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Compound Poisson approximation of word counts in DNA sequences

Published online by Cambridge University Press:  15 August 2002

Sophie Schbath
Sophie Schbath*
Affiliation:
Institut National de la Recherche Agronomique, France
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Abstract

Identifying words with unexpected frequencies is an important problem in the analysis of long DNA sequences. To solve it, we need an approximation of the distribution of the number of occurrences N(W) of a word W. Modeling DNA sequences with m-order Markov chains, we use the Chen-Stein method to obtain Poisson approximations for two different counts. We approximate the “declumped” count of W by a Poisson variable and the number of occurrences N(W) by a compound Poisson variable. Combinatorial results are used to solve the general case of overlapping words and to calculate the parameters of these distributions.

Keywords

DNA sequences / word counts / Poisson approximations / compound Poisson distribution / Chen-Stein method / Markov chains / word periods.
Type
Research Article
Information
ESAIM: Probability and Statistics , Volume 1 , 1997 , pp. 1 - 16
Copyright
© EDP Sciences, SMAI, 1997

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