Inference in molecular population genetics

Journal of the Royal Statistical Society. Series B: Statistical Methodology

Volumn 62, Issue 4, 2000, Pages 605-635

  Stephens, Matthew ^a   Donnelly, Peter ^b  

^a UNIVERSITY OF OXFORD   (United Kingdom)

^b NONE

Author keywords

Ancestral inference; Coalescent; Computationally intensive inference; Importance sampling; Markov chain Monte Carlo methods; Population genetics

Indexed keywords

EID: 0034354581     PISSN: 13697412     EISSN: None     Source Type: Journal    
DOI: 10.1111/1467-9868.00254     Document Type: Article

References (55)

1. Bahlo, M. and Griffiths, R. C. (2000) Inference from gene trees in a subdivided population. Theor. Popln Biol., 57, 79-95.
2. Beaumont, M. (1999) Detecting population expansion and decline using microsatellites. Genetics, 153, 2013-2029.
3. Beerli, P. and Felsenstein, J. (1999) Maximum likelihood estimation of migration rates and effective population numbers in two populations using a coalescent approach. Genetics, 152, 763-773.
4. Chen, M. H. (1994) Importance-weighted marginal Bayesian pos̀terior density-estimation. J. Am. Statist. Ass., 89, 818-824.
5. Cooper, G., Amos, W., Hoffman, D. and Rubinsztein, D. C. (1996) Network analysis of human Y microsatellite haplotypes. Hum. Molec. Genet., 5, 1759-1766.
6. Davison, A. C. and Smith, R. L. (1990) Models for exceedances over high thresholds (with discussion). J. R. Statist. Soc. B, 52, 393-442.
7. Donnelly, P. (1986) Dual processes in population genetics. Lect. Notes Math., 1212, 94-105.
8. Donnelly, P. and Kurtz, T. G. (1996a) A countable representation of the Fleming-Viot measure-valued diffusion. Ann. Probab., 24, 698-742.
9. - (1996b) The asymptotic behaviour of an urn model arising in population genetics. Stochast. Process. Applic., 64, 1-16.
10. - (1999) Particle representations for measure-valued population models. Ann. Probab., 27, 166-205.
11. Donnelly, P. and Tavaré, S. (1995) Coalescents and genealogical structure under neutrality. A. Rev. Genet., 29, 401-421.
12. Edwards, A. W. F. (1970) Estimation of the branch points of a branching diffusion process (with discussion). J. R. Statist. Soc. B, 32, 155-174.
13. Ethier, S. N. and Griffiths, R. C. (1987) The infinitely-many-sites model as a measure-valued diffusion. Ann. Probab., 15, 515-545.
14. Ethier, S. N. and Kurtz, T. (1993) Fleming-viot processes in population genetics. SIAM J. Control Optimsn, 31, 345-386.
15. Evans, G. (1993) Practical Numerical Integration. New York: Wiley.
16. Ewens, W. J. (1979) Mathematical Population Genetics. Berlin: Springer.
17. Fearnhead, P. (2000) Estimating recombination rates by importance sampling. To be published.
18. Felsenstein, J. (1981) Evolutionary trees from DNA sequences: a maximum likelihood approach. J. Molec. Evoln, 17, 368-376.
19. Felsenstein, J., Kuhner, M. K., Yamato, J. and Beerli, P. (1999) Likelihoods on coalescents: a Monte Carlo sampling approach to inferring parameters from population samples of molecular data. IMS Led. Notes Monogr. Ser., 33, 163-185.
20. Gelman, A. and Meng, X. L. (1998) Simulating normalizing constants: from importance sampling to bridge sampling to path sampling. Statist. Sci., 13, 163-185.
21. Geyer, C. J. (1996) Estimation and optimization of functions. In Markov Chain Monte Carlo in Practice (eds W. R. Gilks, S. Richardson and D. J. Spiegelhalter). London: Chapman and Hall.
22. Geyer, C. J. and Thompson, E. A. (1992) Constrained Monte Carlo maximum likelihood for dependent data (with discussion). J. R. Statist. Soc. B, 54, 657-699.
23. Gilks, W. R., Richardson, S. and Spiegelhalter, D. J. (eds) (1996) Markov Chain Monte Carlo in Practice. London: Chapman and Hall.
24. Griffiths, R. C. and Marjoram, P. (1996) Ancestral inference from samples of DNA sequences with recombination. J. Comput. Biol., 3, 479-502.
