The Estimation Of Bayesian Space-Varying Coefficient Econometrics Model Using INLA Method

The most critical and most difficult problem of Bayesian statistical application is the inference and calculation of the marginal posterior distribution of unknown parameters.Rue et al.in 2009 based on Bayesian theory,combining Laplace ap-proximation method and numerical integration technology,proposed an integrated nested Laplace approximation method(INLA)that can replace the Markov chain Monte Carlo(MCMC)method.The INLA algorithm uses the properties of hidden Gaussian Markov random fields,and estimates the hidden Gaussian model by re-peatedly using the Laplacian approximation method,which not only ensures the calculation accuracy of the algorithm,but also avoids MCMC multiple iterative sampling,making it have a faster calculation speed than the traditional MCMC algorithm.At present,the INLA method is very popular in applied science and applied statistics,and has been become a general tool for fast and reliable Bayesian inference.The Bayesian Space Variable Coefficient Model(BSVC)is a generalization of the variable coefficient model,which allows the parameters of covariates to change smoothly with regions in space.In the BSVC model,the parameter setting of the covariate adopts the form of a prior distribution,and at the same time acts as a recognition constraint of the model,avoiding the problem of insufficient recognition of a large number of models.The hierarchical Bayesian spatial variable coefficient model(HBSVC)uses hierarchical modeling to analyze the effects of covariates at different levels.In this paper,conditional autoregression is used as the prior dis-tribution of covariate parameters,and the INLA algorithm is used to estimate the Bayesian space variable coefficient model.It can be seen from the results of sim-ulation experiments and related evaluation indicators that not only can the INLA algorithm be used to estimate the HBSVC model,but also it guarantees the esti-mation results with higher calculation accuracy.The spatial econometric model introduces the spatial weight matrix and con-structs the spatial lag factor to introduce the spatial autocorrelation of the research object into the model,which can process some data related to geographic location.However,most spatial econometric models only analyze spatial autocorrelation and ignore spatial heterogeneity.Based on the accuracy and efficiency of the hierarchi-cal Bayesian spatial variable coefficient model under the INLA algorithm,this paper combines the hierarchical Bayesian spatial variable coefficient model with the spatial lag model to establish a hierarchical Bayesian spatial variable coefficient lag model,at the same time consider the spatial autocorrelation and heterogeneity,and put forward the estimation methods of using the INLA model for statistical inference.Then,according to the idea of INL ABM A function under the INLA framework,com-bined with grid division,the value of the spatial lag factor p is estimated.Through simulation experiments and analysis of the macro-influencing factors of the spatial distribution of the national CO2 emissions,it can be confirmed that apply the INLA method could be used to make the corresponding statistical inference and analysis of the model.Finally,for the geographical data with hierarchical structure,based on the feasibility of the hierarchical Bayesian space variable coefficient lag model under the INLA algorithm,in this paper,the hierarchical Bayesian spatial variable coefficient model and the spatial double-weighted lag model are combined.According to the INLA estimation idea of the hierarchical Bayesian spatial variable coefficient lag model,the INLA algorithm is used to estimate the hierarchical Bayesian space variable coefficient double-weight lag model.The feasibility of the model under the INLA method is proved by the simulation experiment and the empirical analysis on the factors affecting the price of all rental residential land in Beijing.