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Volumn 12, Issue 3, 2002, Pages 941-963

Dirichlet prior sieves in finite normal mixtures

Author keywords

Bose Einstein distribution; Dirichlet process; Identification; Method of sieves; Random probability measure; Relative entropy; Weak convergence

Indexed keywords


EID: 0036661094     PISSN: 10170405     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article
Times cited : (91)

References (44)
  • 3
    • 2242491935 scopus 로고    scopus 로고
    • Computational and inferential difficulties with mixture posterior distributions
    • Celeux, G., Hurn, M and Robert, C.P. (2000). Computational and inferential difficulties with mixture posterior distributions. J. Amer. Assoc. 95, 957-970.
    • (2000) J. Amer. Assoc. , vol.95 , pp. 957-970
    • Celeux, G.1    Hurn, M.2    Robert, C.P.3
  • 4
    • 21844493268 scopus 로고
    • Optimal rate of convergence for finite mixture models
    • Chen, J. (1995). Optimal rate of convergence for finite mixture models. Ann. Statist. 23, 221-233.
    • (1995) Ann. Statist. , vol.23 , pp. 221-233
    • Chen, J.1
  • 5
    • 0041974049 scopus 로고
    • Marginal likelihood from the Gibbs output
    • Chib, S. (1995). Marginal likelihood from the Gibbs output. J. Amer. Statist. Assoc. 90, 1313-1321.
    • (1995) J. Amer. Statist. Assoc. , vol.90 , pp. 1313-1321
    • Chib, S.1
  • 7
    • 0001244941 scopus 로고
    • Estimation of finite mixture distributions through Bayesian sampling
    • Diebolt, J. and Robert, C.P. (1994). Estimation of finite mixture distributions through Bayesian sampling. J. Roy. Statist. Soc. Ser. B 56, 363-375.
    • (1994) J. Roy. Statist. Soc. Ser. B , vol.56 , pp. 363-375
    • Diebolt, J.1    Robert, C.P.2
  • 9
    • 21344479762 scopus 로고
    • Estimating normal means with a Dirichlet process prior
    • Escobar, M.D. (1994). Estimating normal means with a Dirichlet process prior. J. Amer. Statist. Assoc. 89, 268-277.
    • (1994) J. Amer. Statist. Assoc. , vol.89 , pp. 268-277
    • Escobar, M.D.1
  • 10
    • 84950937290 scopus 로고
    • Bayesian density estimation and inference using mixtures
    • Escobar, M.D. and West, M. (1995). Bayesian density estimation and inference using mixtures. J. Amer. Statist. Assoc. 90, 577-588.
    • (1995) J. Amer. Statist. Assoc. , vol.90 , pp. 577-588
    • Escobar, M.D.1    West, M.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
    • 0000780135 scopus 로고
    • Prior distributions on spaces of probability measures
    • Ferguson, T.S. (1974). Prior distributions on spaces of probability measures. Ann. Statist. 2, 615-629.
    • (1974) Ann. Statist. , vol.2 , pp. 615-629
    • Ferguson, T.S.1
  • 13
    • 0001787029 scopus 로고
    • Bayesian density estimation by mixtures of normal distributions
    • Edited by M.H. Rizvi, J. Rustagi and D. Siegmund, Academic Press, New York
    • Ferguson, T.S. (1983). Bayesian density estimation by mixtures of normal distributions. In Recent Advances in Statistics (Edited by M.H. Rizvi, J. Rustagi and D. Siegmund), 287-302. Academic Press, New York.
    • (1983) Recent Advances in Statistics , pp. 287-302
    • Ferguson, T.S.1
  • 14
    • 0001414599 scopus 로고
    • Nonparametric maximum likelihood estimation by the method of sieves
    • Geman, S. and Hwang, C.R. (1982). Nonparametric maximum likelihood estimation by the method of sieves. Ann. Statist. 10, 401-414.
    • (1982) Ann. Statist. , vol.10 , pp. 401-414
    • Geman, S.1    Hwang, C.R.2
  • 15
    • 0034237946 scopus 로고    scopus 로고
    • Rates of convergence for the Gaussian mixture sieve
    • Genovese, C.R. and Wasserman, L. (2000). Rates of convergence for the Gaussian mixture sieve. Ann. Statist. 028, 1105-1127.
    • (2000) Ann. Statist. , vol.28 , pp. 1105-1127
    • Genovese, C.R.1    Wasserman, L.2
  • 16
    • 0033074585 scopus 로고    scopus 로고
    • Posterior consistency of Dirichlet mixtures in density estimation
    • Ghosal, S., Ghosh, J.K. and Ramamoorthi, R.V. (1999). Posterior consistency of Dirichlet mixtures in density estimation. Ann. Statist. 27, 143-158.
    • (1999) Ann. Statist. , vol.27 , pp. 143-158
    • Ghosal, S.1    Ghosh, J.K.2    Ramamoorthi, R.V.3
  • 17
    • 0035470893 scopus 로고    scopus 로고
    • Entropies and rates of convergence for maximum likelihood and Bayes estimation for mixtures of normal densities
    • Ghosal, S. and van der Vaart, A.W. (2001). Entropies and rates of convergence for maximum likelihood and Bayes estimation for mixtures of normal densities. Ann. Statist. 29, 1233-1263.
    • (2001) Ann. Statist. , vol.29 , pp. 1233-1263
