Original Article

Bulletin of Mathematical Biology

, Volume 68, Issue 2, pp 361-384

First online:

A Sufficient Condition for Reducing Recursions in Hidden Markov Models

  • Yun S. SongAffiliated withDepartment of Statistics, University of OxfordDepartment of Computer Science, University of California at Davis Email author 

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In hidden Markov models, the probability of observing a set of strings can be computed using recursion relations. We construct a sufficient condition for simplifying the recursion relations for a certain class of hidden Markov models. If the condition is satisfied, then one can construct a reduced recursion where the dependence on Markov states completely disappears. We discuss a specific example—namely, statistical multiple alignment based on the TKF-model—in which the sufficient condition is satisfied.


Hidden Markov model Recursions Reduction Markov states Statistical alignment