基于吉布斯抽样的相关观测异常值检测的贝叶斯方法

摘要

相关观测的异常值检测是测量数据处理的难题之一.在系统总结和分析前人研究成果的基础上,运用贝叶斯统计推断理论,提出了相关观测异常值检测的贝叶斯方法.首先,基于识别变量的后验概率,提出了相关观测异常值定位的贝叶斯方法；然后设计和构建了计算后验概率的吉布斯抽样方法,基于最大后验估计原理,推导和建立了计算异常值参数的贝叶斯公式；最后对某GPS网相连进行了计算和分析.结果表明,在相关观测条件下,使用新方法能够对多个异常值同时进行检测,有效地消除异常值的不良影响.%Outlier of correlated observation are one of the difficult and important problems in data processing. According to systemically reviewing research history of the puzzle, Bayesian detection method was put forward and applied in the GPS network utilizing the modern Bayesian theories and methods. First of all, on the basis of posterior probabilities of classification variables, the Bayesian methods for positioning outlier of correlated observations was proposed, and based on Gibbs sampling, the algorithm for calculating the posterior probability of classification variables was designed. Secondly, modern Bayesian statistical theory was appliedy to deduce Bayesian estimations for outlier. Then, those new methods in a GPS network adjustment was applied. These numerical examples demonstrated that the new methods were effective. In condition of correlated observations, the methods can detect multiple outliers of correlated observation and eliminate the influence of outlier effectively at the same time.