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Pair Hidden Markov Models (PHMMs) are probabilistic models used for pairwisesequence alignment, a quintessential problem in bioinformatics. PHMMs includethree types of hidden states: match, insertion and deletion. Most previousstudies have used one or two hidden states for each PHMM state type. However,few studies have examined the number of states suitable for representingsequence data or improving alignment accuracy.We developed a novel method toselect superior models (including the number of hidden states) for PHMM. Ourmethod selects models with the highest posterior probability using FactorizedInformation Criteria (FIC), which is widely utilised in model selection forprobabilistic models with hidden variables. Our simulations indicated thismethod has excellent model selection capabilities with slightly improvedalignment accuracy. We applied our method to DNA datasets from 5 and 28species, ultimately selecting more complex models than those used in previousstudies.

Beyond similarity assessment: Selecting the optimal model for sequence alignment via the Factorized Asymptotic Bayesian algorithm