发表机构
University of California, Davis; George Mason University（加州大学戴维斯分校; 乔治梅森大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究提出带图拉普拉斯基准先验的贝叶斯框架，用于小区域估计，通过定制MCMC算法实现后验计算，经模拟和哥伦比亚市级平均家庭规模估计验证，多视图模型表现更优。
AI 中文摘要
小区域估计（SAE）通常需要同时跨区域借用信息，并将估计值基准化为可靠的汇总值。我们开发了一种贝叶斯框架，通过新的基准先验族共同实现这两个目标。这些先验由一个带基准约束的正则化问题导出，所得族包含：无额外跨区域正则化、仅纳入基准约束的基准先验；以及通过基于外部协变量信息构建的区域相似性图拉普拉斯引入正则化的单视图和多视图拉普拉斯基准先验。针对这些退化先验的后验计算，我们开发了基于约束空间降维参数化的定制MCMC算法。我们通过基于数据的模拟评估所提模型，并将该框架应用于2025年哥伦比亚市级平均家庭规模（AHS）的估计。在该应用中，基于图的正则化提升了模型性能，多视图模型通常能产生更精确的市级估计值。
英文摘要
Small area estimation (SAE) often requires both borrowing information across areas and benchmarking estimates to reliable aggregates. We develop a Bayesian framework that addresses these two objectives jointly through a new family of Benchmarking priors. The priors are induced by a benchmark-constrained regularization problem. The resulting family includes a Benchmarking Prior that incorporates the benchmarking restrictions without additional regularization across areas, and Single and Multi-View Laplacian Benchmarking Priors that introduce regularization through graph Laplacians constructed from area similarities based on external covariate information. For posterior computation under these degenerate priors, we develop tailored MCMC algorithms based on a reduced parameterization of the constraint space. We assess the proposed models using a data-based simulation and apply the framework to estimate Average Household Size (AHS) at the municipality level in Colombia in 2025. In this application, graph-based regularization improves model performance, with the Multi-View models generally producing more precise municipality-level estimates.
