Bayesian Quantile Regression Model And Its Application

With the development of the social economy,researchers found that the least squares regression estimation can'not fully explain the relationship between independent variables and dependent variables.Therefore,quantile regression estimation was proposed to supplement the deficiency of least squares estimation.Among the methods of quantile regression estimation,the Bayesian method has more advantages than the traditional frequentist method.Therefore,scholars have paid extensive attention to Bayesian quantile regression estimation,and this method has also been widely used in the socio-economic field.This paper specifies the likelihood function for the Asymmetric Laplace Distribution(ALD)using the binomial distribution when the dependent variable is continuous and discrete.The Gibbs sampling method is used for sampling,and the parameters of the model are estimated by the Bayesian method.Firstly,when the dependent variable is continuous,the likelihood function of ALD is specified by binomial distribution on the basis of the Bayesian quantile regression linear model.Based on the difference in prior distribution,parameter estimation is carried out under parameterized and unparameterized scale parameters respectively.The experimental results show that increasing the sample size or enhancing the prior information can improve the estimation accuracy of parameters.The parameter estimation accuracy obtained by parameterizing the scale parameter is higher than that obtained without parameterization.Therefore,when the dependent variable is continuous,the estimation accuracy of the parameters can be improved by adopting the likelihood function of ALD specified by the binomial distribution,enhancing the prior information,increasing the sample size and parameterizing the scale parameter.Secondly,when the dependent variable is discrete,based on the binary choice model,the parameters of the multivariate binary choice regression model are estimated by using the Bayesian method of specifying the ALD likelihood function from the binomial distribution.At the same time,the parameter estimation accuracy after the scale parameter is parameterized is compared with the parameter estimation accuracy when the scale parameter is not parameterized.The experimental results show that the estimation accuracy of the parameters obtained after parameterizing the scale parameters is higher than that obtained without parameterization.Increasing the sample size improves the estimation accuracy of the parameters.After parameterizing the scale parameter,the estimation accuracy of the parameter is not affected by the prior distribution.Finally,the Bayesian quantile regression method based on ALD is used to analyze the comprehensive economic strength of 31 regions across the country in 2020.The experimental results show that the model can describe the impact of indicators on the comprehensive economic strength of each region under different quantiles,and the local area can adjust the economic development strategy according to the level of development to improve the comprehensive economic strength,narrow the development gap with other regions,and coordinate with each other develop.