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What is Bayesian model averaging (BMA)?

Traditionally, we select a model and perform inference and prediction conditional on this model. Our results typically do not account for the uncertainty in selecting a model and thus may be overly optimistic. They may even be incorrect if our selected model is substantially different from the true data-generating model (DGM). In some applications, we may have strong theoretical or empirical evidence about the DGM. In other applications, usually of complex and unstable natures, such as those in economics, psychology, and epidemiology, choosing one reliable model can be difficult.

Model averaging is a statistical approach that accounts for model uncertainty in your analysis. Instead of relying on just one model, model averaging averages results over multiple plausible models based on the observed data. In BMA, the "plausibility" of the model is described by the posterior model probability (PMP), which is determined using the fundamental Bayesian principles—the Bayes theorem—and applied universally to all data analyses.

BMA can be used to account for model uncertainty when estimating model parameters and predicting new observations to avoid overly optimistic conclusions. It is particularly useful in applications with several plausible models, where there is no one definitive reason to choose a particular model over the others. But even if choosing a single model is the end goal, you can find BMA beneficial. It provides a principled way to identify important models and predictors within the considered classes of models. Its framework allows you to learn about interrelations between different predictors in terms of their tendency to appear in a model together, separately, or independently. It can be used to evaluate the sensitivity of the final results to various assumptions about the importance of different models and predictors. And it provides optimal predictions in the log-score sense.

To learn more about BMA, see [BMA] Intro. See an overview of BMA features and quick examples of BMA features.