Controlling the reinforcement in Bayesian non-parametric mixture models

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

Volumn 69, Issue 4, 2007, Pages 715-740

  Lijoi, Antonio ^a   Mena, Ramsés H ^b   Prünster, Igor ^c  

^a UNIVERSITY OF PAVIA   (Italy)

^b UNIVERSIDAD NACIONAL AUTÓNOMA DE MÉXICO   (Mexico)

^c UNIVERSITY OF TURIN   (Italy)

Author keywords

Bayesian clustering; Bayesian non parametric inference; Dirichlet process; Mixture model; Predictive distribution; Product partition model

Indexed keywords

EID: 34547828069     PISSN: 13697412     EISSN: 14679868     Source Type: Journal    
DOI: 10.1111/j.1467-9868.2007.00609.x     Document Type: Article

References (43)

1. Antoniak, C. E. (1974) Mixtures of Dirichlet processes with applications to Bayesian non-parametric problems. Ann. Statist., 2, 1152 1174.
2. Arratia, R., Barbour, A. D. Tavaré, S. (2003) Logarithmic Combinatorial Structures: a Probabilistic Approach. Zürich : European Mathematical Society.
3. Barry, D. Hartigan, J. A. (1993) A Bayesian analysis for change point problems. J. Am. Statist. Ass., 88, 309 319.
4. Berry, D. A. Christensen, R. (1979) Empirical Bayes estimation of a binomial parameter via mixtures of Dirichlet processes. Ann. Statist., 7, 558 568.
5. Billingsley, P. (1995) Probability and Measure, 3rd edn. New York : Wiley.
6. Brix, A. (1999) Generalized gamma measures and shot-noise Cox processes. Adv. Appl. Probab., 31, 929 953.
7. Bush, C. A. MacEachern, S. N. (1996) A semiparametric Bayesian model for randomised block designs. Biometrika, 83, 275 285.
8. Charalambides, C. (2005) Combinatorial Methods in Discrete Distributions. New York : Wiley.
9. Charalambides, C. A. Singh, J. (1988) A review of the Stirling numbers, their generalizations and statistical applications. Communs Statist. Theory Meth., 17, 2533 2595.
10. De Iorio, M., Müller, P., Rosner, G. L. MacEachern, S. N. (2004) An ANOVA model for dependent random measures. J. Am. Statist. Ass., 99, 205 215.
11. Doornik, J. A. (2002) Object-oriented Matrix Programming Using Ox, 3rd edn. Oxford : Timberlake.
12. Epifani, I., Lijoi, A. Prünster, I. (2003) Exponential functionals and means of neutral-to-the-right priors. Biometrika, 90, 791 808.
13. Escobar, M. D. West, M. (1995) Bayesian density estimation and inference using mixtures. J. Am. Statist. Ass., 90, 577 588.
14. Ewens, W. J. (1972) The sampling theory of selectively neutral alleles. Theor. Popln Biol., 3, 87 112.
15. Gnedin, A. Pitman, J. (2005) Exchangeable Gibbs partitions and Stirling triangles. Zap. Nauchn. Sem. St Peterburg. Otdel. Mat. Inst. Steklov., 325, 83 102.
16. Green, P. J. Richardson, S. (2001) Modelling heterogeneity with and without the Dirichlet process. Scand. J. Statist., 28, 355 375.
17. Hartigan, J. A. (1990) Partition models. Communs Statist. Theory Meth., 19, 2745 2756.
18. Hjort, N. L. (2000) Bayesian analysis for a generalized Dirichlet process prior. Statistics Research Report 7. University of Oslo, Oslo.
19. Ishwaran, H. James, L. F. (2001) Gibbs sampling methods for stick-breaking priors. J. Am. Statist. Ass., 96, 161 173.
20. Ishwaran, H. James, L. F. (2003) Generalized weighted Chinese restaurant processes for species sampling mixture models. Statist. Sin., 13, 1211 1235.
21. James, L. F. (2002) Poisson process partition calculus with applications to exchangeable models and Bayesian nonparametrics. Technical Report. Hong Kong University of Science and Technology, Hong Kong. (Available from http://arxiv.org/pdf/math/0205093.)
