接受-拒绝算法的贝叶斯不确定度评定

针对贝叶斯不确定度评定中获取测量模型后验分布困难的问题，给出一种基于接受-拒绝采样思想实现贝叶斯测量不确定度评定的方法。面向线性/非线性测量模型，先利用贝叶斯假设或蒙特卡洛法获得被测量的先验信息，再基于接受-拒绝采样获得被测量的接受采样点形成后验分布，对被测量进行统计推断得到测量不确定度评定结果。通过规范示例和实际测量评定实例，验证了采用接受-拒绝算法的贝叶斯不确定度评定方法相较于传统GUM和MCM评定方法，能够得到可靠评定结果，且获取贝叶斯后验分布过程简便，在无/有历史信息条件下测量不确定度评定应用中具有可行性和实用性。

Bayesian uncertainty evaluation based on accept-reject algorithm

Aiming at the difficulty of obtaining the posterior distribution of measurement model in Bayesian uncertainty evaluation, a method based on accept-reject sampling is proposed to realize Bayesian measurement uncertainty evaluation. For linear/nonlinear measurement model, the prior information being measured is obtained by using Bayesian hypothesis or Monte Carlo method, the accepted sampling points being measured are obtained based on accept-reject sampling. Then the posterior distribution is formed based on these accepted sampling points, and the measurement uncertainty evaluation results are obtained by statistical inference. Through the two evaluation examples which come from the specification and practical measurement application, it is verified that the Bayesian uncertainty evaluation method using the accept-reject algorithm can obtain reliable evaluation results compared with traditional GUM and MCM methods, the process of obtaining the Bayesian posterior distribution is simple, and it is feasible and practical in the application of measurement uncertainty evaluation under the condition of without/with historical information.