Akaike and Bayesian Information Criteria for Hidden Markov Models

We propose the Bayesian information criterion (BIC) and the Akaike information criterion (AIC) for model selection in hidden Markov models (HMM) when the number of states is unknown. The exact solutions exploit the properties of HMM that allow tractable forms of both criteria to be obtained while transgressing the common assumption in AIC and BIC model selection approaches on the independence of data. The proposed algorithm is presented and evaluated in application to blind channel estimation and symbol detection when the channel length is assumed unknown.