The Practical Implementation of Bayesian Model Selection
Abstract
In principle, the Bayesian approach to model selection is straightforward. Prior probability distributions are used to describe the uncertainty surrounding all unknowns. After observing the data, the posterior distribution provides a coherent post data summary of the remaining uncertainty which is relevant for model selection. However, the practical implementation of this approach often requires carefully tailored priors and novel posterior calculation methods. In this article, we illustrate some of the fundamental practical issues that arise for two different model selection problems: the variable selection problem for the linear model and the CART model selection problem.
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From a Bayesian perspective, testing zero variance components corresponds to hierarchical prior distributions with potential nonnegligible mass near zero.
“From a Bayesian perspective, the corresponding step is to model the variance parameters σ m .Testing for null hypotheses of zero variance components corresponds to hierarchical prior distributions for the variance components that have a potential for nonnegligible mass near zero, as has been discussed in the Bayesian literature on shrinkage and model selection [e.g., Gelman (1992), George and McCu”
From Analysis of variance—why it is more important than ever (2005) · cites this paper as Chipman, George and McCulloch (2001)
Cites
Quinlan, J. R. (1986) · Machine Learning · doi:10.1007/bf00116251 · Cited by 21,439 · see citing works
Hoeting, J. A., Madigan, D., Raftery, A. E., & Volinsky, C. T. (1999) · Statistical Science · doi:10.1214/ss/1009212519 · Cited by 4,118 · cited 1× · see citing works
“However, this prior distribution may not be sensible for model averaging when there are groups of similar variables and does not provide the proper " dilution " of posterior mass over similar models (see Clyde 1999; Hoeting et al. 1999), and discussion therein (George 1999; 1999a).”
BackgroundVariable Selection via Gibbs Sampling
George, E. I., & McCulloch, R. E. (1993) · Journal of the American Statistical Association · doi:10.1080/01621459.1993.10476353 · Cited by 2,828 · see citing works
Self-citationPrediction via Orthogonalized Model Mixing
Clyde, M., Desimone, H., & Parmigiani, G. (1996) · Journal of the American Statistical Association · doi:10.1080/01621459.1996.10476989 · Cited by 145 · see citing works
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A simple new approach to variable selection in regression, with application to genetic fine mapping
Wang, G., Sarkar, A., Carbonetto, P., & Stephens, M. (2020) · Journal of the Royal Statistical Society Series B (Statistical Methodology) · doi:10.1111/rssb.12388 · Cited by 1,121 · see citing works
An exploration of aspects of Bayesian multiple testing
Scott, J. G., & Berger, J. O. (2006) · Journal of Statistical Planning and Inference · doi:10.1016/j.jspi.2005.08.031 · Cited by 330 · see citing works
My Mobile Music: An Adaptive Personalization System for Digital Audio Players
Chung, T. S., Rust, R. T., & Wedel, M. (2009) · Marketing Science · doi:10.1287/mksc.1080.0371 · Cited by 119 · see citing works
Analysis of variance—why it is more important than ever
Gelman, A. (2005) · The Annals of Statistics · doi:10.1214/009053604000001048 · Cited by 861 · see citing works
“…to hierarchical prior distributions for the variance components that have a potential for nonnegligible mass near zero, as has been discussed in the Bayesian literature on shrinkage and model selection [e.g., Gelman (1992), George and McCulloch (1993) and Chipman, George and McCulloch (2001)].”
Background
- Authors
- Chipman, H., George, E. I., & McCulloch, R. E.
- Affiliations
- University of Waterloo (CA)
- The University of Texas at Austin (US)
- University of Chicago (US)
- ORCID
- Chipman, Hugh
- Venue
- Institute of Mathematical Statistics Lecture Notes - Monograph Series
- Publisher
- Institute of Mathematical Statistics
- Published
- 2001
- Pages
- 65-116
- ISSN
- 0749-2170 (ISSN-L)
- OpenAlex
- W1666386643
- Cited by
- 416
- References
- 4
- Citations by year
- 2026: 4 · 2025: 9 · 2024: 15 · 2023: 13 · 2022: 20 · 2021: 21 · 2020: 18 · 2019: 20 · 2018: 22 · 2017: 17 · 2016: 24 · 2015: 15 · 2014: 13 · 2013: 26 · 2012: 17
- FWCI
- 14.19
- Type
- book chapter
- Language
- en
- Open access
- closed
- Locations
- Lecture notes-monograph series (publishedVersion)
- ScholarlyCommons (University of Pennsylvania) (submittedVersion)
- Project Euclid (Cornell University) (submittedVersion)
- Topics
- Physical Sciences › Mathematics › Statistics and Probability › Statistical Methods and Inference
- Physical Sciences › Mathematics › Statistics and Probability › Statistical Methods and Bayesian Inference
- Physical Sciences › Mathematics › Statistics and Probability › Markov Chains and Monte Carlo Methods
- Keywords
- Bayesian model selection, prior distributions, posterior distribution, feature selection, linear models, CART, classification and regression trees, uncertainty quantification
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