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

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).