基于Gibbs-DA算法的贝叶斯分位回归模型研究

Bayesian Quantile Regression Models Based on Gibbs Data-Augumention Algorithm

针对分位回归模型参数的不确定性风险问题,构建了基于Gibbs-DA抽样算法的贝叶斯线性分位回归分析模型.根据非对称Laplace分布的正态-指数分布的混合表示性质,利用数据扩展方法构建了潜变量,给出分位回归模型的似然函数,推断了多元正态先验分布条件下分位回归模型参数的后验分布,证明了潜变量的完全条件分布为广义逆高斯分布;结合Gibbs抽样和数据扩展方法,设计Gibbs-DA的仿真分析方案,并将其应用于我国能源消耗问题分析.研究结果表明:贝叶斯方法可以有效地应用于分位回归的建模以及我国能源消费弹性的分位问题研究.

We constructed a Bayesian quantile linear regression model based on Gibbs-DA sampling al-gorithm for the uncertainty risks of quintile regression model parameters.According to the normal-expo-nential representation property of asymmetric Laplace distribution,we established a working likelihood function for the quantile regression model with latent variables,gave its parameters＆#39;posterior distribution with a multivariate prior distribution,whose full condition distribution is generalized Guassian.We also used Gibbs sampling technique and data argumentation method to design a Gibbs-DA simulation proce-dure.Finally,we made an empirical study to analyze energy consumption in China.The results have shown that Bayesian procedure can be efficiently used to build quantile regression models and applied to the elasticity of energy consumption.