作者：胡红波, 季文晖

作者单位：中国计量科学研究院， 北京 100029

关键词：计量学;不确定度评估;测量方程;观测方程;贝叶斯统计

摘要：

GUM不确定度评估方法以测量方程为基础，通过标准不确定度传递的方法实现被测量标准不确定度的计算，是一种前向的不确定度评估方法；从观察方程入手的贝叶斯分析方法则是一种基于概率密度函数传递的后向的不确定度评估方法。该文详细说明两种方法评估测量不确定度的过程，解释两种方法的相同与差异之处。最后通过典型的不确定度评估实例，说明对于线性的测量模型，依据GUM准则评估的结果与利用被测量无信息先验的贝叶斯统计得到的结果是一致的，但在设定较强被测量先验信息或者非线性测量模型条件下，两种方法评估的结果有一定的差异。

Measurement equation, observation equation and uncertainty evaluation
HU Hongbo, JI Wenhui
National Institute of Metrology, China, Beijing 100029, China
Abstract: The GUM(Guide to the Expression of Uncertainty in Measurement) method is based on measurement equation, and the computational tool is the law of propagation of uncertainty, so it can be termed forward uncertainty evaluation. Bayesian statistics is alternative approach for uncertainty evaluation, which is based on observation equation, and it is an inverse uncertainty evaluation method using propagation of PDF(probability density function). We illustrate the two approached in detail in the paper and explain how and where they differ. Through the application of the proposed techniques, we explain that for linear models, the GUM and Bayesian method using noninformative prior distribution provide consistent results, but for nonlinear measurement model or with strong prior knowledge for Bayesian method, some practical differences of the results exist for the two approaches.
Keywords: metrology;uncertainty evaluation;measurement equation;observation equation;Bayesian statistics
2020, 46(8):7-12  收稿日期: 2020-06-19;收到修改稿日期: 2020-07-22
基金项目: 国家质量基础的共性技术研究与应用（2017YFF0206302）
作者简介: 胡红波（1980-），男，湖北荆州市人，副研究员，硕士，主要从事振动冲击加速度计量与测试技术研究
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