论文标题
改进的贝叶斯模型的信息标准平均晶格场理论
Improved information criteria for Bayesian model averaging in lattice field theory
论文作者
论文摘要
贝叶斯模型平均是一种实用方法，用于处理由于模型规范而导致的不确定性。使用此技术需要估计模型概率权重。在这项工作中，我们重新审视了这些模型权重的估计器的推导。使用kullback-leibler差异作为起点自然会导致许多适合贝叶斯模型重量估计的替代信息标准。我们详细介绍了统计文献的三个这样的标准：Akaike信息标准的贝叶斯类似物，我们称为BAIC，贝叶斯预测信息标准（BPIC）和后验预测信息标准（PPIC）。我们比较了这些信息标准在晶格场理论计算中常见的数值分析问题中的使用。我们发现，PPIC具有最吸引人的理论属性，并且在模型平均不确定性方面可以提供最佳性能，尤其是在存在嘈杂数据的情况下，而BAIC是一种简单可靠的选择。
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.
