modelaveraged

Model averaging is a statistical approach that addresses model uncertainty by combining predictions from multiple candidate models rather than selecting a single best model. This technique recognizes that no single model may capture all aspects of the data, and averaging can improve predictive performance and provide more realistic uncertainty estimates.

Under Bayesian model averaging, each model is assigned a posterior probability given the data, and predictions are formed by taking a weighted average of the models' predictive distributions, with weights equal to these posterior probabilities. The weights reflect both the goodness of fit and the complexity of the model, and sum to one. In practice, weights are proportional to the marginal likelihood of the data under each model times the prior probability of the model. Computing marginal likelihood involves integrating over the model’s parameters and is approximated via analytic, Laplace, or MCMC methods.

Non-Bayesian alternatives include AIC or BIC-based model averaging, where weights are derived from information criteria; stacking and cross-validation based ensemble methods also fall under the broader umbrella. These methods aim to improve predictive accuracy and quantify uncertainty by averaging over model space.

Applications span regression, time-series forecasting, econometrics, epidemiology, and climate modeling. Limitations include dependence on the set of candidate models, computational intensity, sensitivity to priors or criteria, and potential redundancy when models are highly correlated.

In summary, model averaging provides a principled way to incorporate model uncertainty into predictions by using weighted combinations of multiple models rather than relying on a single model. It offers improved predictive performance and a coherent framework for presenting uncertainty in model-based inferences.