Bayesian model averaging is a practical method for dealing with uncertainty due to model specification. Use of this technique requires the estimation of model probability weights. In this work, we revisit the derivation of estimators for these model weights. Use of the Kullback-Leibler divergence as a starting point leads naturally to a number of alternative information criteria suitable for Bayesian model weight estimation. We explore three such criteria, known to the statistics literature before, in detail: a Bayesian analogue of the Akaike information criterion which we call the BAIC, the Bayesian predictive information criterion (BPIC), and the posterior predictive information criterion (PPIC). We compare the use of these information criteria in numerical analysis problems common in lattice field theory calculations. We find that the PPIC has the most appealing theoretical properties and can give the best performance in terms of model-averaging uncertainty, particularly in the presence of noisy data, while the BAIC is a simple and reliable alternative.

翻译：贝叶斯模型平均是一种处理模型规范不确定性的实用方法。使用该技术需要估计模型概率权重。本文重新审视了这些模型权重估计量的推导过程。以Kullback-Leibler散度作为出发点，自然引出了若干适用于贝叶斯模型权重估计的替代信息准则。我们详细研究了统计学文献中已知的三种此类准则：贝叶斯版本的Akaike信息准则（称为BAIC）、贝叶斯预测信息准则（BPIC）以及后验预测信息准则（PPIC）。我们比较了这些信息准则在格点场论计算中常见数值分析问题上的应用效果。研究发现，PPIC具有最理想的理论性质，在模型平均不确定性方面（尤其是存在噪声数据时）表现出最佳性能，而BAIC则是一种简单可靠的替代方案。