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Effect of model space priors on statistical inference with model uncertainty
Anupreet Porwal1, Adrian E Raftery1
1Department of Statistics, University of Washington, Seattle, WA 98195, USA.
The New England Journal of Statistics in Data Science
|October 17, 2024
Summary
Beta-binomial model space priors, which consider prior probability of model size, best handle model uncertainty in Bayesian model averaging (BMA). These priors outperformed others across various statistical tasks and datasets.
Area of Science:
- Statistics
- Computational Statistics
Background:
- Bayesian model averaging (BMA) is crucial for statistical inference, requiring careful specification of model and parameter space priors.
- Model uncertainty is a significant challenge in statistical modeling.
Purpose of the Study:
- To compare the performance of different model space priors within Bayesian model averaging.
- To assess how prior specifications impact variable selection and statistical tasks in linear regression.
Main Methods:
- Evaluated eight reference model space priors and three adaptive parameter priors.
- Conducted an extensive simulation study using 14 real datasets.
- Assessed performance across parameter estimation, interval estimation, inference, and prediction tasks.
Main Results:
- Beta-binomial model space priors, based on prior probability of model size, demonstrated superior average performance.
- These priors outperformed uniform model space priors.
- Recently proposed complexity priors yielded relatively poor results.
Conclusions:
- Beta-binomial priors offer an effective approach for specifying model space priors in BMA, particularly for variable selection in linear regression.
- The choice of model space prior significantly impacts statistical inference and prediction accuracy.
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