Issues of model selection have dominated the theoretical and applied statistical literature for decades. Model selection methods such as ridge regression, the lasso, and the elastic net have replaced ad hoc methods such as stepwise regression as a means of model selection. In the end, however, these methods lead to a single final model that is often taken to be the model considered ahead of time, thus ignoring the uncertainty inherent in the search for a final model. One method that has enjoyed a long history of theoretical developments and substantive applications, and that accounts directly for uncertainty in model selection, is Bayesian model averaging (BMA). BMA addresses the problem of model selection by not selecting a final model, but rather by averaging over a space of possible models that could have generated the data. The purpose of this paper is to provide a detailed and up-to-date review of BMA with a focus on its foundations in Bayesian decision theory and Bayesian predictive modeling. We consider the selection of parameter and model priors as well as methods for evaluating predictions based on BMA. We also consider important assumptions regarding BMA and extensions of model averaging methods to address these assumptions, particularly the method of Bayesian stacking. Simple empirical examples are provided and directions for future research relevant to psychometrics are discussed.

几十年来，模型选择问题一直主导着理论和应用统计文献。岭回归、套索和弹性网等模型选择方法已取代逐步回归等临时方法作为模型选择的手段。然而，最终，这些方法会产生一个单一的最终模型，该模型通常被认为是提前考虑的模型，因此忽略了寻找最终模型所固有的不确定性。一种在理论发展和实质性应用方面享有悠久历史并直接解释模型选择不确定性的方法是贝叶斯模型平均(BMA)。BMA 通过不选择最终模型，而是通过对可能生成数据的可能模型空间进行平均来解决模型选择问题。本文的目的是对 BMA 进行详细和最新的回顾，重点关注其在贝叶斯决策理论和贝叶斯预测建模方面的基础。我们考虑参数和模型先验的选择以及基于 BMA 评估预测的方法。我们还考虑了关于 BMA 的重要假设和模型平均方法的扩展以解决这些假设，特别是贝叶斯堆叠方法。提供了简单的实证例子，并讨论了与心理测量学相关的未来研究方向。