Bavesian Analysis And Application Of Poisson Distribution Based On Hidden Markov Model

Hidden Markov model is a statistical model that describes a random process.The model contains two random variable sequences,one is an invisible Markov state chain,and the other is an observable generated by the invisible state chain according to the probability distribution.Sequence.With the rapid development of hidden Markov model theory,many domestic and foreign scholars have successfully applied the theoretical model in almost all fields such as speech recognition,text mining,face recognition,bioinformatics,economics and finance,etc.One of the most widely used statistical models.Therefore,the research and application of hidden Markov model based on Markov theory is of great significance.In this paper,Bayesian analysis is mainly based on the Poisson distribution of the hidden Markov model with unknown number of hidden states.According to the existing research experience,the hidden state transition probability matrix of the model and the conjugate prior distribution of Poisson distribution parameters are combined,and the Bayesian Derivation of the posterior distribution of each parameter based on the Si principle;in the selection of the number of hidden states of the model,this paper uses the reversible jump MCMC algorithm,combined with the latest improved hidden state transition probability matrix and the decomposition or combination method of Poisson distribution parameters,through the model The size of the posterior probability selects the optimal hidden Markov model;thus,under the condition that the number of hidden states is known,the various parameters of the hidden Markov model are estimated using the ordinary MCMC algorithm.Random simulation results show that under the condition of randomly giving the number of hidden states k=3,Poisson distribution parameters ?=(10,15,20)and state transition probability matrix A,the reversible jump MCMC algorithm can effectively estimate the number of hidden states of the model and then estimate the model parameters (?)=(10.3537,14.6321,20.4824)and the state transition probability matrix A;through the empirical analysis of the hidden Markov model with unknown Poisson distribution of the number of seismic statistics,the maximum posterior probability of the seismic data is estimated to be 3,Poisson distribution parameter (?)=(13.127,19.836,29.754)and state transition probability matrix,thus verifying the feasibility of the model method.