基于Bayesian方法的参数估计和异常值检测

Parameter estimation and outliers detection based on Bayesian method

异常值检测是当前数据分析研究中的一个重要研究领域。模型中的异常值会直接影响建模、参数的估计、预测等问题。基于模型的异常值检测,传统的做法是先对模型参数进行估计,再进行异常值检测。而异常值的存在会影响参数估计,从而导致下一步异常值检测的不可靠;反之异常值检测也会影响参数估计。针对这些不足之处,提出了基于Bayesian方法的参数估计和异常值检测,此方法可以将参数估计和异常值检测同时实现,具体做法是在线性回归模型中引入识别变量,基于Gibbs抽样算法,给出识别变量后验概率的计算方法,通过比较这些识别变量的后验概率进行异常值定位,同时给出参数的估算方法。通过大量的模拟实验,结果表明,与传统方法相比,提出的方法对异常值更灵敏。

Outliers detection is an important research field in the current data analysis. Outliers in the data will affect the modeling,estimating parameters,forecasting and other issues directly. The conventional methods of outliers detection based on the model are to estimate the model parameters firstly,and then detect the abnormal value. The presence of outliers affects the parameter estimation,which results the in unreliability of outlier detection consequently; On the contrary,the presence of outliers will affect the parameter estimation. In this paper,we propose a new outliers detecting method based on Bayesian method,which can estimate parameters and detect outliers simultaneously. This method is introducing classification variables into linear regression model. Using Gibbs sampling a procedure for computing the posterior probabilities of classification variables and obtaining the estimation of parameters is designed. The outliers can be detected by comparing the posterior probabilities of these classification variables. A large number of simulation experiments illustrate that the proposed method is more sensitive to outliers compared with traditional methods.