Analysis and Comparison of Bayesian Methods for Measurement Uncertainty Evaluation

Abstract

Based on the Bayesian principle, the modern uncertainty evaluation methods can fully integrate prior and current sample information, determine the prior distribution according to historical information, and deduce the posterior distribution by integrating prior distribution and the current sample data with the Bayesian model. As such, it is possible to evaluate uncertainty, updating in real time the uncertainty of the measuring instrument according to regular measurement, and timely reflect the latest information on the accuracy of the measurement system. Based on the Bayesian information fusion and statistical inference principle, the model of uncertainty evaluation is established. The maximum entropy principle and the hill-climbing search optimization algorithm are introduced to determine the prior distribution probability density function and the sample information likelihood function. The probability density function of posterior distribution is obtained by the Bayesian formula to achieve the optimization estimation of uncertainty. Three methods of measurement uncertainty evaluation based on Bayesian analysis are introduced: the noninformative prior, the conjugate prior, and the maximum entropy prior distribution. The advantages and limitations of each method are discussed.