变系数空间自相关模型的Bayesian-INLA估计

Bayesian-INLA Estimation of Varying Coefficient Spatial Autocorrelation Model

文章提出了一类变系数空间自相关模型(VCSAM)新的Bayesian-INLA估计方法.在这个模型中,响应变量具有空间自相关性,且包含变系数的非参数部分.尽管已有的工作对该模型已经进行了大量研究,但很少有研究使用贝叶斯方法提出高效求解模型的方法.因此基于上述动机,文章提出了基于Bayesian-INLA技术的方法,以寻求在VCSAM框架内代替MCMC方法的有效解决方案.变系数部分使用B-样条基函数的线性组合进行逼近,空间自相关系数采用M-H算法进行估计,并应用Bayesian-INLA技术来估计变系数函数和相关系数的后验分布.通过模拟研究,展示了文章提出的估计方法在同时处理空间依赖效应和空间非平稳性时的优势.此外,通过对波士顿房价数据的实证分析,展示了文章提出的估计方法优越的性能.

We propose a novel Bayesian Integrated Nested Laplace Approxima-tion(INLA)estimation method for a class of models known as varying coefficient spatial autoregressive models(VCSAM).These models involve a response variable with spatial autocorrelation and a nonparametric component containing varying coefficients.Although extensive research has been conducted on VCSAM,there have been limited studies on using Bayesian methods to propose efficient solutions for model estimation.Motivated by this,the paper introduces a method based on Bayesian-INLA technology to seek an effective alternative to the MCMC method within the VCSAM framework.The varying coefficient component is approximated through a linear combination of B-spline basis functions,and the spatial autocorrelation coefficients are estimated using the M-H algorithm.The Bayesian-INLA technique is applied to estimate the posterior distributions of the varying coefficient function and correlation coefficients.Simulation studies demonstrate that the proposed estimation method exhibits advantages in simultaneously handling spatial dependency effects and spatial non-stationarity.Furthermore,empirical analysis of Boston housing price data showcases the superior performance of the proposed estimation method.