22. James, L. F. (2006) Poisson calculus for spatial neutral to the right processes. Ann. Statist., 34, 416 440.
23. James, L. F. (2007) Spatial neutral to the right species sampling mixture models. In Essays in Honor of Kjell A. Doksum (ed. V. Nair 425 440. Singapore: World Scientific Press.
24. James, L. F., Lijoi, A. Prünster, I. (2005) Bayesian inference for classes of normalized random measures. Working Paper 5/05. International Centre for Economic Research, Turin.
25. Kingman, J. F. C. (1975) Random discrete distributions (with discussion). J. R. Statist. Soc. B, 37, 1 22.
26. Korwar, R. M. Hollander, M. (1973) Contributions to the theory of Dirichlet processes. Ann. Probab., 1, 705 711.
27. Lijoi, A., Mena, R. H. Prünster, I. (2005) Hierarchical mixture modeling with normalized inverse Gaussian priors. J. Am. Statist. Ass., 100, 1278 1291.
28. Liu, J. S. (1996) Nonparametric hierarchical Bayes via sequential imputations. Ann. Statist., 24, 911 930.
29. Lo, A. Y. (1984) On a class of Bayesian nonparametric estimates: I, density estimates. Ann. Statist., 12, 351 357.
30. MacEachern, S. N. (1994) Estimating normal means with a conjugate style Dirichlet process prior. Communs Statist. Simuln Computn, 23, 727 741.
31. MacEachern, S. N. (1998) Computational methods for mixture of Dirichlet process models. In Practical Nonparametric and Semiparametric Bayesian Statistics (eds D. Dey, P. Müller D. Sinha pp. 23 43. New York : Springer.
32. MacEachern, S. N. (1999) Dependent nonparametric processes. Proc. Bayes. Statist. Sci. Sect. Am. Statist. Ass., 50-55.
33. MacEachern, S. N. Müller, P. (1998) Estimating mixture of Dirichlet process models. J. Computnl Graph. Statist., 7, 223 239.
34. Marin, J. M., Mengersen, K. Robert, C. P. (2005) Bayesian modelling and inference on mixtures of distributions. In Handbook of Statistics, vol. 25 (eds D. Dey C. R. Rao pp. 459 507. Amsterdam : North-Holland.
35. Petrone, S. Raftery, A. E. (1997) A note on the Dirichlet process prior in Bayesian nonparametric inference with partial exchangeability. Statist. Probab. Lett., 36, 69 83.
36. Pitman, J. (1995) Exchangeable and partially exchangeable random partitions. Probab. Theory Reltd Flds, 102, 145 158.
37. Pitman, J. (1996) Some developments of the Blackwell-MacQueen urn scheme. In Statistics, Probability and Game Theory: Papers in Honor of David Blackwell (eds T. S. Ferguson, L. S. Shapley J. B. MacQueen pp. 245 267. Hayward : Institute of Mathematical Statistics.
38. Pitman, J. (2003) Poisson-Kingman partitions. In Science and Statistics: a Festschrift for Terry Speed (ed. D. R. Goldstein pp. 1 35. Hayward : Institute of Mathematical Statistics.
39. Pitman, J. (2006) Combinatorial stochastic processes. Lect. Notes Math., 1875.
40. Prünster, I. (2002) Random probability measures derived from increasing additive processes and their application to Bayesian statistics. PhD Thesis. University of Pavia, Pavia.
41. Quintana, F. A. (1998) Nonparametric Bayesian analysis for assessing homogeneity in k×l contingency tables with fixed right margin totals. J. Am. Statist. Ass., 93, 1140 1149.
42. Quintana, F. A. Iglesias, P. L. (2003) Bayesian clustering and product partition models. J. R. Statist. Soc. B, 65, 557 574.
43. Regazzini, E., Lijoi, A. Prünster, I. (2003) Distributional results for means of random measures with independent increments. Ann. Statist., 31, 560 585.