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Analysis and Comparison of Bayesian Methods for Measurement Uncertainty Evaluation

机译：贝叶斯测量不确定度评估方法的分析与比较

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摘要

Based on the Bayesian principle, the modern uncertainty evaluation methods can fully integrate prior and current sample information, determine the prior distribution according to historical information, and deduce the posterior distribution by integrating prior distribution and the current sample data with the Bayesian model. As such, it is possible to evaluate uncertainty, updating in real time the uncertainty of the measuring instrument according to regular measurement, and timely reflect the latest information on the accuracy of the measurement system. Based on the Bayesian information fusion and statistical inference principle, the model of uncertainty evaluation is established. The maximum entropy principle and the hill-climbing search optimization algorithm are introduced to determine the prior distribution probability density function and the sample information likelihood function. The probability density function of posterior distribution is obtained by the Bayesian formula to achieve the optimization estimation of uncertainty. Three methods of measurement uncertainty evaluation based on Bayesian analysis are introduced: the non informative prior, the conjugate prior, and the maximum entropy prior distribution. The advantages and limitations of each method are discussed.
机译：基于贝叶斯原理，现代不确定性评估方法可以将先验样本信息和当前样本信息完全融合，根据历史信息确定先验分布，并通过将先验分布和当前样本数据与贝叶斯模型相结合来推断后验分布。这样，可以评估不确定性，根据常规测量实时更新测量仪器的不确定性，并及时反映有关测量系统准确性的最新信息。基于贝叶斯信息融合和统计推断原理，建立了不确定性评估模型。引入最大熵原理和爬山搜索优化算法确定先验分布概率密度函数和样本信息似然函数。通过贝叶斯公式获得后验分布的概率密度函数，以实现不确定性的优化估计。介绍了基于贝叶斯分析的三种测量不确定度评估方法：无信息先验，共轭先验和最大熵先验分布。讨论了每种方法的优缺点。

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  • 来源
    《Mathematical Problems in Engineering》 |2018年第6期|7509046.1-7509046.10|共10页
  • 作者

    Cheng Yin-bao; Chen Xiao-huai; Li Hong-li; Cheng Zhen-ying; Jiang Rui; Lu Jing; Fu Hua-dong;

  • 作者单位

    Hefei Univ Technol, Sch Instrument Sci & Optoelect Engn, Hefei 230009, Anhui, Peoples R China;

    Hefei Univ Technol, Sch Instrument Sci & Optoelect Engn, Hefei 230009, Anhui, Peoples R China;

    Hefei Univ Technol, Sch Instrument Sci & Optoelect Engn, Hefei 230009, Anhui, Peoples R China;

    Hefei Univ Technol, Sch Instrument Sci & Optoelect Engn, Hefei 230009, Anhui, Peoples R China;

    Xian North Electroopt Sci & Technol Def Co Ltd, Xian 710043, Shaanxi, Peoples R China;

    China Natl Accreditat Serv Conform Assessment, Beijing 100062, Peoples R China;

    China Natl Accreditat Serv Conform Assessment, Beijing 100062, Peoples R China;

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