메뉴 건너뛰기




Volumn 33, Issue 2, 2005, Pages 647-660

Functionals of Dirichlet processes, the Cifarelli-Regazzini identity and Beta-Gamma processes

Author keywords

Beta Gamma processes; Dirichlet process; Gamma process; Markov Krein identity

Indexed keywords


EID: 22944482165     PISSN: 00905364     EISSN: None     Source Type: Journal    
DOI: 10.1214/009053604000001237     Document Type: Review
Times cited : (21)

References (26)
  • 1
    • 0000708831 scopus 로고
    • Mixtures of Dirichlet processes with applications to Bayesian nonparametric problems
    • ANTONI AK, C. E. (1974). Mixtures of Dirichlet processes with applications to Bayesian nonparametric problems. Ann. Statist. 2 1152-1174.
    • (1974) Ann. Statist. , vol.2 , pp. 1152-1174
    • Antoniak, C.E.1
  • 2
    • 0002617436 scopus 로고
    • Ferguson distributions via Pólya urn schemes
    • BLACKWELL, D. and MACQUEEN, J. B. (1973). Ferguson distributions via Pólya urn schemes. Ann. Statist. 1 353-355.
    • (1973) Ann. Statist. , vol.1 , pp. 353-355
    • Blackwell, D.1    Macqueen, J.B.2
  • 3
    • 0034287160 scopus 로고    scopus 로고
    • Some new results for Dirichlet priors
    • CIFARELLI, D. M. and MELILLI, E. (2000). Some new results for Dirichlet priors. Ann. Statist. 28 1390-1413.
    • (2000) Ann. Statist. , vol.28 , pp. 1390-1413
    • Cifarelli, D.M.1    Melilli, E.2
  • 4
    • 0000771631 scopus 로고
    • Distribution functions of means of a Dirichlet process
    • CIFARELLl, D. M. and REG AZZINI, E. (1990). Distribution functions of means of a Dirichlet process. Ann. Statist. 18 429-442.
    • (1990) Ann. Statist. , vol.18 , pp. 429-442
    • Cifarelll, D.M.1    Regazzini, E.2
  • 5
    • 0002284829 scopus 로고    scopus 로고
    • Iterated random functions
    • DIACONIS, P. and FREEDMAN, D. A. (1999). Iterated random functions. SIAM Rev. 41 45-76.
    • (1999) SIAM Rev. , vol.41 , pp. 45-76
    • Diaconis, P.1    Freedman, D.A.2
  • 6
    • 0002694683 scopus 로고    scopus 로고
    • Some new tools for Dirichlet priors
    • (J. M. Bernardo, J. O. Berger, A. P. Dawid and A. F. M. Smith, eds.), Oxford Univ. Press
    • DIACONIS, P. and KEMPERMAN, J. (1996). Some new tools for Dirichlet priors. In Bayesian Statistics 5 (J. M. Bernardo, J. O. Berger, A. P. Dawid and A. F. M. Smith, eds.) 97-106, Oxford Univ. Press.
    • (1996) Bayesian Statistics , vol.5 , pp. 97-106
    • Diaconis, P.1    Kemperman, J.2
  • 7
    • 0009147290 scopus 로고
    • The tails of probabilities chosen from a Dirichlet prior
    • DOSS, H. and SELLKE, T. (1982). The tails of probabilities chosen from a Dirichlet prior. Ann. Statist. 10 1302-1305.
    • (1982) Ann. Statist. , vol.10 , pp. 1302-1305
    • Doss, H.1    Sellke, T.2
  • 8
    • 0001406414 scopus 로고    scopus 로고
    • Algebraic properties of beta and gamma distributions, and applications
    • DUFRESNE, D. (1998). Algebraic properties of beta and gamma distributions, and applications. Adv. in Appl. Math. 20 285-299.
    • (1998) Adv. in Appl. Math. , vol.20 , pp. 285-299
    • Dufresne, D.1
  • 9
    • 0015310384 scopus 로고
    • The sampling theory of selectively neutral alleles
    • EWENS, W. J. (1972). The sampling theory of selectively neutral alleles. Theoret. Population Biology 387-112.
    • (1972) Theoret. Population Biology , vol.3 , pp. 87-112
    • Ewens, W.J.1
  • 10
    • 84974110694 scopus 로고
    • Linear functionals and Markov chains associated with the Dirichlet processes
    • FEIGIN, P. and TWEEDIE, R. (1989). Linear functionals and Markov chains associated with the Dirichlet processes. Math. Proc. Cambridge Philos. Soc. 105 579-585.
    • (1989) Math. Proc. Cambridge Philos. Soc. , vol.105 , pp. 579-585
    • Feigin, P.1    Tweedie, R.2
  • 11
    • 0001120413 scopus 로고
    • A Bayesian analysis of some nonparametric problems
    • FERGUSON, T. S. (1973). A Bayesian analysis of some nonparametric problems. Ann. Statist. 1 209-230.
