计量中回归模型参数值及其不确定度评估

针对计量领域中广泛应用的数据回归处理方法，阐述了在基于正态分布噪声条件下，最小二乘法与贝叶斯推断法用于回归模型参数估计以及相应不确定度评估的过程。GUM系列不确定度评估准则中没有明确指出如何对回归参数进行不确定度评估，同时有些回归模型也无法唯一地转化为相应的测量方程。通过计量校准的实例说明了如何处理相应参数的确定等问题，以此说明2种方法的相同与不同之处。最小二乘方法计算简单直接且便于使用；而基于贝叶斯推断的方法则能充分利用计量校准中的经验和历史数据等信息，但由于其参数后验分布计算通常较为复杂，需采用马尔科夫链-蒙特卡罗(MCMC)法通过数值计算得到关注参数的结果。

Estimates and Its Corresponding Uncertainty Evaluation of Parameters for Regression Model in Metrology

Aiming at the data regression processing method widely used in the field of measurement, the process of least square method and Bayesian inference method used for regression model parameter estimation and corresponding uncertainty evaluation under the condition of normal distribution noise is described. The GUM series uncertainty evaluation criteria do not clearly indicate how to evaluate the uncertainty of regression parameters, and some regression models cannot be uniquely transformed into corresponding measurement equations. Through an example of metrological calibration, how to deal with the determination of the corresponding parameters is illustrated, so as to illustrate the similarities and differences between the two methods. The least square method is simple, direct and easy to use; Bayesian inference based methods can make full use of experience and historical data in metrological calibration. However, since the posterior distribution calculation of parameters is usually complex, Markov Chain Monte Carlo (MCMC) method is required to obtain the results of the concerned parameters through numerical calculation.