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This paper surveys a series of model selection approaches and presents a novel predictive information criterion (PIC) for hidden Markov model (HMM) selection. The approximate Bayesian using Viterbi approach is applied for PIC selection of the best HMMs providing the largest prediction information for generalization of future data. When the perturbation of HMM parameters is expressed by a product of conjugate prior densities, the segmental prediction information is derived at the frame level without Laplacian integral approximation. In particular, a multivariate t distribution is attained to characterize the prediction information corresponding to HMM mean vector and precision matrix. When performing model selection in tree structure HMMs, we develop a top-down prior/posterior propagation algorithm for estimation of structural hyperparameters. The prediction information is determined so as to choose the best HMM tree model. Different from maximum likelihood (ML) and minimum description length (MDL) selection criteria, the parameters of PIC chosen HMMs are computed via maximum a posteriori estimation. In the evaluation of continuous speech recognition using decision tree HMMs, the PIC criterion outperforms ML and MDL criteria in building a compact tree structure with moderate tree size and higher recognition rate.