Abstract
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 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 recursions that, conditional on a user-specified constraint in the number of segments, allow us to (i) find MAP sequences, (ii) compute posterior probabilities, and (iii) simulate sample paths. We collectively call these recursions k-segment algorithms and illustrate their utility using simulated and real examples. We also highlight the prospective and retrospective use of k-segment constraints for fitting HMMs or exploring existing model fits. Supplementary materials for this article are available online.
Highlights
The use of the hidden Markov model (HMM) is ubiquitous in sequence analysis applications across a range of science and engineering domains, including signal processing (Crouse, Nowak, and Baraniuk 1998), genomics (Li and Stephens 2003), and finance (Paas, Vermunt, and Bijmolt 2007)
The k-segment algorithms we present are naturally useful in scientific discovery problems involving (i) the application of HMMs and (ii) where segmental constraints provide an important source of external information or constraints
HMMs can allow for highly efficient analysis of large quantities of sequence data
Summary
The use of the hidden Markov model (HMM) is ubiquitous in sequence analysis applications across a range of science and engineering domains, including signal processing (Crouse, Nowak, and Baraniuk 1998), genomics (Li and Stephens 2003), and finance (Paas, Vermunt, and Bijmolt 2007). Alternative sequence predictions that might lead to different decisions or scientific insights This can be important where the sequence analysis forms only part of an iterative investigative process where the users might later return to the data to explore additional features. Holmes, and Yau: Statistical Inference in HMMs Using k -Segment Constraints we call k-segment inference algorithms These algorithms are constrained to consider only sequences with a prespecified number of transition events allowing diverse sequence predictions to be obtained. These methods can be applied prospectively during model fitting or retrospectively to an existing model.
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