The Annals of Statistics

A Poisson Approximation for Sequence Comparisons with Insertions and Deletions

Claudia Neuhauser

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Abstract

We construct a statistical test for a sequence alignment problem which enables us to decide whether two given sequences are related. Such a test can be used in DNA and protein sequence comparisons. It is based on a comparison of two long sequences of i.i.d. letters taken from a finite alphabet. The test statistic typically employed is the length of the longest matching region between the two sequences in which a certain number of insertions and deletions but no mismatches are allowed. We give a distributional result which enables one to compute $P$-values, and hence to decide whether or not the two sequences are related. Its proof utilizes the Chen-Stein method for Poisson approximation. The test is based on a greedy algorithm that searches for the longest matching region. We show that this algorithm finds the longest matching region with probability approaching 1 as the lengths of the two sequences go to infinity.

Article information

Source
Ann. Statist., Volume 22, Number 3 (1994), 1603-1629.

Dates
First available in Project Euclid: 11 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aos/1176325645

Digital Object Identifier
doi:10.1214/aos/1176325645

Mathematical Reviews number (MathSciNet)
MR1311992

Zentralblatt MATH identifier
0817.62013

JSTOR
links.jstor.org

Subjects
Primary: 62F05: Asymptotic properties of tests
Secondary: 92D20: Protein sequences, DNA sequences

Keywords
Chen-Stein method sequence matching Poisson approximation DNA sequences greedy algorithm

Citation

Neuhauser, Claudia. A Poisson Approximation for Sequence Comparisons with Insertions and Deletions. Ann. Statist. 22 (1994), no. 3, 1603--1629. doi:10.1214/aos/1176325645. https://projecteuclid.org/euclid.aos/1176325645


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