Bayesian methods for partial stochastic orderings

Biometrika

Volumn 90, Issue 2, 2003, Pages 303-317

  Hoff, Peter D ^a  

^a UNIVERSITY OF WASHINGTON   (United States)

Author keywords

Dirichlet process prior; Latent variable model; Mixture model; Nonparametric Bayes; Quantitative trait locus

Indexed keywords

ANIMALIA;

EID: 3843074062     PISSN: 00063444     EISSN: None     Source Type: Journal    
DOI: 10.1093/biomet/90.2.303     Document Type: Article

References (32)

1. ARJAS, E. & GASBARRA, D. (1996). Bayesian inference of survival probabilities, under stochastic ordering constraints. J. Am. Statist. Assoc. 91, 1101-9.
2. BLACKWELL, D. (1973). Discreteness of Ferguson selections. Ann. Statist. 1, 356-8.
3. BLACKWELL, D. & MACQUEEN, J. B. (1973). Ferguson distributions via Pólya urn schemes. Ann. Statist. 1, 353-5.
4. BRUNK, H. D., FRANCK, W. E., HANSON, D. L. & HOGG, R. V. (1966). Maximum likelihood estimation of the distributions of two stochastically ordered random variables. J. Am. Statist. Assoc. 61, 1067-80.
5. DRINKWATER, N. R. & KLOTZ, J. H. (1981). Statistical methods for the analysis of tumor multiplicity data. Cancer Res. 41, 113-9.
6. DYKSTRA, R. L. & FELTZ, C. J. (1989). Nonparametric maximum likelihood estimation of survival functions with a general stochastic ordering and its dual. Biometrika 76, 331-41.
7. ESARY, J. D., PROSCHAN, F. & WALKUP, D. W. (1967). Association of random variables, with applications. Ann. Math. Statist. 38, 1466-74.
8. ESCOBAR, M. D. & WEST, M. (1995). Bayesian density estimation and inference using mixtures. J. Am. Statist. Assoc. 90, 577-88.
9. FERGUSON, T. S. (1973). A Bayesian analysis of some nonparametric problems. Ann. Statist. 1, 209-30.
10. FERGUSON, T. S. (1974). Prior distributions on spaces of probability measures. Ann. Statist. 2, 615-29.
11. FILL, J. A. & MACHIDA, M. (2001). Stochastic monotonicity and realizable monotonicity. Ann. Prob. 29. 938-78.
12. GANGNON, R. E. & KING, W. (2002). Minimum distance estimation of the distribution functions of stochastically ordered random variables. Appl. Statist. 51, 485-92.
13. GELFAND, A. E. & KOTTAS, A. (2001). Nonparametric Bayesian modeling for stochastic order. Ann. Inst. Statist. Math. 3, 865-76.
14. GELMAN, A. & MENG, X.-L. (1998). Simulating normalizing constants: from importance sampling to bridge sampling to path sampling. Statist. Sci. 13, 163-85.
15. HOFF, P. (2000). Constrained nonparametric maximum likelihood via mixtures. J. Comp. Graph. Statist. 9. 633-41.
16. HOFF, P., HALBERG, R., SHEDLOVSKY, A., DOVE, W. & NEWTON, M. (2001). Identifying carriers of a genetic modifier using nonparametric Bayes methods. In Case Studies in Bayesian Statistics, 5, Ed. C. Gatsonis, R. E. Kass, B. Carlin, A. Carriquiry, A. Gelman, I. Verdinelli and M. West, pp. 327-42. New York: Springer-Verlag.
17. HOLLAND, P. W. & WANG, Y. J. (1987). Dependence function for continuous bivariate densities. Commun. Statist. A, 16, 863-76.
18. JOGDEO, K. (1978). On a probability bound of Marshall and Olkin. Ann. Statist. 6, 232-4.
19. KULLBACK., S. (1968). Probability densities with given marginals. Ann. Math. Statist. 39, 1236-43.
20. LAVINE, M. (1992). Some aspects of Pólya tree distributions for statistical modelling. Ann. Statist. 20, 1222-35.
21. LINDSAY, B. G. (1995). Mixture Models: Theory, Geometry and Applications. Hayward, CA: Institute of Mathematical Statistics.
22. MACEACHERN, S. N. & MÜLLER, P. (1998). Estimating mixture of Dirichlet process models. J. Comp. Graph. Statist. 7, 223-38.
23. MAULDIN, R. D., SUDDERTH, W. D. & WILLIAMS, S. C. (1992). Pólya trees and random distributions. Ann. Statist. 20, 1203-21.
24. MENG, X.-L. & WONG, W. H. (1996). Simulating ratios of normalizing constants via a simple identity: a theoretical exploration. Statist. Sinica 6, 831-60.
25. NEAL, R. M. (2000), Markov chain sampling methods for Dirichlet process mixture models. J. Comp. Graph. Statist. 9, 249-65.
26. PLACKETT, R. L. (1981). The Analysis of Categorical Data, 2nd ed. New York: Macmillan.
27. SCHWEIZER, B. & WOLFF, E. F. (1981). On nonparametric measures of dependence for random variables. Ann. Statist. 9, 879-85.
28. SETHURAMAN, J. (1994). A constructive definition of Dirichlet priors. Statist. Sinica 4, 639-50.
29. SETHURAMAN, J. & TIWARI, R. C. (1982). Convergence of Dirichlet measures and interpretation of their parameter. In Statistical Decision Theory and Related Topics, III, 2, Ed. S. Gupta and J. Berger, pp. 305-15. New York: Academic Press.
30. SKLAR, M. (1959). Fonctions de répartition à n dimensions et leurs marges. Publ. Inst. Statist. Univ. Paris 8, 229-31.
31. STRASSEN, V. (1965). The existence of probability measures with given marginals. Ann. Math. Statist. 36, 423-39.
32. WANG, Y. J. (1993). Construction of continuous bivariate density functions. Statist. Sinica 3, 173-87.