信息性抽样下基于样本级权重模型的相干且稳健贝叶斯推断
Coherent and robust Bayesian inference under informative sampling via sample-level weight models
- Iowa State University（爱荷华州立大学）
- Seoul National University（首尔国立大学）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
本文提出两种贝叶斯方法处理信息性抽样下的分析推断：一种通过样本级权重模型构建相干似然，另一种采用Neyman正交化得分与损失似然自助法，实现稳健且高效的可信区间估计。
AI中文摘要：
我们开发了两种互补的贝叶斯程序，用于在信息性抽样下进行分析性推断。第一种程序通过建模给定研究变量时设计权重的样本级分布，并利用Sverchkov和Pfeffermann（2004）的恒等式恢复条件包含概率，从而构建一个相干的似然函数；它是最近提出的条件似然估计量的贝叶斯对应物，在样本级联合模型正确设定下达到基于模型的效率界，否则可能产生偏差。第二种程序仅将相同的权重模型用作Neyman正交化的设计加权得分模拟的输入，并应用损失似然自助法；在泊松抽样下，所得可信区间渐近地具有三明治校正，且在权重模型误设定下后验仍以真值为中心，尽管工作模型仍可能影响一阶方差。对总体包含概率进行beta回归，诱导出beta prime样本级权重分布，作为参数默认设置。第二种程序的数据自适应实现通过设计加权Gamma/对数链接回归估计效率因子$\bar\pi(x,y)=1/E_p(W\mid x,y)$，并将其用于分析参数联合一步损失似然自助法；其有效性不需要对干扰项拟合施加速率条件。我们通过模拟和加拿大劳动力数据说明了这两种程序。
英文摘要：
We develop two complementary Bayesian procedures for analytic inference under informative sampling. The first constructs a coherent likelihood by modeling the sample-level distribution of the design weight given the study variable and recovering the conditional inclusion probability through the identity of Sverchkov and Pfeffermann (2004); it is the Bayesian counterpart of a recently proposed conditional-likelihood estimator, attains the model-based efficiency bound under the correctly specified sample-level joint model, and can be biased otherwise. The second uses the same weight model only as input to a Neyman-orthogonalized analog of the design-weighted score and applies the loss-likelihood bootstrap; the resulting credible intervals are asymptotically sandwich-correct under Poisson sampling, and the posterior remains centered at the truth under misspecification of the weight model, although the working model can still affect the first-order variance. A beta regression on the population-level inclusion probability, inducing a beta prime sample-level weight distribution, serves as the parametric default. A data-adaptive implementation of the second procedure estimates the efficient factor $\barπ(x,y)=1/E_p(W\mid x,y)$ by a design-weighted Gamma/log-link regression and uses it in a joint one-step loss-likelihood bootstrap for the analytic parameter; its validity requires no rate conditions on the nuisance fit. We illustrate both procedures with simulations and Canadian Workforce data.
