A Bayesian framework for multilevel data under model mis-specification

2026-09-22

AI Summary

本文提出了一种贝叶斯框架，用于处理多层数据生成过程中的模型误设问题，通过半参数方法估计总体参数并考虑集群和单元级别变化。

Abstract

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 \citep{gelman2007data}, Programme for International Student Assessment 2022 \citep{OECD2023PISA}, and tuberculosis \citep{nobre2023impact} 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.

Problem

• Bayesian framework
• multilevel data
• model mis-specification
• uncertainty quantification

Innovation

• Bayesian framework
• model mis-specification
• multilevel data
• semi-parametric procedure
• Dirichlet model