基于贝叶斯层次模型对联合分析方法的改进

Bayesian Hierarchical Model for Evaluation Index of Teaching Quality in Higher Education

针对在传统的统计方法中,联合分析方法不能同时对大量参数进行变量估计问题,提出了贝叶斯β回归模型。该模型使用Dirichlet分布作为模型参数的先验分布,并设计相关MCMC(Markov Chain Monte Carlo)算法对模型进行拟合。通过分析将该模型应用于离散指标变量评估中,结果表明该模型对数据拟合效果好且算法收敛速度快,说明贝叶斯层次模型弥补了传统联合分析方法的缺陷,并对联合分析方法进行了优化改进。

In traditional statistical methods,the conjoint analysis method is can not estimate variables for a large number of parameters at the same time,therefore,a Bayesianβregression model is proposed.In the newly established model,the Dirichlet distribution is used as the prior distribution of the model parameters,and the relevant MCMC(Markov Chain Monte Carlo)algorithm is designed to fit the model.By analyzing the results of applying the model to the evaluation of discrete index variables,it is shown that the model has a good fitting effect on the data and the algorithm has a fast convergence speed.It shows that the Bayesian hierarchical model makes up for the defects of the traditional conjoint analysis method,and optimizes and improves the conjoint analysis method.