Title: Determine the number of states in hidden Markov models via marginal likelihood
Authors: Yang Chen - University of Michigan (United States) [presenting]
Chu-Lan Kao - National Chiao-Tung University (Taiwan)
Cheng-Der Fuh - National Central University (Taiwan)
Samuel Kou - Harvard University (United States)
Abstract: Hidden Markov models (HMM) have been widely adopted by scientists from various fields to model stochastic systems: the underlying process is a discrete Markov chain and the observations are noisy realizations of the underlying process. Determining the number of hidden states for an HMM is a model selection problem, which has yet to be satisfactorily solved, especially for the popular Gaussian HMM with heterogeneous covariance. We propose a consistent method for determining the number of hidden states of HMM based on the marginal likelihood, which is obtained by integrating out both the parameters and hidden states. Moreover, we show that the model selection problem of HMM includes the order selection problem of finite mixture models as a special case. We give a rigorous proof of the consistency of the proposed marginal likelihood method, which is based on the notion of asymptotic ``path-ignorance'', and provide simulation studies to compare the proposed method with the currently mostly adopted method, the Bayesian information criterion (BIC), demonstrating the effectiveness of the proposed marginal likelihood method.