Poisson calculus for spatial neutral to the right processes

Annals of Statistics

Volumn 34, Issue 1, 2006, Pages 416-440

  James, Lancelot F ^a  

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

Author keywords

Bayesian nonparametrics; Inhomogeneous Poisson process; L vy processes; Neutral to the right processes; Regenerative compositions; Survival analysis

Indexed keywords

EID: 33744827696     PISSN: 00905364     EISSN: None     Source Type: Journal    
DOI: 10.1214/009053605000000732     Document Type: Article

References (41)

1. ANTONIAK, C. E. (1974). Mixtures of Dirichlet processes with applications to Bayesian non-parametric problems. Ann. Statist. 2 1152-1174. MR0365969
2. BERTOIN, J. and YOR, M. (2001). On subordinators, self-similar Markov processes and some factorizations of the exponential variable. Electron. Comm. Probab. 6 95-106. MR1871698
3. BLACKWELL, D. and MACQUEEN, J. B. (1973). Ferguson distributions via Póly a urn schemes. Ann. Statist. 1 353-355. MR0362614
4. BRIX, A. (1999). Generalized gamma measures and shot-noise Cox processes. Adv. in Appl. Probab. 31 929-953. MR1747450
5. CARMONA, P., PETIT, F. and YOR, M. (1997). On the distribution and asymptotic results for exponential functionals of Lévy processes. In Exponential Functional and Principal Values Related to Brownian Motion (M. Yor, ed.) 73-130. Biblioteca de la Revista Matematica Iberoamericana, Madrid. MR1648657
6. DALEY, D. J. and VERE-JONES, D. (1988). An Introduction to the Theory of Point Processes. Springer, New York. MR0950166
7. DEY, J. (1999). Some properties and characterizations of neutral-to-the-right priors and beta processes. Ph.D. dissertation, Michigan State Univ.
8. DEY, J., ERICKSON, R. V. and RAMAMOORTHI, R. V. (2003). Some aspects of neutral to right priors. Internat. Statist. Rev. 71 383-401.
9. DOKSUM, K. A. (1974). Tailfree and neutral random probabilities and their posterior distributions. Ann. Probab. 2 183-201. MR0373081
10. DONNELLY, P. and JOYCE, P. (1991). Consistent ordered sampling distributions: Characterization and convergence. Adv. in Appl. Probab. 23 229-258. MR1104078
11. EPIFANI, I., LIJOI, A. and PRÜNSTER, I. (2003). Exponential functionals and means of neutral-to-the-right priors. Biometrika 90 791-808. MR2024758
12. EWENS, W. J. (1972). The sampling theory of selectively neutral alleles. Theoret. Population Biology 3 87-112. MR0325177
13. FERGUSON, T. S. (1973). A Bayesian analysis of some nonparametric problems. Ann. Statist. 1 209-230. MR0350949
14. FERGUSON, T. S. (1974). Prior distributions on spaces of probability measures. Ann. Statist. 2 615-629. MR0438568
15. FERGUSON, T. S. and PHADIA, E. (1979). Bayesian nonparametric estimation based on censored data. Ann. Statist. 7 163-186. MR0515691
16. FREEDMAN, D. A. (1963). On the asymptotic behavior of Bayes estimates in the discrete case. Ann. Math. Statist. 34 1386-1403. MR0158483
17. GNEDIN, A. V. (1997). The representation of composition structures. Ann. Probab. 25 1437-1450. MR1457625
18. GNEDIN, A. V. and PITMAN, J. (2005). Regenerative composition structures. Ann. Probab. 33 445-479. MR2122798
19. GNEDIN, A. V., PITMAN, J. and YOR, M. (2006). Asymptotic laws for regenerative compositions: Gamma subordinators and the like. Probab. Theory Related Fields. To appear.
20. GNEDIN, A. V., PITMAN, J. and YOR, M. (2006). Asymptotic laws for compositions derived from transformed subordinators. Ann Probab. 34. To appear.
21. HJORT, N. L. (1990). Nonparametric Bayes estimators based on beta processes in models for life history data. Ann. Statist. 18 1259-1294. MR1062708
22. ISHWARAN, H. and JAMES, L. F. (2001). Gibbs sampling methods for stick-breaking priors. J. Amer. Statist. Assoc. 96 161-173. MR1952729
23. ISHWARAN, H. and JAMES, L. F. (2003). Generalized weighted Chinese restaurant processes for species sampling mixture models. Statist. Sinica 13 1211-1235. MR2026070
24. JAMES, L. F. (2002). Poisson process partition calculus with applications to exchangeable models and Bayesian nonparametrics. Available at arxiv.org/abs/math.pr/0205093.
25. JAMES, L. F. (2003). Poisson calculus for spatial neutral to the right processes. Available at ihome.ust.hk/~lancelot.
26. JAMES, L. F. (2005). Bayesian Poisson process partition calculus with an application to Bayesian Lévy moving averages. Ann. Statist. 33 1771-1799. MR2166562
27. JAMES, L. F. and KWON, S. (2000). A Bayesian nonparametric approach for the joint distribution of survival time and mark variables under univariate censoring. Technical report, Dept. Mathematical Sciences, Johns Hopkins Univ.
28. KALLENBERG, O. (2002). Foundations of Modern Probability, 2nd ed. Springer, New York. MR1876169
29. KIM, Y. (1999). Nonparametric Bayesian estimators for counting processes. Ann. Statist. 27 562-588. MR1714717
30. KINGMAN, J. F. C. (1993). Poisson Processes. Oxford Univ. Press, New York. MR1207584
31. LAST, G. and BRANDT, A. (1995). Marked Point Processes on the Real Line: The Dynamic Approach. Springer, New York. MR1353912
32. Lo, A. Y. (1984). On a class of Bayesian nonparametric estimates. I. Density estimates. Ann. Statist. 12 351-357. MR0733519
33. Lo, A. Y. (1993). A Bayesian bootstrap for censored data. Ann. Statist. 21 100-123. MR1212168
34. PITMAN, J. (1996). Some developments of the Blackwell-MacQueen urn scheme. In Statistics, Probability and Game Theory (T. S. Ferguson, L. S. Shapley and J. B. MacQueen, eds.) 245-267. IMS, Hayward, CA. MR1481784
35. PITMAN, J. (1997). Partition structures derived from Brownian motion and stable subordinators. Bernoulli 3 79-96. MR 1466546
36. PITMAN, J. (1999). Coalescents with multiple collisions. Ann. Probab. 27 1870-1902. MR1742892
37. PITMAN, J. (2002). Combinatorial stochastic processes. Technical Report 621, Dept. Statistics, Univ. California, Berkeley. Available at stat-www.berkeley.edu/users/pitman/bibliog.html.
38. PITMAN, J. (2003). Poisson-Kingman partitions. In Statistics and Science: A Festschrift for Terry Speed (D. R. Goldstein, ed.) 1-34. IMS, Beachwood, OH. MR2004330
39. PITMAN, J. and YOR, M. (1997). The two-parameter Poisson-Dirichlet distribution derived from a stable subordinator. Ann. Probab. 25 855-900. MR1434129
40. REGAZZINI, E., LIJOI, A. and PRÜNSTER, I. (2003). Distributional results for means of normalized random measures with independent increments. Ann. Statist. 31 560-585. MR 1983542
41. WALKER, S. and MULIERE, P. (1997). Beta-Stacy processes and a generalization of the Pólyaurn scheme. Ann. Statist. 25 1762-1780. MR 1463574