25. Griffiths, R. C. and Tavaré, S. (1994a) Simulating probability distributions in the coalescent. Theor. Popln Biol., 46, 131-159.
26. - (1994b) Ancestral inference in population genetics. Statist. Sci., 9, 307-319.
27. - (1994c) Sampling theory for neutral alleles in a varying environment. Phil. Trans. R. Soc. Lond. B, 344, 403-410.
28. - (1995) Unrooted tree probabilities in the infinitely-many-sites model. Math. Biosci., 127, 77-98.
29. - (1997) Computational methods for the coalescent. IMA Vol. Math. Applic., 87, 165-182.
30. - (1999) The ages of mutations in gene trees. Ann. Appl. Probab., 9, 567-590.
31. Hesterberg, T. C. (1995) Weighted average importance sampling and defensive mixture distributions. Technometrics, 37, 185-194.
32. Hoppe, F. M. (1984) Polya-like urns and the Ewens sampling formula. J. Math. Biol., 20, 91-94.
33. Irwin, M., Cox, N. and Kong, A. (1994) Sequential imputation for multilocus linkage analysis. Proc. Natn Acad. Sci. USA, 91, 11684-11688.
34. Kingman, J. F. C. (1982a) On the genealogy of large populations. J. Appl. Probab. A, 19, 27-43.
35. - (1982b) Exchangeability and the evolution of large populations. In Exchangeability in Probability and Statistics (eds G. Koch and F. Spizzichino), pp. 97-112. Amsterdam: North-Holland.
36. - (1982c) The coalescent. Stochast. Process. Applic., 13, 235-248.
37. Kong, A., Liu, J. S. and Wong, W. H. (1994) Sequential imputation and Bayesian missing data problems. J. Am. Statist. Ass., 89, 278-288.
38. Kuhner, M. K., Yamato, J. and Felsenstein, J. (1995) Estimating effective population size and mutation rate from sequence data using Metropolis-Hastings sampling. Genetics, 140, 1421-1430.
39. - (1998) Maximum likelihood estimation of population growth rates based on the coalescent. Genetics, 149, 429-434.
40. - (1999) Recombine. Computer Program. University of Washington, Seattle. (Available from http://www. evolution.genetics.washington/lamarc.html.)
41. Liu, J. S., Chen, R. and Wong, W. H. (1999) Rejection control and sequential importance sampling. J. Am. Statist. Ass., 93, 1022-1031.
42. Moran, P. A. P. (1975) Wandering distributions and the electrophoretic profile. Theor. Popln Biol., 8, 318-330.
43. Nielsen, R. (1997) A likelihood approach to population samples of microsatellite alleles. Genetics, 146, 711-716.
44. Raftery, A. E. (1996) Hypothesis testing and model selection. In Markov Chain Monte Carlo in Practice (eds W. R. Gilks, S. Richardson and D. J. Spiegelhalter). London: Chapman and Hall.
45. Ripley, B. D. (1987) Stochastic Simulation. New York: Wiley.
46. Sheather, S. J. and Jones, M. C. (1991) A reliable data-based bandwidth selection method for kernel density estimation. J. R. Statist. Soc. B, 53, 683-690.
47. Shephard, N. (2000) Discussion on 'Time series analysis of non-Gaussian observations based on state space models from both classical and Bayesian perspectives' (by J. Durbin and S. J. Koopman). J. R. Statist. Soc., B, 62, 30-32.
48. Slade, P. (2000) Simulation of selected genealogies. Theor. Popln Biol., to be published.
49. Stephens, M. (1999) Problems with computational methods in population genetics. Bull. 52nd Sess. Int. Statist. Inst., book 1, 273-276.
50. - (2000) Times on trees and the age of an allele. Theor. Popln Biol., 57, 109-119.
51. Tanner, M. (1993) Tools for Statistical Inference, 2nd edn. New York: Springer.
52. Venables, W. N. and Ripley, B. D. (1997) Modern Applied Statistics with S-Plus, 2nd edn. New York: Springer.
53. Whittle, P. (1970) Discussion on 'Estimation of the branch points of a branching diffusion process' (by A. W. F. Edwards). J. R. Statist. Soc. B, 32, 167-169.
54. Wilson, I. J. and Balding, D. J. (1998) Genealogical inference from microsatellite data. Genetics, 150, 499-510.
55. Wright, S. (1969) Evolution and the Genetics of Populations, vol. 2, The Theory of Gene Frequencies. Chicago: University of Chicago Press.