    • (1973) Ann. Statist. , vol.1 , pp. 209-230
    • Ferguson, T.S.1
  • 12
    • 0000202123 scopus 로고
    • On the asymptotic behavior of Bayes estimates in the discrete case
    • FREEDMAN, D. A. (1963). On the asymptotic behavior of Bayes estimates in the discrete case. Ann. Math. Statist. 34 1386-1403.
    • (1963) Ann. Math. Statist. , vol.34 , pp. 1386-1403
    • Freedman, D.A.1
  • 13
    • 0035528673 scopus 로고    scopus 로고
    • The history of the Dirichlet and Liouville distributions
    • GUPTA, R. D. and RICHARDS, D. ST. P. (2001). The history of the Dirichlet and Liouville distributions. Internat. Statist. Rev. 69 433-446.
    • (2001) Internat. Statist. Rev. , vol.69 , pp. 433-446
    • Gupta, R.D.1    Richards, D.St.P.2
  • 14
    • 0038785429 scopus 로고    scopus 로고
    • Topics in non-parametric Bayesian statistics
    • (P. J. Green, N. L. Hjort and S. Richardson, eds.). Oxford Univ. Press
    • HJORT, N. L. (2003). Topics in non-parametric Bayesian statistics. In Highly Structured Stochastic Systems (P. J. Green, N. L. Hjort and S. Richardson, eds.) 455-487. Oxford Univ. Press.
    • (2003) Highly Structured Stochastic Systems , pp. 455-487
    • Hjort, N.L.1
  • 18
    • 3042549467 scopus 로고    scopus 로고
    • Means of a Dirichlet process and multiple hypergeometric functions
    • LIJOI, A. and REGAZZINI, E. (2004). Means of a Dirichlet process and multiple hypergeometric functions. Ann. Probab. 32 1469-1495.
    • (2004) Ann. Probab. , vol.32 , pp. 1469-1495
    • Lijoi, A.1    Regazzini, E.2
  • 19
    • 0001876649 scopus 로고
    • On a class of Bayesian nonparametric estimates. I
    • LO, A. Y. (1984). On a class of Bayesian nonparametric estimates. I. Density estimates Ann. Statist. 12 351-357.
    • (1984) Density Estimates Ann. Statist. , vol.12 , pp. 351-357
    • Lo, A.Y.1
  • 20
    • 0000396415 scopus 로고
    • On a class of Bayesian nonparametric estimates. II. Hazard rate estimates
    • LO, A. Y. and WENG, C.-S. (1989). On a class of Bayesian nonparametric estimates. II. Hazard rate estimates. Ann. Inst. Statist. Math. 41 227-245.
    • (1989) Ann. Inst. Statist. Math. , vol.41 , pp. 227-245
    • Lo, A.Y.1    Weng, C.-S.2
  • 21
    • 0000130672 scopus 로고    scopus 로고
    • Some developments of the Blackwell-MacQueen urn scheme
    • (T. S. Ferguson, L. S. Shapley and J. B. MacQueen, eds.). IMS, Hayward, CA
    • 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.
    • (1996) Statistics, Probability and Game Theory , pp. 245-267
    • Pitman, J.1
  • 22
    • 0036432576 scopus 로고    scopus 로고
    • Theory and numerical analysis for exact distributions of functionals of a Dirichlet process
    • REGAZZINI, E., GUGLIELMI, A. and DI NUNNO, G. (2002). Theory and numerical analysis for exact distributions of functionals of a Dirichlet process. Ann. Statist. 30 1376-1411.
    • (2002) Ann. Statist. , vol.30 , pp. 1376-1411
    • Regazzini, E.1    Guglielmi, A.2    Di Nunno, G.3
  • 23
    • 0038702581 scopus 로고    scopus 로고
    • Distributional results for means of normalized random measures with independent increments
    • REGAZZINI, E., LIJOI, A. and PRÜNSTER, I. (2003). Distributional results for means of normalized random measures with independent increments. Ann. Statist. 31 560-585.
    • (2003) Ann. Statist. , vol.31 , pp. 560-585
    • Regazzini, E.1    Lijoi, A.2    Prünster, I.3
  • 24
    • 0000720609 scopus 로고
    • A constructive definition of Dirichlet priors
    • SETHURAMAN, J. (1994). A constructive definition of Dirichlet priors. Statist. Sinica 4 639-650.
    • (1994) Statist. Sinica , vol.4 , pp. 639-650
    • Sethuraman, J.1
  • 26
    • 22944440075 scopus 로고    scopus 로고
    • In Russian. Translation in
    • [In Russian. Translation in J. Math. Sci. (N. Y.) 121 (2004) 2303-2310.]
    • (2004) J. Math. Sci. (N. Y.) , vol.121 , pp. 2303-2310


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.