We wish to congratulate the authors with this paper, as it is a nice mix of important conceptual ideas, strong theoretical results and relevant applications. The paper introduces a novel empirical Bayes framework for data integration in high-dimensional regression models, with a particular focus on variable selection. The main objective is to improve the identification of relevant variables by incorporating external information from previous studies or related sources. Such external information is referred to as meta-covariates. Others have used equivalent terms like 'co-data' (Neuenschwander et al. ; van Nee et al. ) or 'features-of-features' (Tay et al. ).
We congratulate Rognon-Vael and Rossell () on a stimulating paper on empirical Bayes (EB) for data integration, where external information is available only through meta-covariates. It gives a clear account of why EB can be especially attractive for transfer learning, compared to a full Bayesian counterpart. The focus on structural learning is highly relevant in modern scientific applications, where external evidence is more naturally interpreted as information about sparsity or support than as a probabilistic description of the target data-generating mechanism. In particular, the authors allow external summaries to modify prior inclusion probabilities and estimate the corresponding hyperparameters. Their theoretical results further show that suitably chosen priors can weaken the conditions required for model selection consistency, and that the proposed EB procedure can recover these gains without knowledge of the oracle hyperparameters. The paper also develops a computationally attractive representation of the marginal-likelihood gradient, leading to practical algorithms.Our comments explore three possible extensions of the proposed framework: variable-specific transfer effects, empirical Bayes calibration beyond structural learning, and variational approximations for scalable computation.
We provide a rejoinder to the various questions raised, including the discussion of issues associated to model misspecification, consideration of more flexible models, extensions to high-dimensional meta-covariates and computational issues, among others.
This work focuses on providing a commentary on the paper titled "Robust Inference for Step-Stress Experiments under Interval-Censoring", authored by Balakrishnan et al. (). Following an introductory overview that clearly outlines the scope of the study, the paper highlights the most valuable aspects and the remarkable contributions of the authors. It then addresses potential directions for future research stemming from this contribution. Finally, the commentary concludes with a concise section summarizing the key takeaways. First of all, I would like to thank the editors of TEST for the opportunity to comment on this interesting paper, as well as the authors for their contribution to robust inference for step-stress experiments under interval censoring in the field of reliability.
