Maximum Likelihood Estimation Of Non-Homogeneous Hidden Markov Model Parameters And Its Application

Hidden Markov model is a statistical probability model based on a stochastic process.The model contains two parts:a state sequence and an observation sequence.Among them,the Markov sequence representing the state is not observable,and is usually called a hidden state.Hidden Markov models have been widely applied in the fields of natural language processing,bioinformatics,financial stock forecasting,and environmental quality detection,and have attracted widespread attention from many researchers.This paper improves the traditional hidden Markov state transition method,considers the influence of covariates on state transition,and constructs a non-homogeneous hidden Markov model.In the parameter estimation of the model,the hidden state of the observed variables is first determined by K-means clustering analysis and the label exchange problem is solved by comparing the single component means.Second,use maximum likelihood estimation to estimate unknown parameters in the model.Then using non-homogeneous hidden Markov multiple normal distribution and non-homogeneous hidden Markov multiple linear regression as examples,the reliability of the parameter estimation results is verified by numerical simulation.Finally,a non-homogeneous hidden Markov model was used to model and analyze the air quality data of Beijing from November 1,2018 to October 31,2019,the transition probability of different air quality states is obtained under heating and non-heating periods.The air quality status and specific AQI index values of Beijing in the future are predicted through different state transition probabilities.The results show that compared with the homogeneous hidden Markov model,the prediction accuracy of the non-homogeneous hidden Markov model is higher.The innovation of this article:The traditional hidden Markov state transfer method is improved by adding covariates in the Markov chain of the transfer model,solved the problem of modeling the transition relationship between different hidden states of the model when the observed variables of the model have fixed covariates;The K-means clustering analysis and maximum likelihood estimation are combined to estimate the unknown parameters of the model,and the corresponding label exchange problem is solved,the traditional hidden Markov model parameter estimation method is simplified,the reliability of the parameter estimation method is verified;Finally,using the non-homogeneous hidden Markov model to model the actual air quality data provides a new idea for predicting the air quality state.