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.

翻译：贝叶斯模型平均是处理模型规范所致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散度为起点，自然推导出多种适用于贝叶斯模型权重估计的替代信息准则。我们详细探究了统计学文献中已知的三种准则：贝叶斯类比赤池信息准则（记为BAIC）、贝叶斯预测信息准则（BPIC）和后验预测信息准则（PPIC）。我们比较了这些信息准则在格子场论计算常见数值分析问题中的应用效果。研究发现，PPIC具有最理想的理论性质，并在模型平均不确定性方面展现出最优性能，尤其在数据存在噪声的情况下表现突出。