基于MCMC方法的贝叶斯统计模型应用研究  

Research on the Application of Bayesian Statistical Model Based on MCMC Method

作　　者：张宗宇 徐军 姜奎 陈士超 ZHANG Zongyu;XU Jun;JIANG Kui;CHEN Shichao(School of Computer and Data Engineering,Bengbu College of Business and Industry,Bengbu 233000,China)

机构地区：[1]蚌埠工商学院计算机与数据工程学院,安徽蚌埠233000

出　　处：《景德镇学院学报》2024年第3期70-74,共5页Journal of JingDeZhen University

基　　金：安徽省高等学校自然科学重点项目(KJ2021A1236、KJ2021A1237)。

摘　　要：为验证贝叶斯统计后验分布计算的收敛性,文章研究并构建了线性回归和时间序列两类经典的贝叶斯统计模型。基于马尔可夫链蒙特卡罗方法,运用birdextinct数据集验证了贝叶斯线性回归模型,并分析鸟类的平均灭绝时间与平均筑巢数、种群规模、栖息状态三个量之间的关系。此外,根据1982-2021年居民消费指数(CPI)的序列,结合差分处理数据,建立了AR(p)时间序列预测模型。结果表明,贝叶斯线性回归模型和贝叶斯时间序列预测模型的马尔可夫链均收敛,且贝叶斯时间序列预测模型的预测误差仅为0.78%。MCMC方法能有效应用于贝叶斯统计模型分析。To verify the convergence of Bayesian statistical posterior distribution calculation,two classic Bayesian statistical models,namely linear regression and time series,are investigated and constructed in this paper.Based on the Markov Chain Monte Carlo(MCMC)method,the Bayesian linear regression model is validated using the Birdextinct dataset to analyze the relationship between the average extinction time of birds and three variables:average number of nests,population size,and habitat status.Furthermore,based on the series of Consumer Price Index(CPI)from 1982 to 2021,an AR(p)time series forecasting model is established,incorporating differential processing data.The results indicate that both the Bayesian linear regression model and the Bayesian time series forecasting model have converged Markov chains,with the error of only 0.78% for the Bayesian time series forecasting model.The MCMC method can be effectively applied to analysis of Bayesian statistical models.

关 键 词：MCMC方法 贝叶斯统计 收敛性诊断 时间序列预测 

分 类 号：O212.8[理学—概率论与数理统计]