论文标题
贝叶斯模型平均用于分析晶格场理论结果
Bayesian model averaging for analysis of lattice field theory results
论文作者
论文摘要
统计建模是从晶格场理论计算中提取物理结果的关键组成部分。尽管所使用的一般模型通常是由物理学强的，但对于相同的晶格数据，经常可以考虑许多模型变化。在所有模型变化中，模型平均概率加权的平均值，可以将与模型选择相关的系统误差纳入而不过分保守。我们从贝叶斯统计的角度讨论了模型平均的框架，并为最小二乘拟合的特定情况提供了有用的公式和近似值，这通常用于建模晶格结果。此外，我们将数据子集选择的常见问题（例如，将最小和最大时间分离的选择用于拟合两点相关函数）作为模型选择问题，并将研究模型平均作为手动选择范围的直接替代方案。给出了涉及模拟和真实晶格数据的数值示例。
Statistical modeling is a key component in the extraction of physical results from lattice field theory calculations. Although the general models used are often strongly motivated by physics, many model variations can frequently be considered for the same lattice data. Model averaging, which amounts to a probability-weighted average over all model variations, can incorporate systematic errors associated with model choice without being overly conservative. We discuss the framework of model averaging from the perspective of Bayesian statistics, and give useful formulae and approximations for the particular case of least-squares fitting, commonly used in modeling lattice results. In addition, we frame the common problem of data subset selection (e.g. choice of minimum and maximum time separation for fitting a two-point correlation function) as a model selection problem and study model averaging as a straightforward alternative to manual selection of fit ranges. Numerical examples involving both mock and real lattice data are given.
