隐非齐次马尔可夫模型的贝叶斯推断

曲靖师范学院学报 ›› 2023, Vol. 42 ›› Issue (3): 1-8.

• 数学研究 • 下一篇

隐非齐次马尔可夫模型的贝叶斯推断

沈秀娟, 耿谜

曲靖师范学院数学与统计学院,云南曲靖 655011

收稿日期:2023-03-02 出版日期:2023-05-26 发布日期:2023-06-30
作者简介:沈秀娟,曲靖师范学院数学与统计学院讲师,主要从事数理统计研究.
基金资助:
云南省教育厅研究项目“无人机协同搜索最优路径规划问题”(2023J1028)、“基于Bayes数据删除模型对数正态分布的影响分析”(2023J1029)、“基于人脸特征的智能身份认证算法研究”(2023J1030)、“有序分类型异质纵向数据的建模与分析方法研究”(2022J0810).

Bayesian Inference of Hidden Nonhomogeneous Markov Model

SHEN Xiujuan, GENG Mi

School of Mathematics and Statistics,Qujing Normal University,Qujing Yunnan 655011,China

Received:2023-03-02 Published:2023-05-26 Online:2023-06-30

摘要/Abstract

摘要： 当前,在教育学、心理学、经济学、社会学等许多领域经常会遇到异质纵向数据.隐马尔可夫模型因其对异质纵向数据良好的建模和分析效果而受到广泛关注.在传统隐马尔可夫模型的基础上,引入非齐次马尔可夫状态转移方式,并与多元正态分布相结合,提出了隐非齐次马尔可夫多元正态分布模型.首先,介绍隐非齐次马尔可夫多元正态分布模型的数学定义;其次,详细介绍模型参数后验分布的推导过程及MCMC算法设计;最后,设定了四个模拟实验进行比较分析,结果表明贝叶斯推断方法是可靠的.研究发现隐非齐次马尔可夫模型可以覆盖齐次隐马尔可夫模型,应用更广泛.

关键词: 隐非齐次马尔可夫模型, 多元正态分布, 贝叶斯推断, MCMC算法

Abstract: At present, heterogeneous longitudinal data are often encountered in many fields such as pedagogy, psychology, economics, and sociology. Hidden Markov model has attracted extensive attention because of its good modeling and analysis effect on heterogeneous longitudinal data. This paper introduces the non-homogeneous Markov state transition mode and combines it with multivariate normal distribution to propose a hidden nonhomogeneous Markov multivariate normal distribution model. Firstly, the mathematical definition of hidden nonhomogeneous Markov multivariate normal distribution model is introduced. Then, the derivation process of the posterior distribution of model parameters and the design of MCMC algorithm are introduced in detail, and four simulation experiments are set for comparative analysis. The results show that the Bayesian inference method is reliable. In addition, the main contribution of this paper is to show that hidden nonhomogeneous Markov model can cover homogeneous hidden Markov model, which is more widely used.

Key words: hidden nonhomogeneous Markov model, multivariate normal distribution, Bayesian inference, MCMC algorithm

中图分类号:

O212.8

沈秀娟, 耿谜. 隐非齐次马尔可夫模型的贝叶斯推断[J]. 曲靖师范学院学报, 2023, 42(3): 1-8.

SHEN Xiujuan, GENG Mi. Bayesian Inference of Hidden Nonhomogeneous Markov Model[J]. Journal of Qujing Normal University, 2023, 42(3): 1-8.

参考文献

[1]BAUM L E, PETRIE T.Statistical inference for probabilistic functions of finite state Markov chains[J].Annals of Mathematical Statistics,1966,37(1):1554-1563.
[2]RABINER L R.A tutorial on hidden Markov model and selected applications in speech recognition system[J].Proc IEEE,1989,77(2):259-286.
[3]ALTMAN R M.Mixed hidden Markov models[J].Journal of the American Statiastical Association,2007(102):201-210.
[4]Robert C P,Celeux G,Diebolt J. Bayesian estimation of hidden Markov chains: a stochastic implementation[J]. Statistics Probability Letters,1993,16(1):77-83.
[5]GASSIAT E,ROUSSEAU J. About the posterior distribution in hidden Markov models with unknown number of states[J]. Bernoulli,2014,20(4):2039-2075.
[6]张波,刘鹤飞,王坤.隐马尔可夫多元正态分布参数的极大似然估计[J].应用概率统计,2020,36(2):162-172.
[7]刘鹤飞,王坤,蒋成飞.隐状态个数未知的隐马尔可夫多元正态分布的贝叶斯推断[J].统计研究,2017,34(12):119-125.
[8]王坤,刘鹤飞,蒋成飞.隐马尔可夫结构方程及其贝叶斯估计[J].数理统计与管理,2018,37(2):273-279.
[9]楼振凯,侯福均,楼旭明.部分状态可见的隐马尔可夫模型状态序列的估计方法[J].统计研究,2019,36(6):107-114.
[10]朱慧明,黄仁存,游万海.贝叶斯隐马尔科夫异质面板模型及应用研究[J]. 统计研究,2014,14(7):97-104.
[11]王坤,沈秀娟,刘鹤飞.隐非齐次马尔可夫多元线性回归模型及其贝叶斯估计[J]. 统计与决策,2022(2):16-20.
[12]SONG X Y,KANG K,OU Y M,et al. Bayesian analysis of semiparametric hidden Markov models with latent variable[J].Structural Equation Modeling: A Multidisciplinary Journal, 2018,25(1):1-20.
[13]LIU H F, SONG X Y, TANG Y L, et al. Bayesian quantile nonhomogenous hidden Markov models [J].Statistical Methods in Medical Research,2021, 30(1):112-128.
[14]LIU H F, SONG X Y,ZHNAG B X. Varying-coefficient hidden Markov models with zero-effect regions[J].Computational Statistics and Data,2022(173):1-17.
[15]LIU H F, SONG X Y. Bayesian analysis of hidden Markov structural equation models with an unknown number of hidden states [J]. Econometrics and Statistics,2021, 18(C):29-43.
[16]刘鹤飞,王坤,宗凤喜. 混合个数未知的多元正态混合模型的贝叶斯推断[J]. 统计与决策,2019(2):26-29.

隐非齐次马尔可夫模型的贝叶斯推断

Bayesian Inference of Hidden Nonhomogeneous Markov Model

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