An asymptotic analysis of Bayesian state estimation in hidden Markov models

Hidden Markov models are widely used for modeling underlying dynamics of sequence data. The accurate hidden state estimation is one of the central issues on practical application since the dynamics is described as a sequence of hidden states. However, while there are many studies on parameter estimation, mathematical properties of the hidden state estimation have not been clarified yet. The present paper analyzes the accuracy of a Bayesian hidden state estimation and shows that the dominant order of an error function depends on redundancy of states.