engleski

A compound Poisson approximation for local sequence alignment

We study ungapped local alignments of two independent i.i.d. sequences of letters from a finite alphabet. The motivation comes from measuring similarity between different biological sequences. The scores of all local alignments form a so–called score matrix in which, due to an interesting dependence structure, extreme scores appear in clusters along the diagonal lines. It is known that the number of clusters with extreme scores is approximately Poisson distributed. In particular, this determines the asymptotic distribution of the maximum local alignment score, see Dembo et al. [1994] and also Hansen [2006]. We show that it is possible to obtain a Poisson cluster limit for the point process of all local alignment scores together with their locations in the score matrix. Our approach is based on the theory of regularly varying random fields on the two-dimensional integer lattice and a point process version of the Poisson approximation result from Arratia et al. [1989]. This work is an extension of the previous joint work with Philippe Soulier (Université Paris Nanterre), see Basrak et al. [2018+].

local sequence alignment ; regular variation ; point process ; Poisson approximation

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