In Nonparametric and High-Dimensional Models, Bayesian Ignorability is an Informative Prior

• 成果类型: Article
• 署名作者: Linero, Antonio R.
• 署名单位: University of Texas System; University of Texas Austin
• 刊物名称: JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
• ISSN/ISSBN: 0162-1459
• DOI: 10.1080/01621459.2023.2278202
• 发表日期: 2024
• 页码: 2785-2798
• 关键词: propensity score; inference; regression; selection

摘要

In problems with large amounts of missing data one must model two distinct data generating processes: the outcome process, which generates the response, and the missing data mechanism, which determines the data we observe. Under the ignorability condition of Rubin, however, likelihood-based inference for the outcome process does not depend on the missing data mechanism so that only the former needs to be estimated; partially because of this simplification, ignorability is often used as a baseline assumption. We study the implications of Bayesian ignorability in the presence of high-dimensional nuisance parameters and argue that ignorability is typically incompatible with sensible prior beliefs about the amount of confounding bias. We show that, for many problems, ignorability directly implies that the prior on the selection bias is tightly concentrated around zero. This is demonstrated on several models of practical interest, and the effect of ignorability on the posterior distribution is characterized for high-dimensional linear models with a ridge regression prior. We then show both how to build high-dimensional models that encode sensible beliefs about the confounding bias and also show that under certain narrow circumstances ignorability is less problematic. Supplementary materials for this article are available online.