Generalized weighted Chinese restaurant processes for species sampling mixture models

Statistica Sinica

Volumn 13, Issue 4, 2003, Pages 1211-1235

  Ishwaran, Hemant ^a   James, Lancelot F ^b  

^a LERNER RESEARCH INSTITUTE   (United States)

^b HONG KONG UNIVERSITY OF SCIENCE AND TECHNOLOGY   (Hong Kong)

Author keywords

Dirichlet process; Exchangeable partition; Finite dimensional Dirichlet prior; Prediction rule; Random probability measure; Species sampling sequence; Two parameter Poisson Dirichlet process

Indexed keywords

EID: 0346338291     PISSN: 10170405     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (57)

1. Aldous, D. J. (1985). Exchangeability and related topics. In École d'Été de Probabilités de Saint-Flour XII (Edited by P. L. Hennequin). Springer Lecture Notes in Mathematics, Vol. 1117.
2. Antoniak, C. E. (1974). Mixtures of Dirichlet processes with applications to Bayesian nonparametric problems. Ann. Statist. 2, 1152-1174.
3. Blackwell, D. and MacQueen, J. B. (1973). Ferguson distributions via Pólya urn schemes. Ann. Statist. 1, 353-355.
4. Brunner, L. J., Chan, A. T., James, L. F. and Lo, A. Y. (2001). Weighted Chinese restaurant processes and Bayesian mixture models. Unpublished Manuscript.
5. Carlton, M. A. (1999). Applications of the two-parameter Poisson-Dirichlet distribution. Unpublished Ph.D. thesis, Dept. of Statistics, University of California, Los Angeles.
6. Cifarelli, D. M. and Regazzini, E. (1990). Some remarks on the distribution of the means of a Dirichlet process. Ann. Statist. 18, 429-442.
7. Daley, D. J. and Vere-Jones, D. (1988). An Introduction to the Theory of Point Processes. Springer-Verlag, New York.
8. Diaconis, P. and Kemperman, J. (1996). In Some new tools for Dirichlet priors. Bayesian Statistics 5 (Edited by J. M. Bernardo, J. O. Berger, A. P. Dawid and A. F. M. Smith), 97-106, Oxford University Press.
9. Donnelly, P. and Tavaré, S. (1987). The population genealogy of the infinitely-many neutral alleles model. J. Math. Biol. 25, 381-391.
10. Escobar, M. D. (1988). Estimating the means of several normal populations by nonparametric estimation of the distribution of the means. Unpublished Ph.D. thesis, Department of Statistics, Yale University.
11. Escobar, M. D. (1994). Estimating normal means with a Dirichlet process prior, J. Amer. Statist. Assoc. 89, 268-277.
12. Escobar, M. D. and West, M. (1995). Bayesian density estimation and inference using mixtures. J. Amer. Statist. Assoc. 90, 577-588.
13. Ewens, W. J. (1972). The sampling theory of selectively neutral alleles. Theor. Popul. Biol. 3, 87-112.
14. Ewens, W. and Tavaré, S. (1997). Multivariate Ewens distribution. In Discrete Multivariate Distributions (Edited by S. Kotz and N. Balakrishnan). Wiley, New York.
15. Ferguson, T. S. (1973). A Bayesian analysis of some nonparametric problems Ann. Statist. 1, 209-230.
16. Ferguson, T. S. (1974). Prior distributions on spaces of probability measures Ann. Statist. 2, 615-629.
17. Fisher, R. A., Corbet, A. S. and Williams C. B. (1943). The relation between the number of species and the number of individuals in a random sample of an animal population J. Animal Ecology 12, 42-58.
18. Gelfand, A. and Kottas, A. (2002). A computational approach for full nonparametric Bayesian inference under Dirichlet process mixture models. J. Comput. Graph. Statist. 11, 289-305.
19. Gyllenberg, M. and Koski, T. (2001). Probabilistic models for bacterial taxonomy Internat. Statist. Rev. 69, 249-276.
20. Hansen, B. and Pitman, J. (2000). Prediction rules for exchangeable sequences related to species sampling. Statist. Probab. Lett. 46, 251-256.
21. Hoshino, N. (2001). Applying Pitman's sampling formula to microdata disclosure risk assesment J. Official Statist. 17, 499-520.
22. Hoppe, F. M. (1987). The sampling theory of neutral alleles and an urn model in population genetics. J. Math. Biol. 25, 123-159.
23. Ishwaran, H. and James, L. F. (2001). Gibbs sampling methods for stick-breaking priors. J. Amer. Statist. Assoc. 96, 161-173.
24. Ishwaran, H. and James, L. F. (2002). Computational methods for multiplicative intensity models using weighted gamma processes: proportional hazards, marked point processes and panel count data. Manuscript
25. Ishwaran H., James, L. F. and Sun, J. (2001). Bayesian model selection in finite mixtures by marginal density decompositions. J. Amer. Statist. Assoc. 96, 1316-1332.
26. Ishwaran, H. and Zarepour, M. (2002a). Exact and approximate sum-representations for the Dirichlet process. Canad. J. Statist. 30, 269-283.
