Comment: A Bayesian Approach to the Nonresponse Problem, Using Covariates à la Freedman
评论：借助 Freedman 式协变量处理无应答问题的贝叶斯视角AI 解读 ↓
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评论：借助 Freedman 式协变量处理无应答问题的贝叶斯视角
- 研究问题
- 当协变量提供订单规模和地理分布信息时，这些信息如何改变对无应答偏差大小的判断，并支持将其视为可忽略的论证？
- 方法与思路
- 作者从主观贝叶斯视角审视 Freedman 使用协变量论证偏差较小的一般结构与细节，并提出可进一步形式化的非正式分析。
- 材料陈述的贡献
- 摘要将该论证解释为新增协变量信息对初始信念的更新，指出其中有需从主观贝叶斯角度理解的细微问题，但未报告具体结论。
- 阅读关注点
- 阅读时核对协变量怎样约束无应答机制、先验信念如何更新，以及非正式论证能否写成完整概率模型并支持偏差可忽略的判断。
- 阅读边界
- 这是评论性文章；摘要只说明将进行可形式化的非正式贝叶斯分析，未给出先验、似然或完整模型，不能据此认定偏差可忽略。
原文摘要
David Freedman has presented an ingenious and deceptively simple argument that should prove to be of value in many nonrespondent problems. I would like to discuss both the general form of the argument and the specific details from a subjective Bayesian viewpoint, as I believe the argument implicitly involves some delicate questions that are best understood from this viewpoint. The basic structure of Freedman's argument is that although he concedes in general that there may be substantial nonrespondent bias, in the present situation this can be largely ignored because of additional data, in the form of covariates representing the distributions of orders by size and by geographical residence. He does not take a formal inferential point of view, but it seems clear that his argument must be to the effect that the additional information he supplies regarding the covariates must somehow change one's initial opinions about the magnitude of the nonrespondent bias, making it in some sense more probable, given this additional data, that the nonrespondent bias is negligible or at least can be ignored. This is sufficiently close to the subjective Bayesian scenario that it may be worth examining the argument from this point of view. I shall present an informal Bayesian analysis, but one that can easily be made formal.