格点场论中贝叶斯模型平均的改进信息准则
Improved information criteria for Bayesian model averaging in lattice field theory
AI总结：
该研究针对格点场论中贝叶斯模型平均的权重估算问题，基于Kullback-Leibler散度推导并对比了BAIC、BPIC、PPIC三类信息准则，发现PPIC性能最优、BAIC可靠易用。
摘要：
贝叶斯模型平均是处理模型设定带来的不确定性的一种实用方法。使用该技术需要估算模型概率权重。在本研究中，我们重新推导了这些模型权重的估计量。以Kullback-Leibler散度为出发点，可自然推导出多种适用于贝叶斯模型权重估算的替代信息准则。我们详细探讨了统计学文献中已有的三类此类准则：我们称之为BAIC的Akaike信息准则贝叶斯版本、贝叶斯预测信息准则（BPIC）以及后验预测信息准则（PPIC）。我们在格点场论计算中常见的数值分析问题里对比了这些信息准则的应用效果。研究发现，PPIC具备最具吸引力的理论性质，在模型平均不确定性方面能实现最优性能，尤其是在存在噪声数据的情况下，而BAIC则是一种简单可靠的替代方案。
英文摘要：
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.
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