Compound Poisson approximation of word counts in DNA sequences

Schbath, Sophie

doi:10.1051/ps:1997100

Cited by 64 publications

(83 citation statements)

References 9 publications

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“…When counting copies of a word w in a sequence, this becomes a problem if the word can form clumps of overlapping occurrences. The effect of clumping in Markov chains was dealt with in [7] and, more extensively, in [10]. Our main attention here is restricted to words that do not clump; we present additional results on clumped words in Appendix A.…”

Section: Distribution Of N X (W)mentioning

confidence: 99%

Exact distribution of word counts in shuffled sequences

Rødland

2006

Adv. Appl. Probab.

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In DNA sequences, specific words may take on biological functions as marker or signalling sequences. These may often be identified by frequent-word analyses as being particularly abundant. Accurate statistics is needed to assess the statistical significance of these word frequencies. The set of shuffled sequences -letter sequences having the same k-word composition, for some choice of k, as the sequence being analysed -is considered the most appropriate sample space for analysing word counts. However, little is known about these word counts. Here we present exact formulae for word counts in shuffled sequences.

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Section: Distribution Of N X (W)mentioning

confidence: 99%

Exact distribution of word counts in shuffled sequences

Rødland

2006

Adv. Appl. Probab.

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“…See also Lladser et al [16]. Approximations using the normal distribution and the Poisson distribution are in Schbath [31], Nicodème et al [21], Reinert et al [28] and Roquain and Schbath [30]. Large deviations asymptotics are in Régnier and Szpankowski [27], Régnier [25] and Régnier and Denise [26].…”

Section: P Pudlomentioning

confidence: 99%

“…The leading term of the asymptotics of g a (n, it) when t is close to the origin is due to Mann [17] (pp. [24][25][26][27][28][29][30][31][32][33], and is given in Proposition 4.2 below.…”

Section: Asymptotics On the Fourier Transform Of S Nmentioning

confidence: 99%

Large deviations and full Edgeworth expansions for finite Markov chains with applications to the analysis of genomic sequences

Pudlo

2010

ESAIM: PS

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Abstract.To establish lists of words with unexpected frequencies in long sequences, for instance in a molecular biology context, one needs to quantify the exceptionality of families of word frequencies in random sequences. To this aim, we study large deviation probabilities of multidimensional word counts for Markov and hidden Markov models. More specifically, we compute local Edgeworth expansions of arbitrary degrees for multivariate partial sums of lattice valued functionals of finite Markov chains. This yields sharp approximations of the associated large deviation probabilities. We also provide detailed simulations. These exhibit in particular previously unreported periodic oscillations, for which we provide theoretical explanations.Mathematics Subject Classification. 60J10, 60F10, 60J55, 92D20, 60F05.

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“…In a number of DNA related studies (e.g., Arratia et al, 1990Arratia et al, , 1996Reinert et al, 2000;Reinert and Schbath, 1998;Schbath, 1995), the differences between two random processes are quantified by the total variation distance d TV between them. However, as explained in Chapter 10 of Barbour et al (1992), the total variation distance is too strong to be useful for point processes like Ξ and Z λ .…”

Section: The Palindrome Process and Wasserstein Distancementioning

confidence: 99%

Nonrandom Clusters of Palindromes in Herpesvirus Genomes

Leung

Choi

Xia

et al. 2005

Journal of Computational Biology

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Palindromes are symmetrical words of DNA in the sense that they read exactly the same as their reverse complementary sequences. Representing the occurrences of palindromes in a DNA molecule as points on the unit interval, the scan statistics can be used to identify regions of unusually high concentration of palindromes. These regions have been associated with the replication origins on a few herpesviruses in previous studies. However, the use of scan statistics requires the assumption that the points representing the palindromes are independently and uniformly distributed on the unit interval. In this paper, we provide a mathematical basis for this assumption by showing that in randomly generated DNA sequences, the occurrences of palindromes can be approximated by a Poisson process. An easily computable upper bound on the Wasserstein distance between the palindrome process and the Poisson process is obtained. This bound is then used as a guide to choose an optimal palindrome length in the analysis of a collection of 16 herpesvirus genomes. Regions harboring significant palindrome clusters are identified and compared to known locations of replication origins. This analysis brings out a few interesting extensions of the scan statistics that can help formulate an algorithm for more accurate prediction of replication origins.

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Compound Poisson approximation of word counts in DNA sequences

Cited by 64 publications

References 9 publications

Exact distribution of word counts in shuffled sequences

Exact distribution of word counts in shuffled sequences

Large deviations and full Edgeworth expansions for finite Markov chains with applications to the analysis of genomic sequences

Nonrandom Clusters of Palindromes in Herpesvirus Genomes

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