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

Our comment on Garc\'ia-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 Garc\'ia-Donato et al. (2025). To be published as "Invited discussion" in Bayesian Analysis.