隐马尔可夫多元正态分布参数的极大似然估计  

Maximum Likelihood Estimation of Hidden Markov Multivariate Normal Distribution Parameters

作　　者：张波 刘鹤飞 王坤 ZHANG Bo;LIU Hefei;WANG Kun(Graduate School,Yunnan University,Kunming,650504,China;School of Mathematics and Statistics,Qujing Normal University,Qujing,655011,China)

机构地区：[1]云南大学研究生工作部,昆明650504 [2]曲靖师范学院数学与统计学院,曲靖655011

出　　处：《应用概率统计》2020年第2期162-172,共11页Chinese Journal of Applied Probability and Statistics

基　　金：云南省科技厅科研项目(批准号:2018FH001-109);云南省教育厅科研项目(批准号:2019J0602,2020J0629);曲靖师范学院校级科研项目(批准号:2018QN004)资助.

摘　　要：隐马尔可夫模型广泛应用于时间、空间、状态转移数据的统计建模.文章给出了隐马尔可夫多元正态分布的定义,介绍了用聚类分析确定观测变量隐状态的原理,推导了模型中未知参数的极大似然估计量,模拟生成观测数据集检验了该方法的估计效果和稳定性.特色之处是首次提出用聚类分析、极大似然估计等简单的经典统计推断方法解决隐马尔可夫模型的参数估计问题.Hidden Markov model is widely used in statistical modeling of time,space and state transition data.The definition of hidden Markov multivariate normal distribution is given.The principle of using cluster analysis to determine the hidden state of observed variables is introduced.The maximum likelihood estimator of the unknown parameters in the model is derived.The simulated observation data set is used to test the estimation effect and stability of the method.The characteristic is simple classical statistical inference such as cluster analysis and maximum likelihood estimation.The method solves the parameter estimation problem of complex statistical models.

关 键 词：隐马尔可夫模型 多元正态分布 聚类分析 极大似然估计 

分 类 号：O212.8[理学—概率论与数理统计]