The analysis of key comparison reference value and its uncertainty using Markov chain Monte Carlo method

Haiyun Zhang; Dinghua Xu; Jianli Liu; Tiepeng Zhao

doi:10.1117/12.2511633

7 March 2019 The analysis of key comparison reference value and its uncertainty using Markov chain Monte Carlo method

Haiyun Zhang, Dinghua Xu, Jianli Liu, Tiepeng Zhao

Proceedings Volume 11053, Tenth International Symposium on Precision Engineering Measurements and Instrumentation; 1105320 (2019) https://doi.org/10.1117/12.2511633
Event: 10th International Symposium on Precision Engineering Measurements and Instrumentation (ISPEMI 2018), 2018, Kunming, China

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.

Citation Download Citation

Haiyun Zhang, Dinghua Xu, Jianli Liu, and Tiepeng Zhao "The analysis of key comparison reference value and its uncertainty using Markov chain Monte Carlo method", Proc. SPIE 11053, Tenth International Symposium on Precision Engineering Measurements and Instrumentation, 1105320 (7 March 2019); https://doi.org/10.1117/12.2511633

ACCESS THE FULL ARTICLE

INSTITUTIONAL
Select your institution to access the SPIE Digital Library.

SELECT YOUR INSTITUTION

PERSONAL
Sign in with your SPIE account to access your personal subscriptions or to use specific features such as save to my library, sign up for alerts, save searches, etc.

PERSONAL SIGN IN

No SPIE Account? Create one

PURCHASE THIS CONTENT

SUBSCRIBE TO DIGITAL LIBRARY

50 downloads per 1-year subscription

Members: $195

Non-members: $335 ADD TO CART

25 downloads per 1 - year subscription

Members: $145

Non-members: $250 ADD TO CART

PURCHASE SINGLE ARTICLE

Includes PDF, HTML & Video, when available