基于观测误差后验分布的粗差探测的Bayes方法

Bayesian Approach to Detection of Gross Errors Based on Posterior Distribution of Observation Error

从观测误差出发,运用3σ-原理提出了一种粗差探测的Bayes方法——基于观测误差的后验概率法。针对非等权独立观测情形,在一定先验分布下推导了观测误差的后验分布;建立了与观测误差有关的后验概率的计算公式;给出了粗差估算的Bayes方法;提出了基于观测误差的后验概率进行粗差探测的实施过程。最后结合算例说明了其效果,并且与其他粗差探测方法进行了比较。大量试验表明,给出的探测粗差的Bayes方法是切实可行的。它不仅有效地发现了粗差,而且结果比较理想。

By 3σ-principle about normal distribution, a new Bayesian method for gross error detection is proposed based on posterior probability of observation error in this paper. Under the condition of unequal weight and independent observations, the posterior distribution of observation error is concluded based on certain prior distribution. Then, the computational formula of the posterior probability of observation error is established, the Bayesian estimate of gross error is given and the process of gross error detection based on the posterior probability of observation error is introduced. Finally, the effect is illustrated by a numerical example and the comparison with the other approaches to gross error detection is also made. Numerical experiments show that the given method is feasible. It not only detects the gross errors efficiently, but has a practical good result.