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Proceedings Paper

The analysis of key comparison reference value and its uncertainty using Markov chain Monte Carlo method
Author(s): Haiyun Zhang; Dinghua Xu; Jianli Liu; Tiepeng Zhao
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Paper Abstract

The analysis of Key Comparison data is to determine the Key Comparison Reference Value (KCRV) and its uncertainty. In the current model, the weighted mean is used as KCRV which is put forward by M, G, Cox. However, the method qualifies the measurement results as Gaussian distribution and does not apply to T distribution or other, which causes the risks of chi-square test failure. When the data analysis is invalid based on conventional statistics, the Bayesian approach may be a valid and welcome alternative. Bayesian inference is often required to solve high-dimensional integrations which Markov chain Monte Carlo (MCMC) is such a method. Here is a simple example used to illustrate the application of this method in metrology. The Metropolis-Hastings algorithm is the most flexible and efficient algorithm in MCMC method. In this paper, its basic concepts are explained and the algorithm steps are given. Besides, we obtain the KCRV and its uncertainty using the Metropolis-Hastings algorithm through MATLAB. Then, the convergence of MCMC is diagnosed. In principle, the MCMC method works for any starting value and any proposal distribution. In practice, however, both choices affect performance. We illustrate this influence with the example.

Paper Details

Date Published: 7 March 2019
PDF: 7 pages
Proc. SPIE 11053, Tenth International Symposium on Precision Engineering Measurements and Instrumentation, 1105320 (7 March 2019); doi: 10.1117/12.2511633
Show Author Affiliations
Haiyun Zhang, National Institute of Metrology (China)
Dinghua Xu, National Institute of Metrology (China)
Jianli Liu, Henan Institute of Meteorological Science (China)
Tiepeng Zhao, China Academy of Building Research (China)

Published in SPIE Proceedings Vol. 11053:
Tenth International Symposium on Precision Engineering Measurements and Instrumentation
Jiubin Tan; Jie Lin, Editor(s)

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