关键词: 隐马尔可夫模型, 可逆跳跃MCMC, 贝叶斯推断

Abstract: In this paper, we study the hidden Markov model with unknown number of hidden state and multidimensional observe data. Firstly, the reversible jump MCMC algorithm is used to select the number of hidden state. After determining the number of hidden state, the traditional MCMC algorithm is used to estimate the parameters of the model. In using reversible jump MCMC algorithm, the parameters of the model are required to split and merge, this paper has two theoretical contributions: one is that improve the hidden state transition probability matrix splitting and merging method to improve the accept probability of the split process. The other is a new method for splitting and merging the covariance matrix is proposed, based on the basic requirements of the reversible jump MCMC algorithm, and also satisfied with the special requirement that the covariance matrix must be positive.

Key words: Hidden Markov Model, Reversible Jumping MCMC, Bayesian Inference