Gustafson Paul
University of British Columbia, Canada.
Int J Biostat. 2010;6(2):Article 17. doi: 10.2202/1557-4679.1206.
Identification can be a major issue in causal modeling contexts, and in contexts where observational studies have various limitations. Partially identified models can arise, whereby the identification region for a target parameter--the set of values consistent with the law of the observable data--is strictly contained in the set of a priori plausible values, but strictly contains the single true value. The first part of this paper reviews the use of Bayesian inference in partially identified models, and describes the large-sample limit of the posterior distribution over the target parameter. This limiting distribution will have the identification region as its support. The second part of the paper focuses on the informativeness of the shape of the limiting distribution. This provides a point of departure with non-Bayesian approaches, since they focus on inferring the identification region without attempting to speak to relative plausibilities of values inside the identification region. The utility of the shape is investigated in several partially identified models.
在因果建模背景以及观察性研究存在各种局限性的背景下，识别可能是一个主要问题。可能会出现部分可识别模型，即目标参数的识别区域（与可观测数据规律一致的值的集合）严格包含在先验合理值的集合中，但严格包含单一真实值。本文的第一部分回顾了贝叶斯推断在部分可识别模型中的应用，并描述了目标参数后验分布的大样本极限。这个极限分布将以识别区域为其支撑。本文的第二部分关注极限分布形状的信息性。这提供了与非贝叶斯方法的一个出发点，因为非贝叶斯方法专注于推断识别区域，而不试图探讨识别区域内值的相对合理性。在几个部分可识别模型中研究了形状的效用。
