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Sampling Formulae for Symmetric Selection
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Kenji Handa, Saga University
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Abstract
We study partition distributions in a population genetics model
incorporating symmetric selection and mutation.
They generalize Ewens distributions
in the infinitely-many-neutral-alleles model,
an explicit expression of which is known as
the Ewens sampling formula.
A sampling formula for the generalized model is obtained
by means of calculus for Poisson and gamma processes.
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Full text: PDF
Pages: 223-234
Published on: November 14, 2005
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Bibliography
-
R. Arratia, A. D. Barbour, S. Tavaré.
Logarithmic Combinatorial Structures: a Probabilistic Approach.
European Mathematical Society, Zurich, 2003.
MR2032426 (2004m:60004)
-
P. Billingsley.
Convergence of Probability Measures. 2nd edition.
John Wiley & Sons, Inc., New York, 1999.
MR1700749 (2000e:60008)
-
W. J. Ewens.
The sampling theory of selectively neutral alleles.
Theoret. Population Biology 3 (1972), 87-112;
erratum, ibid. 3 (1972), 240;
erratum, ibid. 3 (1972), 376.
MR0325177 (48 #3526)
-
W. J. Ewens, S. Tavaré.
Multivariate Ewens distribution.
in: N. Johnson, S. Kotz, N. Balakrishnan (Eds.).
Discrete Multivariate Distributions.
John Wiley & Sons, Inc., New York, 1997, pp. 232-246.
Math. Review number not available.
-
M. N. Grote, T. P. Speed.
Approximate Ewens formulae for symmetric overdominance selection.
Ann. Appl. Probab. 12 (2002), 637-663.
MR1910643 (2003c:62020)
-
L. F. James.
Poisson process partition calculus with
applications to exchangeable models and Bayesian nonparametrics.
preprint, 2002.
available at http://front.math.ucdavis.edu/math.PR/0205093
-
L. F. James.
Bayesian Poisson process partition calculus with
an application to Bayesian Lévy moving averages.
Ann. Statistics 33 (2005), 1771-1799.
-
J. F. C. Kingman.
Random discrete distribution.
J. Roy. Statist. Soc. Ser. B 37 (1975), 1-22.
MR0368264 (51 #4505)
-
J. F. C. Kingman.
Random partitions in population genetics.
Proc. Roy. Soc. London Ser. A 361 (1978), 1-20.
MR0526801 (58 #26167)
-
J. F. C. Kingman.
The representation of partition structures.
J. London Math. Soc. (2) 18 (1978), 374-380.
MR0509954 (80a:05018)
-
J. F. C. Kingman.
Poisson Processes.
Oxford University Press, New York, 1993.
MR1207584 (94a:60052)
-
A. Y. Lo, C.-S. Weng.
On a class of Bayesian nonparametric estimates, II,
Hazard rate estimates.
Ann. Inst. Statist. Math. 41 (1989), 227-245.
MR1006487 (90j:62149)
-
J. Pitman.
Poisson-Kingman partitions. preprint, 1995.
-
J. Pitman.
Combinatorial stochastic processes.
Technical Report No. 621, Dept. Statistics.,
U. C. Berkeley, 2002;
Lecture notes for St. Flour course, July 2002.
available at http://www.stat.berkeley.edu/users/pitman
-
J. Pitman.
Poisson-Kingman partitions.
in: D. R. Goldstein (Ed.).
Science and Statistics: A Festschrift for Terry Speed.
Institute of Mathematical Statistics Hayward, California,
2003, pp. 1-34.
MR2004330 (2004j:60019)
-
J. Pitman, M. Yor.
The two-parameter Poisson-Dirichlet distribution
derived from a stable subordinator.
Ann. Probab. 25 (1997), 855-900.
MR1434129 (98f:60147)
-
N. Tsilevich, A. Vershik, M. Yor.
Distinguished properties of the gamma process,
and related topics.
Prépublication du Laboratoire de Probabilités
et Modèles Aléatoires. No. 575, 2000.
available at http://xxx.lanl.gov/ps/math.PR/0005287
-
N. Tsilevich, A. Vershik, M. Yor.
An infinite-dimensional analogue of the Lebesgue
measure and distinguished properties of the gamma process.
Journ. Funct. Anal. 185 (2001), 274-296.
MR1853759 (2002g:46071)
-
G. A. Watterson.
Heterosis or neutrality ?
Genetics 85 (1977), 789-814.
MR0504021 (58 #20595)
-
G. A. Watterson.
The homozygosity test of neutrality.
Genetics 88 (1978), 405-417.
Math. Review number not available.
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Electronic Communications in Probability. ISSN: 1083-589X |
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