufficient for most applications. We then address from two different perspectives the question of when the mar/car assumption is warranted. First we provide a static analysis that characterizes the admissibility of the car assumption in terms of the support structure of the joint probability distribution of complete data and incomplete observations. Here we obtain an equivalence characterization that improves and extends a recent result by Grunwald and Halpern. We then turn to a procedural analysis that characterizes the admissibility of the car assumption in terms of procedural models for the actual data (or observation) generating process. The main result of this analysis is that the stronger coarsened completely at random (ccar) condition is arguably the most reasonable assumption, as it alone corresponds to data coarsening procedures that satisfy a natural robustness property.
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PDF链接：
https://arxiv.org/pdf/1109.2143
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