The analysis of Key Comparison Reference Value and its uncertainty using Markov Chain Monte Carlo method

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.