Random partition models and exchangeability for bayesian identification of population structure

Bulletin of Mathematical Biology

Volumn 69, Issue 3, 2007, Pages 797-815

  Corander, Jukka ^a   Gyllenberg, Mats ^a   Koski, Timo ^a,b  

^a UNIVERSITY OF HELSINKI   (Finland)

^b LINKÖPING UNIVERSITY   (Sweden)

Author keywords

Bayesian inference; Genetic population structure; Statistical learning theory

Indexed keywords

ANIMAL; ARTICLE; BAYES THEOREM; BIOLOGICAL MODEL; DROSOPHILA MELANOGASTER; EVOLUTION; GENETICS; POPULATION GENETICS;

ANIMALS; BAYES THEOREM; DROSOPHILA MELANOGASTER; EVOLUTION; GENETICS, POPULATION; MODELS, GENETIC;

EID: 33947540482     PISSN: 00928240     EISSN: 15229602     Source Type: Journal    
DOI: 10.1007/s11538-006-9161-1     Document Type: Article

References (40)

1. Bernardo, J.M., Smith, A.F.M., 1994. Bayesian Theory. Wiley, Chichester.
2. Corander, J., Waldmann, P., Marttinen, P., Sillanpää, M. J., 2004. BAPS 2: Enhanced possibilities for the analysis of genetic population structure. Bioinformatics 20, 2363-2369.
3. Corander, J., Waldmann, P., Sillanp̈aä, M.J., 2003. Bayesian analysis of genetic differentiation between populations. Genetics, 163, 367-374.
4. Corander, J., Gyllenberg, M. and Koski, T., 2006a. Bayesian unsupervised classification framework based on stochastic partitions of data and a parallel search strategy. submitted to J. Statist. Comput. Simulation.
5. Corander, J., Gyllenberg, M. and Koski, T., 2006b. Bayesian model learning based on a parallel MCMC strategy. Stat. Comput. 16, 355-362.
6. de Finetti, B., 1974. Theory of Probability, vol. I. Wiley, Chichester.
7. Dawson, K.J., Belkhir, K., 2001. A Bayesian approach to the identification of panmictic populations and the assignment of individuals. Genet. Res. Camb. 78, 59-77.
8. Diaconis, P., Zabell, S.L., 1982. Updating subjective probability. J. Amer. Stat. Assoc. 77, 822-830.
9. Dieringer, D., Nolte, V., Schlötterer, C., 2005. Population structure in African Drosophila melanogaster revealed by microsatellite analysis. Mol. Ecol. 14, 563-573.
10. Donnelly, P., 1986. Partition structures, Poly'a urns, the Ewens sampling formula, and the ages of alleles. Theor. Pop. Biol. 30, 271-288.
11. Draper, D., Hodges, J.S., Mallows, C.L., Pregibon, D., 1993. Exchangeability and data analysis. J. R. Stat. Soc. A 156, 9-37.
12. Duda, R.O., Hart, P.E., Stork, D.G., 2000. Pattern Classification and Scene Analysis, 2nd edition. Wiley, New York.
13. Ewens, W.J., 1990. Population genetics theory - the past and the future. In: Lessard, S. (Ed.), Mathematical and StatisticalDevelopments of Evolutionary Theory. Kluwer, Dordrecht, pp. 177-227.
14. Ewens, W.J., 2004. Mathematical Population Genetics, 2nd edition. Springer-Verlag, New York.
15. Geiger, D., Heckerman, D., 1997. A characterization of the Dirichlet distribution through global and local parameter independence. Ann. Stat. 25, 1344-1369.
16. Geisser, S., 1966. Predictive discrimination. In: Krishnajah, P.R. (Ed.), Multivariate Analysis. Academic Press, New York, London.
17. Good, I.J., 1965. Estimation of Probabilities. MIT Press, Cambridge, MA.
18. Gyllenberg, M., Koski, T., 2002. Bayesian predictiveness, exchangeability and sufficientness in bacterial taxonomy. Math. Biosc. 177-178, 161-184.
19. Holst, L., 1981. On numbers related to partitions of unlike objects and occupancy problems. Eur. J. Combinatorics 2, 231-237.
20. Hoppe, F.M., 1984. Poly'a-like urns and the Ewens' sampling formula. J. Math. Biol. 20, 91-94.
21. Joyce, P., 1991. Estimating the frequency of the oldest allele: A Bayesian approach. Adv. Appl. Prob. 23, 456-475.
22. Joyce, P., 1998. Partition Structures and sufficient statistics J. Appl. Prob. 35, 622-632.
23. Kallenberg, O., 2005. Probabilistic Symmetries and Invariance Principles. Springer-Verlag, New York.
24. Kingman, J.F.C., 1977. The population structure associated with the Ewens sampling formula. Theor. Pop. Biol. 11, 274-283.
25. Kingman, J.F.C., 1978a. The representation of partition structures. J. Lond. Math. Soc. 18, 374-380.
26. Kingman, J.F.C., 1978b. Random partitions in population genetics. Proc. R. Soc. Lond. A 361, 1-20.
27. Kingman, J.F.C., 1978c. Uses of exchangeability. Ann. Prob. 6, 183-197.
28. Kingman, J.F.C., 1980. Mathematics of Genetic Diversity. SIAM, Philadelphia.
29. Nagylaki, T., 1992. Theoretical Population Genetics. Springer-Verlag, Berlin.
30. Pitman, J., 1997. Some probabilistic aspects of set partitions. Amer. Math. Month. 104, 201-209.
31. Pritchard, J.K., Stephens, M., Donnelly, P., 2000. Inference of population structure using multilocus genotype data. Genetics 155, 945-959.
32. Robert, C.P., Casella, G., 2005. Monte Carlo Statistical Methods. 2nd edition. Springer-Verlag, New York.
33. Rota, G.-C., 1964. The number of partitions of a set. Amer. Math. Month. 71, 498-504.
34. Schervish, M. J., 1995. Theory of Statistics. Springer-Verlag, New York.
35. Simon, H.A., 1955. On a class of skew distribution functions. Biometrika 42, 425-440.
36. Stam, A.J., 1983. Generation of a random partition of a finite set by an urn model. J. Combin. Theor. Ser. A 35, 231-240.
37. Stigler, S.M., 1982. Thomas Bayes's Bayesian inference. J. R. Stat. Soc. A 145, 250-258.
38. Yule, G.U., 1925. A mathematical theory of evolution, based on the conclusions of Dr. J.C. Willis, F.R.S.. Philos. Trans. R. Soc. B 213, 431-444.
39. Zabell, S.L., 1982. W.E. Johnson's 'sufficientness' postulate. Ann. Stat. 10, 1091-1099.
40. Zabell, S.L., 1992. Predicting the unpredictable. Synthese 90, 205-232.