重庆工商大学学报（自然科学版）2024，Vol.41Issue(3)：104-112,9.DOI:10.16055/j.issn.1672-058X.2024.0003.014
基于贝叶斯估计的空间函数型自回归模型及其应用
Spatial Function Autoregressive Model Based on Bayesian Estimation and Its Application
摘要
Abstract
Objective To study the spatial correlation of response variables in functional data,according to existing research methods,functional data with spatial dependence were studied and the Bayesian estimation method was proposed.Methods Based on the typical spatial autoregressive model and according to the spatial dependence of the functional response variables,the spatial function autoregressive model was generated by assuming that there was an endogenous relationship between the response variables and the explanatory variables.The functional components in the model were changed into discrete types by the principal component analysis,and then the complete conditional posterior distribution of the parameters in the calculation model was calculated under a given prior condition.The parameters in the model were estimated using the Bayesian MCMC method.Results The Metropolis-Hastings algorithm,which combined Gibbs sampling and random walk,was used to estimate the parameters in the model.Through simulation research,it was found that the functional coefficients of the model and the estimation deviations and mean square errors of other parameters under different parameter models were small,which verified the effectiveness of the Bayesian estimation method.At the same time,the spatial function model was applied to the empirical analysis of the average price of new houses in the main urban area of Chongqing.The results show that the Bayesian estimation method of the proposed model is effective.Conclusion The estimation effect of functional explanatory variables using Bayesian estimation method to estimate the parameters in the model is always better under different circumstances,and its estimation effect is also more and more effective as the sample size increases.Thus,it can be considered that using spatial function model to estimate the spatial function autoregressive model is effective and feasible.Meanwhile,the empirical analysis shows that the average house price of new houses in the main urban area of Chongqing has spatial autocorrelation,and it will be affected by the listing volume of second-hand houses.关键词
函数型数据分析/贝叶斯估计/Gibbs采样/随机游动的Metropolis-Hastings算法Key words
functional data analysis/Bayesian estimation/Gibbs sampling/random walk based Metropolis-Hastings algorithm分类
数理科学引用本文复制引用
杨炜明,李明杰..基于贝叶斯估计的空间函数型自回归模型及其应用[J].重庆工商大学学报（自然科学版）,2024,41(3):104-112,9.基金项目
重庆市自然科学基金项目资助(CSTC2020JCYJ-MSXMX0394). （CSTC2020JCYJ-MSXMX0394）
