# Publication details

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 2002. Springer.

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## Abstract

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 O(nd m^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 O(n^3m^2) time). 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.