分层等级反应模型的贝叶斯推断及其应用  

Bayesian inference and application of hierarchical graded response model

作　　者：付志慧 刘红梅 FU Zhi-hui;LIU Hong-mei(School of Mathematics and Statistics,Minnan Normal University,Zhangzhou,Fujian 363000,China;Fujian Key Laboratory of Granular Computing and Applications,Zhangzhou,363000,China)

机构地区：[1]闽南师范大学数学与统计学院,福建漳州363000 [2]福建省粒计算及其应用重点实验室,福建漳州363000

出　　处：《吉林师范大学学报（自然科学版）》2024年第4期58-64,共7页Journal of Jilin Normal University:Natural Science Edition

基　　金：国家社会科学基金项目(21BTJ036)。

摘　　要：探讨了MCMC算法在分层等级反应模型参数估计中的应用,并针对该模型提出了一种基于Pólya-Gamma数据扩充方法的Gibbs抽样算法.通过模拟实验比较了该方法与哈密顿蒙特卡罗算法在参数估计及计算效率下的性能.实证分析表明了该方法的有效性和实用性.The application of the Markov Chain Monte Carlo(MCMC)algorithm in estimating parameters for a hierarchical graded response model was explored,and a Gibbs sampling algorithm based on the Pólya-Gamma data augmentation method was proposed for this model.Simulation studies were conducted to compare the performances(including parameter estimation accuracy and computational efficiency)of the proposed method with Hamiltonian Monte Carlo algorithm.Empirical analysis demonstrated the effectiveness and practicality of the proposed method.

关 键 词：分层等级反应模型 Pólya-Gamma分布 Gibbs抽样算法 

分 类 号：O212.1[理学—概率论与数理统计]