# Full posterior vs Bayesian Information Criterion for selecting number of HMM states

So I'm looking into methods in selecting the best number of hidden states for a hidden markov model, given I don't know what how many states "generated" my data. One method I've seen a lot is to learn lots of models with different numbers of states and then perform BIC on them. Another method is too place a dirichlet process (which I know nothing about) over the number of states and learn the posterior of the states.

So, why is obtaining the posterior of states worth the expense and time compared to using the BIC? Do I gain more information this way?

Just trying to figure out if its worth, trying to build a HMM with a DP in my work

• The one advantage i can see for the prior approach is that you get a probability density for the number of states, while the BIC will only tell you that one number of states is more likely than the others. – richiemorrisroe Mar 14 '12 at 14:36
• could I interpret that the posterior over the states is actually better since I'm integrating out over the parameters of the model? As in a model with 5 states is most likely given the data over all parameters ..... where as with the iterate over number of states its purely based on how well the parameters are optimised for those instances of the HMM? – Nathan Harmston Mar 14 '12 at 21:55
• BIC gives you a rudimentary ranking of the models under comparison, but it does not tell you how (more) likely one model is compared with the others. The posterior distribution over the models (states) contains in addition information about the parameters of each of the models under comparison. You can condition on a model (state) or average across models to run predictive evaluations. This is much richer than using a single-dimensional approximate criterion like BIC (or any other IC)... – Xi'an May 19 '12 at 8:05