Variational Bayesian inference for logistic regression models for group testing data: Comparing a new hybrid variational inference approach to traditional methods.
- 1Department of Epidemiology and Biostatistics, University of South Carolina, 915 Greene St, Columbia, SC 29208 USA.
- 2Department of Statistics, University of South Carolina, 1523 Greene Street, Columbia, SC 29208 USA.
Abstract
Group testing is an efficient means of screening for infectious disease that combines specimens from multiple individuals and tests them as a single 'pooled' specimen. If a pool tests positive, subsequent tests are usually conducted to determine the disease status of the contributing individuals; if a pool tests negative, all samples in the pool are considered disease free. In recent years, Bayesian regression frameworks for group testing data have been developed, offering flexibility across group testing protocols and enabling the estimation of unknown assay accuracies. However, existing Bayesian methods rely heavily on Markov chain Monte Carlo (MCMC) sampling for estimation and inference, which becomes increasingly computationally inefficient as sample sizes grow, creating a bottleneck that limits the applicability of these models to large datasets. Variational Bayes (VB), an optimization-based algorithm that provides an analytical approximation to the posterior distribution, offers a more computationally efficient alternative to MCMC. To overcome the computational challenges of current Bayesian group testing methods, we develop a VB algorithm for group testing regression. Because VB methods are known to underestimate the posterior variance, we also propose an alternative inference method that exploits the asymptotic normality of VB estimators. We demonstrate with numerical studies that this hybrid inference approach achieves comparable inference to the MCMC approach while being more computationally scalable. We then apply the proposed VB method to COVID-19 group testing data from 43,185 individuals in the National Institutes of Health's All of Us Research Program. The online version contains supplementary material available at https://doi.org/10.1007/s11222-026-11013-5.
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BibTeX
@article{zhao2026variational,
title = {{Variational Bayesian inference for logistic regression models for group testing data: Comparing a new hybrid variational inference approach to traditional methods.}},
author = {Xingpei Zhao and Alexander C McLain and Bo Cai and Dewei Wang and Stella Self},
journal = {Statistics and computing},
year = {2026},
month = nov,
doi = {10.1007/s11222-026-11013-5},
url = {https://europepmc.org/article/MED/42996424},
note = {CC BY},
}
RIS
TY - JOUR
TI - Variational Bayesian inference for logistic regression models for group testing data: Comparing a new hybrid variational inference approach to traditional methods.
AU - Xingpei Zhao
AU - Alexander C McLain
AU - Bo Cai
AU - Dewei Wang
AU - Stella Self
PY - 2026
DA - 2026/11/05
JO - Statistics and computing
DO - 10.1007/s11222-026-11013-5
UR - https://europepmc.org/article/MED/42996424
AB - Group testing is an efficient means of screening for infectious disease that combines specimens from multiple individuals and tests them as a single 'pooled' specimen. If a pool tests positive, subsequent tests are usually conducted to determine the disease status of the contributing individuals; if a pool tests negative, all samples in the pool are considered disease free. In recent years, Bayesian regression frameworks for group testing data have been developed, offering flexibility across group testing protocols and enabling the estimation of unknown assay accuracies. However, existing Bayesian methods rely heavily on Markov chain Monte Carlo (MCMC) sampling for estimation and inference, which becomes increasingly computationally inefficient as sample sizes grow, creating a bottleneck that limits the applicability of these models to large datasets. Variational Bayes (VB), an optimization-based algorithm that provides an analytical approximation to the posterior distribution, offers a more computationally efficient alternative to MCMC. To overcome the computational challenges of current Bayesian group testing methods, we develop a VB algorithm for group testing regression. Because VB methods are known to underestimate the posterior variance, we also propose an alternative inference method that exploits the asymptotic normality of VB estimators. We demonstrate with numerical studies that this hybrid inference approach achieves comparable inference to the MCMC approach while being more computationally scalable. We then apply the proposed VB method to COVID-19 group testing data from 43,185 individuals in the National Institutes of Health's All of Us Research Program. The online version contains supplementary material available at https://doi.org/10.1007/s11222-026-11013-5.
SN - 0960-3174
ER -