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Keywords: Bayesian model averaging, interval estimation, LASSO, model selection, parameter estimation, penalized likelihood, prediction, statistical inference, Zellner's $g$-prior.
Choosing a statistical model and accounting for uncertainty about this choice are important parts of the scientific process, and are required for common statistical tasks such as parameter estimation, interval estimation, statistical inference, point prediction and interval prediction. A canonical example is the choice of variables in a linear regression model. Many ways of doing this have been proposed, including Bayesian and penalized regression methods, and it is not clear which are best. We compare 21 popular methods via an extensive simulation study based on a wide range of real datasets. We found that three adaptive Bayesian model averaging (BMA) methods performed best across all the statistical tasks, and that two of these were also among the most computationally efficient.