Brona Brejova, Tomas Vinar. A Better Method for Length Distribution Modeling in HMMs and Its Application to Gene Finding . In A. Apostolico, M. Takeda, ed., Combinatorial Pattern Matching, 13th Annual Symposium (CPM), 2373 volume of Lecture Notes in Computer Science, pp. 190-202, Fukuoka, Japan, July 3-5 2002. Springer.

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Hidden Markov models (HMMs) have proved to be a useful abstraction in 
modeling biological sequences. In some situations it is necessary to use 
generalized HMMs in order to model the length distributions of some 
sequence elements because basic HMMs force geometric-like distributions. In 
this paper we suggest the use of an arbitrary length distributions with 
geometric tails to model lengths of elements in biological sequences. We 
give an algorithm for annotation of a biological sequence in (ndm^2\Delta)$
time using such length distributions coupled with a suitable generalization 
of the HMM; here n is the length of the sequence, m is the number of states 
in the model, d is a parameter of the length distribution, and $\Delta$ is 
a small constant dependent on model topology (compared to previously 
proposed algorithms with (n^3m^2)$ time [10]). Our techniques can be 
incorporated into current software tools based on HMMs.

To validate our approach, we demonstrate that many length distributions in 
gene finding can be accurately modeled with geometric-tail length 
distribution, keeping parameter d small.

Keywords: computational biology, hidden Markov models, gene finding, length