Poisson approximation for search of rare words in DNA sequences

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dc.creatorVergne, Nicolas
dc.creatorAbadi, Miguel
dc.date2007-11-15
dc.date.accessioned2026-07-07T08:43:05Z
dc.date.available2026-07-07T08:43:05Z
dc.descriptionUsing recent results on the occurrence times of a string of symbols in a stochastic process with mixing properties, we present a new method for the search of rare words in biological sequences generally modelled by a Markov chain. We obtain a bound on the error between the distribution of the number of occurrences of a word in a sequence (under a Markov model) and its Poisson approximation. A global bound is already given by a Chen-Stein method. Our approach, the psi-mixing method, gives local bounds. Since we only need the error in the tails of distribution, the global uniform bound of Chen-Stein is too large and it is a better way to consider local bounds. We search for two thresholds on the number of occurrences from which we can regard the studied word as an over-represented or an under-represented one. A biological role is suggested for these over- or under-represented words. Our method gives such thresholds for a panel of words much broader than the Chen-Stein method. Comparing the methods, we observe a better accuracy for the psi-mixing method for the bound of the tails of distribution. We also present the software PANOW (available at http://stat.genopole.cnrs.fr/software/panowdir/) dedicated to the computation of the error term and the thresholds for a studied word.
dc.description29 pages, 0 figures
dc.identifierhttps://arxiv.org/abs/0711.2382
dc.identifierhttp://arxiv.org/abs/0711.2382
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/142193
dc.subjectProbability
dc.subjectStatistics Theory
dc.subjectApplications
dc.subject60F05, 60G10, 92D20 (Primary); 60-04 (Secondary)
dc.titlePoisson approximation for search of rare words in DNA sequences
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