Ewens sampling formulae with and without selection

Journal of Computational and Applied Mathematics

Volumn 206, Issue 2, 2007, Pages 755-773

  Huillet, Thierry ^a  

^a UNIVERSITÉ DE CERGY PONTOISE   (France)

Author keywords

Bell polynomials; Ewens sampling formulae; Gibbs Dirichlet partition; Poisson Dirichlet; Random discrete distribution; Selection

Indexed keywords

POISSON DISTRIBUTION; POLYNOMIALS;

BELL POLYNOMIALS; EWENS SAMPLING FORMULAE; GIBBS-DIRICHLET PARTITION; POISSON-DIRICHLET; RANDOM DISCRETE DISTRIBUTION;

INTEGRAL EQUATIONS;

EID: 34249793209     PISSN: 03770427     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cam.2006.08.022     Document Type: Article

References (33)

1. Billingsley P. Convergence of Probability Measures. second ed. (1999), Wiley, New York
2. Blackwell D., and MacQueen J.B. Ferguson distributions via Pólya urn schemes. Ann. Statist. 1 (1973) 353-355
3. Comtet L. Analyse combinatoire (1970), Tomes 1 et 2 Presses Universitaires de France, Paris
4. Devroye L. Non-Uniform Random Variate Generation (1986), Springer, New York
5. Donnelly P. Partition structures, Pòlya urns, the Ewens sampling formula and the age of alleles. Theoret. Popul. Biol. 30 (1986) 271-288
6. Donnelly P. The heaps process, libraries and size-biased permutation. J. Appl. Probab. 28 (1991) 321-335
7. Engen S. Stochastic abundance models. Monographs on Applied Probability and Statistics (1978), Chapman & Hall, London
8. Ewens W.J. The sampling theory of selectively neutral alleles. Theoret. Popul. Biol. 3 (1972) 87-112
9. Ewens W.J. Population genetics theory-the past and the future. In: Lessard S. (Ed). Mathematical and Statistical Developments of Evolutionary Theory (1990), Kluwer, Dordrecht
10. W.J. Ewens, Some remarks on the law of succession, Athens Conference on Applied Probability and Time Series Analysis, vol. I, pp. 229-244; Lecture Notes in Statistics, vol. 114, Springer, New York, 1995.
11. Genz A., and Joyce P. Computation of the normalizing constant for exponentially weighted Dirichlet distribution integrals. Comput. Sci. Statist. 35 (2003) 557-563
12. Grote M.N., and Speed T.P. Approximate Ewens formulae for symmetric overdominance selection. Ann. Appl. Probab. 12 2 (2002) 637-663
13. K. Handa, Partition distributions for symmetric overdominance selection, Sixth World Congress of the Bernoulli Society for Mathematical Statistics and Probability, Barcelona, 2004.
14. Handa K. Sampling formulae for symmetric selection. Electron. Commun. Probab. 10 (2005) 223-234
15. L. Holst, The Poisson-Dirichlet distribution and its relatives revisited, Preprint of the Royal Institute of Technology, Stockholm, Sweden, 2001.
16. Hoppe F.M. The sampling theory of neutral alleles and an urn model in population genetics. J. Math. Biol. 25 2 (1987) 123-159
17. Huillet T. Sampling problems for randomly broken sticks. J. Phys. A 36 14 (2003) 3947-3960
18. Huillet T. Sampling formulae arising from random Dirichlet populations. Comm. Statist.-Theory and Methods 34 5 (2005) 1019-1040
19. Huillet T., and Martinez S. Sampling from finite random partitions. Methodol. Comput. Appl. Probab. 5 4 (2003) 467-492
20. Joyce P., Krone S.M., and Kurtz T.G. When can one detect overdominant selection in the infinite-alleles model?. Ann. Appl. Probab. 13 1 (2003) 181-212
21. Kingman J.F.C. Random discrete distributions. J. Roy. Statist. Soc., Ser. B 37 (1975) 1-22
22. Kingman J.F.C. Random partitions in population genetics. Proc. Roy. Soc. London Ser. A 361 1704 (1978) 1-20
23. Kingman J.F.C. Poisson Processes (1993), Clarendon Press, Oxford
24. Patil G.P., and Taillie C. Diversity as a concept and its implications for random environments. Bulletin de l'Institut International de Statistique 4 (1977) 497-515
25. J. Pitman, Combinatorial stochastic processes, Bell polynomials, composite structures and Gibbs partitions, Technical Report 621, Department of Statistics, University of California at Berkeley, Lecture Notes for St. Flour Course, 2002 (Chapter 1).
26. Tavaré S., and Ewens W.J. Multivariate Ewens distribution. In: Johnson N.L., Kotz S., and Balakrishnan N. (Eds). Discrete Multivariate Distributions (1997), Wiley, New York 232-246 (Chapter 41)
27. Watterson G.A. The stationary distribution of the infinitely-many neutral alleles diffusion model. J. Appl. Probab. 13 4 (1976) 639-651
28. Watterson G.A. Heterosis or neutrality?. Genetics 85 (1977) 789-814
29. Watterson G.A. The homozygosity test of neutrality. Genetics 88 (1978) 405-417
30. Zabell S.L. W.E. Johnson's sufficientness postulate. Ann. Statist. 10 4 (1982) 1090-1099
31. Zabell S.L. Predicting the unpredictable. Synthese 90 2 (1992) 205-232
32. Zabell S.L. The continuum of inductive methods revisited. In: Earman J., and Norton J. (Eds). The Cosmos of Science (1996), University of Pittsburgh Press, University of Konstanz 351-385
33. Zabell S.L. Confirming universal generalizations. Probability, dynamics and causality (Luino, 1995). Erkenntnis 45 2-3 (1996) 267-283