论文标题
部分可观测时空混沌系统的无模型预测
Hubble tensions: a historical statistical analysis
论文作者
论文摘要
对Hubble-LemaTre常数的测量值的统计分析$ H_0 $（1976年至2019年之间的163个测量值）表明，与观察到的参数测量相关的统计误差栏已被低估了 - 或者在至少15-20-20 \％中未正确考虑系统错误。 $ H_0 $的错误条低估的事实是如此普遍，这可能解释了值的明显差异，该值今天被正式称为Hubble张力。在这里，我们通过此测量样本对概率进行了重新校准。我们发现，$xσ$偏差确实在正态分布中等于$ x _ {\ rm eq。}σ$ s偏差的频率，其中$ x _ {\ rm eq。} = 0.83x^{0.62} $。因此，张力为4.4 $σ$，在本地的头孢虫 - 苏珀诺瓦距离阶梯和宇宙微波背景（CMB）数据之间估计，实际上是2.1 $σ$的张力，等效于正态分布，具有相关概率$ p（> x _ _ {x _ {\ rm eq。在最坏的情况下，这可以增加至2.5 $σ$的等效张力，而声称为6 $σ$张力，无论如何，这可能是随机的统计波动而发生的。
Statistical analyses of the measurements of the Hubble-Lemaître constant $H_0$ (163 measurements between 1976 and 2019) show that the statistical error bars associated with the observed parameter measurements have been underestimated -- or the systematic errors were not properly taken into account -- in at least 15-20\% of the measurements. The fact that the underestimation of error bars for $H_0$ is so common might explain the apparent discrepancy of values, which is formally known today as the Hubble tension. Here we have carried out a recalibration of the probabilities with this sample of measurements. We find that $xσ$ deviation is indeed equivalent in a normal distribution to $x_{\rm eq.}σ$s deviation in the frequency of values, where $x_{\rm eq.}=0.83x^{0.62}$. Hence, a tension of 4.4$σ$, estimated between the local Cepheid-supernova distance ladder and cosmic microwave background (CMB) data, is indeed a 2.1$σ$ tension in equivalent terms of a normal distribution of frequencies, with an associated probability $P(>x_{\rm eq.})=0.036$ (1 in 28). This can be increased up to a equivalent tension of 2.5$σ$ in the worst of the cases of claimed 6$σ$ tension, which may anyway happen as a random statistical fluctuation.
