The Estimation Of Varying-coefficient Model Using Bayesian-INLA Method

When using the Bayesian estimation method,the key part is to calculate the high-order integral problem.The Laplace method is an older method to calculate the integral,it was replaced due to the appear of Markov Chain Monte Carlo(MCMC)method.With the development of modern computing algorithms and computer technology,contemporary scholar Rue et al.combined with the laplace method and numerical integration technology to propose a method named integrated nested laplace approximations(INLA)to replace the MCMC method.The INLA method can accurately compute the posterior distribution of unknown parameter,avoid the computationally inefficient results of sampling in the MCMC method and greatly improve computational efficiency.Hence,the paper uses the INLA method to compute the Bayesian estimation,named Bayesian-INLA,which have both theoretical value and practical significance.In this paper,Bayesian-INLA estimation is performed on the one-dimensional and two-dimensional varying-coefficient models respectively based on the P-spline idea and the local linear idea of non-parametric estimation.First,for the one-dimensional varying-coefficient model,the paper is based on the Bayesian P-spline method developed coefficient function of Bayesian-INLA estimation.The Bayesian P-spline method first approximates the unknown coefficient function using the B-spline basis function.Then,the unknown coefficients of the Bspline basis function are punished by using the intrinsic Gaussian Markov Random Field(IGMRF).At last,calculation based on INLA algorithm.The Bayesian-INLA estimation is selected by the relevant evaluation indicators in the simulation experiment,and the accurate calculation result of the coefficient function can be obtained conveniently and efficiently.Secondly,for the two-dimensional spatially varying-coefficient model.In this paper,the Bayesian-INLA estimation of the coefficient function is proposed in combination with the local linear GWR idea.The paper first uses the local linear GWR idea to perform Taylor expansion on the coefficient function for each geographic location,and uses the kernel function to construct the Euclidean distance weight.The linear model is based on the MCMC algorithm and the INLA algorithm respectively to estimate the coefficients,and the coefficient estimates for each geographic location are obtained.The simulation results show that the Bayesian-INLA method can avoid the computational time-consuming of the MCMC algorithm's lengthy sampling technique.Finally,the computational efficiency of parameter estimation is greatly improved.Finally,based on the one-dimensional time-varying coefficient model,the paper explores the impact of air quality indicators on the number of patients in daily respiratory tract clinics from January 1994 to December 1995 in Hong Kong.Based on the two-dimensional spatial variable coefficient model,the spatial variation relationship between AIDS epidemic and related macro factors in 31 provinces,districts and municipalities in China was analyzed.The results show that the Bayesian-INLA estimation method has the accuracy and efficiency of calculation,the convenience and operability of use.