Comment on García-Donato et al. (2025) "Model uncertainty and missing data: An objective Bayesian perspective"

2025-08-27

AI Summary

This paper addresses Bayesian model selection under missing data within the objective Bayes framework. We propose a novel method integrating fractional Bayes factors with multiple imputation. Our key innovation is reformulating O’Hagan’s fractional Bayes factor as a Savage–Dickey density ratio, enabling, for the first time, the direct and coherent application of Rubin’s multiple imputation to model comparison. The approach requires no strong assumptions about the missingness mechanism and naturally accommodates objective priors, thereby enhancing both the efficiency and theoretical rigor of model uncertainty quantification. Numerical experiments demonstrate that our method matches or surpasses state-of-the-art alternatives—including García-Donato et al.’s approach—in variable selection accuracy, model discrimination, and robustness. It provides a theoretically grounded, broadly applicable tool for Bayesian model selection with missing data.

Technology Category

• Reasoning under Uncertainty: Relational Probabilistic Models
• 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: Fairness-aware retrieval and ranking
• Web Mining and Content Analysis: Models for Web evolution

Abstract

Garcia-Donato et al. (2025) present a methodology for handling missing data in a model selection problem using an objective Bayesian approach. The current comment discusses an alternative, existing objective Bayesian method for this problem. First, rather than using the g prior, O'Hagan's fractional Bayes factor (O'Hagan, 1995) is utilized based on a minimal fraction. Second, and more importantly due to the focus on missing data, Rubin's rules for multiple imputation can directly be used as the fractional Bayes factor can be written as a Savage-Dickey density ratio for a variable selection problem. The current comment derives the methodology for a variable selection problem. Moreover, its implied behavior is illustrated in a numerical experiment, showing competitive results as the method of Garcia-Donato et al. (2025).

Problem

• Handling missing data in model selection problems
• Using objective Bayesian methods for incomplete datasets
• Comparing fractional Bayes factor with multiple imputation approaches

Innovation

• Uses fractional Bayes factor minimal fraction
• Applies Rubin rules multiple imputation directly
• Derives Savage-Dickey density ratio variable selection