The Annals of Statistics

A Poisson Approximation for Sequence Comparisons with Insertions and Deletions

Claudia Neuhauser

Full-text: Open access


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

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

First available in Project Euclid: 11 April 2007

Permanent link to this document

Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier


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

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


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.

Export citation