27. Ishwaran, H. and Zarepour, M. (2002b). Dirichlet prior sieves in finite normal mixtures Statist. Sinica 12, 941-963.
28. James, L. F. (2002). Poisson process partition calculus with applications to exchangeable models and Bayesian nonparametrics. The arXiv, arXiv:math.PR/0205093
29. James, L. F. (2003). Bayesian calculus for gamma processes with applications to semiparametric models, Sankhyā Ser. A 65, 196-223.
30. Kallenberg, O. (1986). Random Measures. 4th edition. Akademie-Verlag and Academic Press, Berlin and London.
31. Kerov, S. (1998). Interlacing measures, Amer. Math. Soc. Transl. 181, 35-83.
32. Kerov, S. and Tsilevich, N. V. (1998). The Markov-Krein correspondence in several dimensions. PDMI Preprint 1.
33. Kong, A., Liu, J. S. and Wong, W. H. (1994). Sequential imputations and Bayesian missing data problems. J. Amer. Statist. Assoc. 89, 278-288.
34. Kingman, J. F. C. (1978). The representation of partition structures. J. London Math. Soc. 18, 374-380.
35. Kuo, L. (1986). Computations of mixtures of Dirichlet processes SIAM J. Sci. Statist. Comput. 7, 60-71.
36. LeCam, L. (1986), Asymptotic Methods in Statistical Decision Theory. Springer-Verlag, New York.
37. Lee, Y. F. (1999). Some studies oj the weighted Chinese restaurant processes. Unpublished Masters thesis, Hong Kong University of Science and Technology.
38. Liu, J. S. (1996). Nonparametric hierarchical bayes via sequential imputations. Ann. Statist. 24, 911-930.
39. Lo, A. Y. (1984). On a class of Bayesian nonparametric estimates: I. Density estimates. Ann. Statist. 12, 351-357.
40. Lo, A. Y., Brunner, L. J. and Chan, A. T. (1996). Weighted Chinese restaurant processes and Bayesian mixture models. Research Report 1, Hong Kong University of Science and Technology.
41. Lo, A. Y. and Weng, C. S. (1989). On a class of Bayesian nonparametric estimates: II. Hazard rates estimates, Ann. Inst. Statist. Math. 41, 227-245.
42. MacEachern, S. N. (1994). Estimating normal means with a conjugate style Dirichlet process prior. Comm. Statist. Simulation Comput. 23, 727-741.
43. MacEachern, S. N., Clyde, M. and Liu, J. S. (1999). Sequential importance sampling for nonparametric Bayes models: the next generation. Canad. J. Statist. 27, 251-267.
44. MacEachern, S. N and Müller, P. (1998). Estimating mixture of Dirichlet process models. J. Comput. Graph. Statist. 7, 223-238.
45. Matthes, K. Kerstan, J., and Mecke, J. (1978). Infinitely Divisible Point Processes. English Edition Wiley, Chichester.
46. Mekjian A. Z. and Chase, K. C. (1997). Disordered systems, power laws and random processes. Phys. Lett. A 229, 340-346.
47. Muliere P. and Tardella, L. (1998). Approximating distributions of random functionals of Ferguson-Dirichlet priors. Canad. J. Statist. 26, 283-297.
48. Pitman, J. (1995). Exchangeable and partially exchangeable random partitions. Probab. Theory Related Fields 102, 145-158.
49. Pitman, J. (1996). Some developments of the Blackwell-MacQueen urn scheme. In Statistics, Probability and Game Theory (Edited by T. S. Ferguson, L. S. Shapley and J. B. MacQueen), 245-267. IMS Lecture Notes-Monograph series, Vol. 30.
50. Pitman, J. and Yor, M. (1997). The two-parameter Poisson-Dirichlet distribution derived from a stable subordinator. Ann. Probab. 25, 855-900.
51. Quintana, F. A. (1998). Nonparametric Bayesian analysis for assessing homogeneity in k × l contingency tables with fixed right margin totals. J. Amer. Statist. Assoc. 93, 1140-1149.
52. Quintana, F. A. and Newton, M. A. (2000). Computationals aspects of nonparametric Bayesian analysis with applications to the modeling of multiple binary sequences. J. Comput. Graph. Statist. 9, 711-737.
53. Roeder, K. (1990). Density estimation with confidence sets exemplified by superclusters and voids in the galaxies. J. Amer. Statist. Assoc. 85, 617-624.
54. Tsilevich, N. V. (1997). Distribution of the mean value for certain random measures. POMI preprint No. 240, Steklov Institute of Mathematics, St. Petersburg.
55. Tsilevich, N. V., Vershik A. M. and Yor, M. (2000). Distinguished properties of the gamma process and related topics. Prépublications du Laboratoire de Probabilités et Modèles aléatoires, no. 575.
56. Watterson, G. A. (1976). The stationary distribution of the infinitely-many neutral alleles diffusion model. J. Appl. Probab. 13, 639-651.
57. Wolpert R. L. and Ickstadt K. (1998). Poisson/gamma random field models for spatial statistics. Biometrika 85, 251-267.