复杂异质纵向数据的贝叶斯统计建模与分析——基于隐马尔可夫变系数回归模型

doi:10.16088/j.issn.1001-6600.2025072303

广西师范大学学报（自然科学版） ›› 2026, Vol. 44 ›› Issue (4): 147-158.doi: 10.16088/j.issn.1001-6600.2025072303

复杂异质纵向数据的贝叶斯统计建模与分析——基于隐马尔可夫变系数回归模型

刘鹤飞¹, 彭守静¹, 沈秀娟^2*

1.云南财经大学数学与统计学院, 云南昆明 650221;
2.曲靖师范学院数学与经济学学院, 云南曲靖 655011

收稿日期:2025-07-23 修回日期:2025-09-17 出版日期:2026-07-05 发布日期:2026-07-01
通讯作者: 沈秀娟(1985—),女,山东潍坊人,曲靖师范学院讲师。E-mail: xjsqushi2012@163.com
基金资助:
国家自然科学基金(12361061);曲靖市科技局·曲靖师范学院联合项目(KJLH2023YB09;KJLH2023YB10)

Bayesian statistical modeling and analysis of complex heterogeneous longitudinal data: based on regression model of hidden Markov variable coefficients

Liu Hefei¹, Peng Shoujing¹, Shen Xiujuan^2*

1. School of Mathematics and Statistics, Yunnan University of Finance and Economics, Kunming Yunnan 650221, China;
2. School of Mathematics and Economics, Qujing Normal University, Qujing Yunnan 655011, China

Received:2025-07-23 Revised:2025-09-17 Online:2026-07-05 Published:2026-07-01

摘要/Abstract

摘要： 在实际应用中,隐马尔可夫变系数回归模型面临2个主要挑战:强影响点和缺失数据。强影响点可能会严重扭曲模型参数估计,导致预测性能下降;而缺失数据则可能导致信息丢失,影响模型的准确性和可靠性。因此,有效处理这2类问题对提高模型性能至关重要。针对这些问题,本文使用基于贝叶斯方法的离群值检测方案,并引入示性变量来处理缺失数据机制,利用MH算法与Gibbs抽样获得缺失数据的贝叶斯估计。研究结果表明,隐马尔可夫变系数回归模型结合贝叶斯推断能够适应具有复杂动态特性的数据集,并在面对强影响点和缺失数据时展现出良好性能。模拟试验验证了本文提出方法的有效性,显示模型能够在含有复杂的数据结构中保持较高的准确性。

关键词: 复杂异质纵向数据, 隐马尔可夫, 变系数回归模型, 贝叶斯推断, 强影响点, 缺失数据

Abstract: In practice, HMVCM faces two main challenges: the presence of strong influence points and the absence of data. Strong influence points may seriously distort the model parameter estimation and lead to poor prediction performance. Missing data may lead to information loss, affecting the accuracy and reliability of the model. Therefore, effectively addressing these two types of problems is critical to improve model performance. In order to solve these problems, this paper uses an outlier detection scheme based on Bayesian method, introduces indicative variables to deal with the missing data mechanism, and uses MH algorithm and Gibbs sampling to obtain Bayesian estimation of missing data. The results show that HMVCM combined with Bayesian inference can adapt to datasets with complex dynamic characteristics, and shows good performance in the face of strong influence points and missing data. The effectiveness of the proposed method is verified in simulation experiments, which shows that the model can maintain high accuracy and robustness in the dataset with complex structures.

Key words: complex heterogeneous longitudinal data, hidden Markov, variable coefficient regression model, Bayesian inference, strong points of influence, missing data

中图分类号: O212.8

刘鹤飞, 彭守静, 沈秀娟. 复杂异质纵向数据的贝叶斯统计建模与分析——基于隐马尔可夫变系数回归模型[J]. 广西师范大学学报（自然科学版）, 2026, 44(4): 147-158.

Liu Hefei, Peng Shoujing, Shen Xiujuan. Bayesian statistical modeling and analysis of complex heterogeneous longitudinal data: based on regression model of hidden Markov variable coefficients[J]. Journal of Guangxi Normal University(Natural Science Edition), 2026, 44(4): 147-158.

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复杂异质纵向数据的贝叶斯统计建模与分析——基于隐马尔可夫变系数回归模型

Bayesian statistical modeling and analysis of complex heterogeneous longitudinal data: based on regression model of hidden Markov variable coefficients

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