论文标题
贝叶斯对重力常数的系统误差的分析
Bayesian analysis of systematic errors in the determination of the constant of gravitation
论文作者
论文摘要
众所周知，重力常数$ g $的测量很难。单个最先进的实验设法以高精度确定了$ g $的价值：尽管总体考虑$ g $的测量值的范围远远超过了个体的不确定性，这表明存在未计算的系统效果。 在这里，我们提出了一个贝叶斯框架，以说明$ g $的各种测量中存在系统错误的同时，同时提出共识值，遵循两条路径：基于最大熵原理的参数方法，而不是非参数，后者是对任何特定功能的非常灵活的方法。 通过我们的两种方法，我们发现该基本常数的不确定性（一旦包括系统）的不确定性明显大于Codata 2018中引用的不确定性。此外，非参数分布的形态暗示了存在几种无偏见的系统源的存在源。因此，我们建议重力常数$ g = 6.6740^{+0.0015} _ { - 0.0015} \ times 10^{ - 11} { - 11} \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ Mathrm {kg}^{ - 1} $ { - 2}
Measurements of the gravitational constant $G$ are notoriously difficult. Individual state-of-the-art experiments have managed to determine the value of $G$ with high precision: although, when considered collectively, the range in the measured values of $G$ far exceeds individual uncertainties, suggesting the presence of unaccounted for systematic effects. Here, we propose a Bayesian framework to account for the presence of systematic errors in the various measurement of $G$ while proposing a consensus value, following two paths: a parametric approach, based on the Maximum Entropy Principle, and a non-parametric one, the latter being a very flexible approach not committed to any specific functional form. With both our methods, we find that the uncertainty on this fundamental constant, once systematics are included, is significantly larger than what quoted in CODATA 2018. Moreover, the morphology of the non-parametric distribution hints towards the presence of several sources of unaccounted for systematics. In light of this, we recommend a consensus value for the gravitational constant $G = 6.6740^{+0.0015}_{-0.0015} \times 10^{-11}\ \mathrm{m}^3\ \mathrm{kg}^{-1}\ \mathrm{s}^{-2}$.
