标题： 基于信息抽样的贝叶斯估计 显示英文标题

标题： Bayesian Estimation Under Informative Sampling

摘要： 贝叶斯分析在社会科学研究和其他数据来自信息性样本的应用领域中越来越受欢迎。 信息性抽样设计会导致包含概率与感兴趣的结果变量相关。 在信息性抽样下，对从总体中抽取的观测样本进行模型推断会偏向总体生成模型，因为样本数据中的信息平衡与总体不同。 在贝叶斯估计下，考虑信息性抽样设计的典型方法通常难以实现，因为它们需要重新参数化假设的生成模型，或者专注于设计而非模型的推断。 我们提出构建一个伪后验分布，该分布利用基于边缘包含概率的抽样权重来提升每个抽样单元的似然贡献，从而将样本中的信息重新加权到总体。 我们的方法提供了一种几乎自动化的估计过程，适用于数据分析师为总体指定的任何模型，并保留总体模型的参数化和后验采样几何结构。 我们建立了对已知边缘和成对包含概率的条件，这些条件定义了一个抽样设计类，在该类中，伪后验的$L_{1}$一致性得到保证。 我们在涉及劳动统计局职位空缺和劳动力流动调查的应用中展示了我们的方法。 显示英文摘要

摘要： Bayesian analysis is increasingly popular for use in social science and other application areas where the data are observations from an informative sample. An informative sampling design leads to inclusion probabilities that are correlated with the response variable of interest. Model inference performed on the observed sample taken from the population will be biased for the population generative model under informative sampling since the balance of information in the sample data is different from that for the population. Typical approaches to account for an informative sampling design under Bayesian estimation are often difficult to implement because they require re-parameterization of the hypothesized generating model, or focus on design, rather than model-based, inference. We propose to construct a pseudo-posterior distribution that utilizes sampling weights based on the marginal inclusion probabilities to exponentiate the likelihood contribution of each sampled unit, which weights the information in the sample back to the population. Our approach provides a nearly automated estimation procedure applicable to any model specified by the data analyst for the population and retains the population model parameterization and posterior sampling geometry. We construct conditions on known marginal and pairwise inclusion probabilities that define a class of sampling designs where $L_{1}$ consistency of the pseudo posterior is guaranteed. We demonstrate our method on an application concerning the Bureau of Labor Statistics Job Openings and Labor Turnover Survey.