发表机构
Universidade Federal do Rio de Janeiro; McGill University（里约热内卢联邦大学; 麦吉尔大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
提出一种贝叶斯半参数框架，通过富化狄利克雷模型的多层次权重扩展贝叶斯自助法，以处理工作模型误设定下的多层次数据，实现总体参数估计与不确定性量化。
AI 中文摘要
我们提出一个贝叶斯框架，用于在多层次数据生成过程的设定下，从工作模型被误设定的角度进行不确定性量化。我们关注误设定未能匹配均值结构函数形式的场景，并讨论在工作模型与数据生成模型不匹配所引发的依赖关系下，目标参数的贝叶斯估计。该提议代表一种贝叶斯半参数程序，旨在估计总体层面参数，同时考虑估计函数中的聚类和单元层面变异。该提议扩展了常规贝叶斯自助法，通过来自富化狄利克雷模型的多层次权重来考虑聚类和单元层面的变异。模拟研究表明，当数据生成过程和所提议模型诱导出与未知感兴趣量相关的部分可交换序列时，所提方法具有良好的频率学性质。为说明目的，展示了应用于氡数据集（Gelman等，2007）、2022年国际学生评估项目（OECD，2023）和结核病数据集（Nobre等，2023）的实例。结果表明，所提方法与多层次模型的变体相比具有竞争力，主要差异体现在可信区间范围上，这由所提方法背后的非参数假设所证明。
英文摘要
We propose a Bayesian framework for uncertainty quantification from the perspective that the working model is mis-specified in settings of a multilevel data-generating process. We focus on settings in which the mis-specification fails to match the functional form of the mean structure, and discuss Bayesian estimation of target parameters under dependence induced by a mismatch between working and data-generating models. The proposal represents a Bayesian semi-parametric procedure aimed at estimating population-level parameters while accounting for cluster- and unit-level variation in the estimating function. The proposal extends the regular Bayesian bootstrap to account for cluster- and unit-level variation using multilevel weights from an enriched Dirichlet model. Simulation studies indicate that the proposed approach has good frequentist properties when the data-generating process and the proposed model induce a partially exchangeable sequence associated with the unknown quantity of interest. Applications to radon (Gelman and Hill, 2007), Programme for International Student Assessment 2022 (OECD, 2023), and tuberculosis (Nobre et al., 2023) datasets are presented for illustrative purposes. The results demonstrate that the proposed method is competitive with variations of multilevel models, with major differences observed in the range of credible intervals, which are justified by the nonparametric assumptions underlying the proposed method.
