We present in this article a compound Poisson approximation for computing probabilities involved in significance tests for conserved genomic regions between different species. We consider the case when the conserved genomic regions are found by the reference region approach. An important aspect of our computations is the fact that we are taking into account the existence of multigene families. We obtain convergence results for the error of our approximation by using the Stein-Chen method for compound Poisson approximation.
Get full access to this article
View all access options for this article.
References
1.
Abi-RachedL., GillesA., ShiinaT.et al.2002. Evidence of en bloc duplication in vertebrate genomes. Nat. Genet., 31:100–105.
2.
BarbourA., ChenL., LohW.1992. Compound Poisson approximation for nonnegative random variables via Stein's method. Ann. Probabil., 20:1843–1866.
BergeronA., CorteelS., RaffinotM.2002. The algorithmic of gene teams. Lect. Notes Comput. Sci., 2452:464–476.
5.
ChenL.H.Y.1975. Poisson approximation for dependent trials. Ann. Probabil., 3:534–545.
6.
DanchinE., PontarottiP.2004. Statistical evidence for a more than 800-million-year-old evolutionarily conserved genomic region in our genome. J. Mol. Evol., 59:587–597.
7.
DurandD., SankoffD.2003. Tests for gene clustering. J. Comput. Biol., 10:453–482.
8.
GlazJ., NausJ.1983. Multiple clusters on the line. Commun. Stat. Theor. M., 12:1961–1986.
9.
GlazJ., NausJ., WallensteinS.2001. Scan Statistics. Springer Verlag: New York.
10.
GruseaS.2008. Applications of probability calculus to the detection of conserved genomic regions [Ph.D. dissertation]. Univ. de Provence, Marseille.
11.
HobermanR., DurandD.2005. The incompatible desiderata of gene cluster properties. Lect. Notes Bioinform., 3678:73–87.
12.
HobermanR., SankoffD., DurandD.2005. The statistical significance of max-gap clusters. Lect. Notes Bioinform., 3388:55–71.
13.
HuntingtonR., NausJ.1975. A simpler expression for kth nearest neighbor coincidence probabilities. Ann. Probabil., 3:894–896.
14.
Lopez RascolV., LevasseurA., ChabrolO.et al.2009. CASSIOPE: an expert system for conserved regions searches. BMC Bioinform, 10:284.
15.
PykeR.1965. Spacings. J. R. Stat. Soc. B, 27:395–449.
RoosM.1993a. Stein-Chen method for compound Poisson approximation [Ph.D. dissertation]. Univ. of Zurich.
20.
RoosM.1993b. Compound Poisson approximations for the number of extreme spacings. Adv. Appl. Probabil., 25:847–874.
21.
SteinC.1972. A bound for the error in the normal approximation to the distribution of a sum of dependent random variables. Proc. Sixth Berkeley Symp. Math. Stat. Probabil.
22.
SteinC.1986. Approximate computation of expectations. IMS Lect. Notes. Monograph Series, 7. IMS: Hayward, CA.
23.
ZucchettiI., De SantisR., GruseaS.et al.2009. Origin and evolution of the vertebrate leukocyte receptors: the lesson from tunicates. Immunogenetics, 61:463–481.
