贝叶斯模型选择：在基本物理常数平差中的应用
Bayesian model selection: Application to adjustment of fundamental physical constants
摘要：
位置-尺度模型通常存在于物理学和化学中，与用于调整基本物理常数（如普朗克常量或牛顿引力常数）的Birge比率方法有关，而随机效应模型是医学中荟萃分析的常用方法。这两个竞争模型用于增加测量结果的引用不确定度，使其一致。内禀贝叶斯因子（IBF）的随机效应模型的位置-尺度模型的比较，我们回答的问题，该模型执行更好的确定牛顿引力常数。经验说明的结果支持Birge比率方法的应用，该方法目前用于调整CODATA 2018牛顿引力常数及其不确定性的值。模拟研究的结果表明，建议的模型选择程序是决定性的，即使数据包括几个测量结果。
英文摘要：
The location-scale model is usually present in physics and chemistry in connection to the Birge ratio method for the adjustment of fundamental physical constants such as the Planck constant or the Newtonian constant of gravitation, while the random effects model is the commonly used approach for meta-analysis in medicine. These two competitive models are used to increase the quoted uncertainties of the measurement results to make them consistent. The intrinsic Bayes factor (IBF) is derived for the comparison of the random effects model to the location-scale model, and we answer the question which model performs better for the determination of the Newtonian constant of gravitation. The results of the empirical illustration support the application of the Birge ratio method which is currently used in the adjustment of the CODATA 2018 value for the Newtonian constant of gravitation together with its uncertainty. The results of the simulation study illustrate that the suggested procedure for model selection is decisive even when data consist of a few measurement results.
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