分位数贝叶斯组变量选择及其在变点检测中应用

Quantile Bayesian Variable Selection and Its Application in Change Point Detection

本文研究分位数回归的组变量选择问题。基于分位数回归和贝叶斯统计推断方法,通过引入系数的组“spike and slab”先验分布,提出了分位数回归的贝叶斯组变量选择方法,并给出易于实施的Gibbs后验抽样算法。进一步,本文还将所建立的贝叶斯组变量选择方法应用到变点检测中,变点的数量和位置的探测准确率较高。数值模拟和两个实例分析验证了所提方法的有效性。

In this paper,we study the group variable selection problem of quantile regression.Based on quantile regression and Bayesian statistical inference methods,the Bayesian group variable selection method for quantile regression is established by introducing the group "spike and slab" prior distribution of regression coefficients,and a Gibbs posterior sampling algorithm is obtained which is easy to implement.Furthermore,this paper also applies the established Bayesian group variable selection method to change point detection.We obtain a higher detection accuracy of the number and location of change points.Numerical simulation and two examples are used to illustrate the effectiveness of the proposed method.