Statistical Inference in Hidden Markov Models using $k$-segment Constraints

Hidden Markov models (HMMs) are one of the most widely used statistical methods for analyzing sequence data. However, the reporting of output from HMMs has largely been restricted to the presentation of the most-probable (MAP) hidden state sequence, found via the Viterbi algorithm, or the sequence of most probable marginals using the forward-backward (F-B) algorithm. In this article, we expand the amount of information we could obtain from the posterior distribution of an HMM by introducing linear-time dynamic programming algorithms that, we collectively call $k$-segment algorithms, that allow us to i) find MAP sequences, ii) compute posterior probabilities and iii) simulate sample paths conditional on a user specified number of segments, i.e. contiguous runs in a hidden state, possibly of a particular type. We illustrate the utility of these methods using simulated and real examples and highlight the application of prospective and retrospective use of these methods for fitting HMMs or exploring existing model fits.

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