On the adjustment of inconsistent data using the Birge ratio
On the adjustment of inconsistent data using the Birge ratio
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DOI：
10.1088/0026-1394/51/5/516
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发表时间：
2014-10-01
期刊：
影响因子：
2.4
通讯作者：
Elster, Clemens
中科院分区：
文献类型：
--
作者：
Bodnar, Olha;Elster, Clemens
伯奇比在计量学中的应用是为了在同一被测量上组合不一致的测量结果时放大引用的不确定性。我们讨论了这种程序背后的统计模型，并认为与调整值相关的不确定性被低估了。我们基于客观贝叶斯推理对这种不确定性进行了简单的修改。虽然所提出的不确定性方法是通过传统程序获得的大量 n 的组合测量结果，但对于小 n 来说差异是显着的。例如，对于 n = 4，与调整值相关的标准不确定度增加了 73%，而对于 n = 10，增加仍为 13%。我们导出了封闭形式的调整值的后验分布，包括 95% 的可信区间。此外，我们表明，我们的结果不仅在假设测量结果分布为高斯分布时成立，而且对于整个（椭圆形轮廓）位置尺度分布系列也成立。我们通过对 2002 年牛顿引力常数调整数据的应用来说明改进的 Birge 方法。
The Birge ratio is applied in metrology to enlarge quoted uncertainties when combining inconsistent measurement results on the same measurand. We discuss the statistical model underlying such a procedure and argue that the resulting uncertainty associated with the adjusted value is underrated. We provide a simple modification of this uncertainty on the basis of an objective Bayesian inference. While the proposed uncertainty approaches that obtained by the conventional procedure for a large number n of combined measurement results, differences are significant for small n. For example, for n = 4 we get an increase of 73% in the standard uncertainty associated with the adjusted value, and for n = 10 the increase is still 13%. We derive the posterior distribution for the adjusted value in closed form, including a 95% credible interval. In addition, we show that our results do not only hold when the distribution of the measurement results is assumed to be Gaussian, but for a whole family of (elliptically contoured) location-scale distributions. We illustrate the modified Birge method by its application to data from the 2002 adjustment of the Newtonian constant of gravitation.