https://orcid.org/0000-0002-1001-011X
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Abstract
For many decades now, Bayesian Model Averaging (BMA) has been a popular framework to systematically account for model uncertainty that arises in situations when multiple competing models are available to describe the same or similar physical process. The implementation of this framework, however, comes with a multitude of practical challenges including posterior approximation via Markov chain Monte Carlo and numerical integration. We present a Variational Bayesian Inference approach to BMA as a viable alternative to the standard solutions which avoids many of the aforementioned pitfalls. The proposed method is “black box” in the sense that it can be readily applied to many models with little to no model-specific derivation. We illustrate the utility of our variational approach on a suite of examples and discuss all the necessary implementation details. Fully documented Python code with all the examples is provided as well.
Supplementary Materials
The supplementary material contains some additional numerical results for the VBMA of linear regression models, logistic regression models, and nuclear mass models. The results were obtained using the RMSprop adaptive learning rate as compared to the Adam learning rate results presented in the main article.
Funding
The research is partially supported by the National Science Foundation funding DMS-1952856, DMS-2124605, DMS-1924724, and OAC-2004601.
Acknowledgments
The authors thank the reviewers, the Associate Editor, and the Editor for their helpful comments and ideas. This work was supported in part through computational resources and services provided by the Institute for Cyber-Enabled Research at Michigan State University.