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Moderate Deviations for Word Counts in Biological Sequences

Part of: Markov processes Limit theorems Stochastic processes

Published online by Cambridge University Press:  14 July 2016

Sarah Behrens  and
Matthias Löwe
Sarah Behrens*
Affiliation:
Max Planck Institute for Molecular Genetics
Matthias Löwe*
Affiliation:
University of Münster
*
∗ Postal address: Max Planck Institute for Molecular Genetics, Department for Computational Molecular Biology, Ihnestraβe 63-73, 14195 Berlin, Germany. Email address: sbehrens@molgen.mpg.de
∗∗ Postal address: Fachbereich Mathematik und Informatik, Universität Münster, Einsteinstr. 62, 48149, Münster, Germany. Email address: maloewe@math.uni-muenster.de
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Abstract

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We derive a moderate deviation principle for word counts (which is extended to counts of multiple patterns) in biological sequences under different models: independent and identically distributed letters, homogeneous Markov chains of order 1 and m, and, in view of the codon structure of DNA sequences, Markov chains with three different transition matrices. This enables us to approximate P-values for the number of word occurrences in DNA and protein sequences in a new manner.

Keywords

Moderate deviationsMarkov chainword countsmotifsbiological sequence analysis

MSC classification

Secondary: 60F99: None of the above, but in this section 92D20: Protein sequences, DNA sequences 60J10: Markov chains (discrete-time Markov processes on discrete state spaces) 60J20: Applications of Markov chains and discrete-time Markov processes on general state spaces (social mobility, learning theory, industrial processes, etc.) 60G50: Sums of independent random variables; random walks

Information

Type
Research Article
Information
Journal of Applied Probability , Volume 46 , Issue 4 , December 2009 , pp. 1020 - 1037
Copyright
Copyright © Applied Probability Trust 2009 

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