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An improved approximation for assessing the statistical significance of molecular sequence features

Part of: Stochastic processes Applications

Published online by Cambridge University Press:  14 July 2016

S. Mercier ,
D. Cellier  and
D. Charlot
S. Mercier*
Affiliation:
Université Toulouse II
D. Cellier*
Affiliation:
Université Toulouse II
D. Charlot*
Affiliation:
Université Rouen
*
∗ Postal address: GRIMM, Département de Mathématiques et Informatique, Université Toulouse II, 31058 Toulouse cedex 9, France. Email address: mercier@univ-tlse2.fr
∗∗ Postal address: LMRS, UMR CNRS 6085, Université Rouen, 76821 Mont-Saint-Aignan, France.
∗∗ Postal address: LMRS, UMR CNRS 6085, Université Rouen, 76821 Mont-Saint-Aignan, France.
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Abstract

Using random walk theory, we first establish explicitly the exact distribution of the maximal partial sum of a sequence of independent and identically distributed random variables. This result allows us to obtain a new approximation of the distribution of the local score of one sequence. This approximation improves the one given by Karlin et al., which can be deduced from this new formula. We obtain a more accurate asymptotic expression with additional terms. Examples of application are given.

Keywords

Statistical significancesequence analysislocal scorerandom walk

MSC classification

Primary: 60G50: Sums of independent random variables; random walks
Secondary: 62P10: Applications to biology and medical sciences
Type
Research Papers
Information
Journal of Applied Probability , Volume 40 , Issue 2 , June 2003 , pp. 427 - 441
Copyright
Copyright © Applied Probability Trust 2003 

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