A Bayesian framework for multilevel data under model mis-specification
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 (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.
Related
- Amortized Bayesian Inference on Multilevel Models of Arbitrary Structure
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- Sequential Entropic Optimal Transport for Bayesian Inverse Problems via Multilevel Monte Carlo
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- bacontrees: An extensible framework for Bayesian Context Trees in R
BibTeX
@misc{nobre2026bayesian,
title = {{A Bayesian framework for multilevel data under model mis-specification}},
author = {Widemberg S. Nobre and David A. Stephens and Alexandra M. Schmidt and Erica E. M. Moodie},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.27112},
eprint = {2609.27112},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.27112},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - A Bayesian framework for multilevel data under model mis-specification
AU - Widemberg S. Nobre
AU - David A. Stephens
AU - Alexandra M. Schmidt
AU - Erica E. M. Moodie
PY - 2026
DA - 2026/09/24
PB - arXiv
DO - 10.48550/arxiv.2609.27112
UR - https://arxiv.org/abs/2609.27112
AB - 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.
ER -