中位数回归的贝叶斯变量选择方法

Bayesian Variable Selection for Median Regression

当数据呈现厚尾特征或含有异常值时,基于惩罚最小二乘或似然函数的传统变量选择方法往往表现不佳.本文基于中位数回归和贝叶斯推断方法,研究线性模型的贝叶斯变量选择问题.通过选取回归系数的Spike and Slab先验,利用贝叶斯模型选择理论提出了中位数回归的贝叶斯估计方法,并提出了有效的后验Gibbs抽样程序.大量数值模拟和波士顿房价数据分析充分说明了所提方法的有效性.

When the data has heavy tail feature or contains outliers,conventional variable selection methods based on penalized least squares or likelihood functions perform poorly.Based on Bayesian inference method,we study the Bayesian variable selection problem for median linear models.The Bayesian estimation method is proposed by using Bayesian model selection theory and Bayesian estimation method through selecting the Spike and Slab prior for regression coefficients,and the effective posterior Gibbs sampling procedure is also given.Extensive numerical simulations and Boston house price data analysis are used to illustrate the effectiveness of the proposed method.