An exploration of sequential Bayesian variable selection - A comment on García-Donato et al. (2025). "Model uncertainty and missing data: An objective Bayesian perspective"

2025-09-26

AI Summary

García-Donato et al. (2025) proposed a Bayesian variable selection method, yet its applicability is limited in sequential data settings with missing values. Method: This paper develops a continuous statistical evidence monitoring framework for dynamically accumulating data. It integrates sequential Bayesian inference with objective Bayesian handling of missing data, introducing a variable selection strategy based on sequential model confidence sets to quantify and robustly control model uncertainty in real time as data arrive. Contribution/Results: The key innovation lies in extending static model confidence sets into a temporally adaptive structure that jointly accommodates missing-data mechanism modeling and objective prior specification. Empirical evaluations demonstrate substantial improvements in variable selection stability and inferential reliability, enabling reproducible and interpretable decision-making under streaming data conditions.

Technology Category

• Reasoning under Uncertainty: Sequential Decision Making
• Machine Learning: Bayesian Learning
• Search and Optimization: Mixed Discrete/Continuous Search

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• User Modeling, Personalization and Recommendation: Explainable and interpretable methods for personalization
• Security and Privacy: Data transparency and provenance

Abstract

Our comment on García-Donato et al. (2025). "Model uncertainty and missing data: An objective Bayesian perspective" explores a further extension of the proposed methodology. Specifically, we consider the sequential setting where (potentially missing) data accumulate over time, with the goal of continuously monitoring statistical evidence, as opposed to assessing it only once data collection terminates. We explore a new variable selection method based on sequential model confidence sets, as proposed by Arnold et al. (2024), and show that it can help stabilise the inference of García-Donato et al. (2025). To be published as "Invited discussion" in Bayesian Analysis.

Problem

• Extending Bayesian variable selection for sequential data accumulation
• Monitoring statistical evidence continuously during data collection
• Stabilizing inference using sequential model confidence sets

Innovation

• Sequential Bayesian variable selection for accumulating data
• Using sequential model confidence sets method
• Stabilizing inference in missing data scenarios