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| Estimates and Its Corresponding Uncertainty Evaluation of Parameters for Regression Model in Metrology |
| BAI Jie,HU Hong-bo |
| National Institute of Metrology, Beijing 100029, China |
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Abstract 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.
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Received: 29 December 2021
Published: 28 December 2022
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2022, Vol. 43 