    • Ghosal, S.1    Van der Vaart, A.W.2
  • 18
    • 0035531242 scopus 로고    scopus 로고
    • Modelling heterogeneity with and without the Dirichlet process
    • Green, P., and Richardson, S. (2001). Modelling heterogeneity with and without the Dirichlet process. Scand. J. Statist. 28, 355-377.
    • (2001) Scand. J. Statist. , vol.28 , pp. 355-377
    • Green, P.1    Richardson, S.2
  • 20
    • 1842816362 scopus 로고    scopus 로고
    • Gibbs sampling methods for stick-breaking priors
    • Ishwaran, H. and James, L.F. (2001). Gibbs sampling methods for stick-breaking priors. J. Amer. Statist. Assoc. 96, 161-173.
    • (2001) J. Amer. Statist. Assoc. , vol.96 , pp. 161-173
    • Ishwaran, H.1    James, L.F.2
  • 21
    • 1542469706 scopus 로고    scopus 로고
    • Bayesian model selection in finite mixtures by marginal density decompositions
    • 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.
    • (2001) J. Amer. Statist. Assoc. , vol.96 , pp. 1316-1332
    • Ishwaran, H.1    James, L.F.2    Sun, J.3
  • 22
    • 0001677650 scopus 로고    scopus 로고
    • Markov chain Monte Carlo in approximate Dirichlet and beta two-parameter process hierarchical models
    • Ishwaran, H. and Zarepour, M. (2000). Markov chain Monte Carlo in approximate Dirichlet and beta two-parameter process hierarchical models. Biometrika 87, 371-390.
    • (2000) Biometrika , vol.87 , pp. 371-390
    • Ishwaran, H.1    Zarepour, M.2
  • 23
    • 0036623091 scopus 로고    scopus 로고
    • Exact and approximate sum-representations for the Dirichlet process
    • Ishwaran, H. and Zarepour, M. (2002). Exact and approximate sum-representations for the Dirichlet process. Canad. J. Statist. 30, 1-15.
    • (2002) Canad. J. Statist. , vol.30 , pp. 1-15
    • Ishwaran, H.1    Zarepour, M.2
  • 24
    • 0001698345 scopus 로고
    • On the optimum rate of transmitting information
    • Kemperman, J.H.B. (1969). On the optimum rate of transmitting information. Ann. Math. Statist. 40, 2156-2177.
    • (1969) Ann. Math. Statist. , vol.40 , pp. 2156-2177
    • Kemperman, J.H.B.1
  • 27
    • 0002033276 scopus 로고
    • Computations of mixtures of Dirichlet processes
    • Kuo, L. (1986). Computations of mixtures of Dirichlet processes. SIAM J. Sci. Statist. Comput. 7, 60-71.
    • (1986) SIAM J. Sci. Statist. Comput. , vol.7 , pp. 60-71
    • Kuo, L.1
  • 29
    • 0001876649 scopus 로고
    • On a class of Bayesian nonparametric estimates: I. Density estimates
    • Lo, A.Y. (1984). On a class of Bayesian nonparametric estimates: I. Density estimates. Ann. Statist. 12, 351-357.
    • (1984) Ann. Statist. , vol.12 , pp. 351-357
    • Lo, A.Y.1
  • 30
    • 84972808999 scopus 로고
    • Estimating normal means with a conjugate style Dirichlet process prior
    • MacEachern, S.N. (1994). Estimating normal means with a conjugate style Dirichlet process prior. Comm. Statist. Simulation Comput. 23, 727-741.
    • (1994) Comm. Statist. Simulation Comput. , vol.23 , pp. 727-741
    • Maceachern, S.N.1
  • 32
    • 0003937579 scopus 로고
    • Technical report No. 18, Dipartimento di Economia Politica e Metodi Quantitativi, Università degli Sudi di Pavia
    • Muliere P. and Secchi, P. (1995). A note on a proper Bayesian bootstrap. Technical report No. 18, Dipartimento di Economia Politica e Metodi Quantitativi, Università degli Sudi di Pavia.
    • (1995) A note on a proper Bayesian bootstrap
    • Muliere, P.1    Secchi, P.2
  • 33
    • 77950032550 scopus 로고    scopus 로고
    • Markov chain sampling methods for Dirichlet process mixture models
    • Neal, R.M. (2000). Markov chain sampling methods for Dirichlet process mixture models. J. Comput. Graph. Statist. 9, 249-265.
    • (2000) J. Comput. Graph. Statist. , vol.9 , pp. 249-265
    • Neal, R.M.1
  • 34
    • 0000130672 scopus 로고    scopus 로고
    • Some developments of the Blackwell-MacQueen urn scheme
    • Statistics, Probability and Game Theory (Edited by T.S. Ferguson, L.S. Shapley and J.B. MacQueen), Hayward CA: Institute of Mathematical Statistics
    • 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. Hayward CA: Institute of Mathematical Statistics.
    • (1996) IMS Lecture Notes-Monograph series , vol.30 , pp. 245-267
    • Pitman, J.1
  • 37
    • 18244378520 scopus 로고    scopus 로고
    • On Bayesian analysis of mixtures with an unknown number of components
    • Richardson, S. and Green, P.J. (1997). On Bayesian analysis of mixtures with an unknown number of components. J. Roy. Statist. Soc. Ser. B 59, 731-792.
    • (1997) J. Roy. Statist. Soc. Ser. B , vol.59 , pp. 731-792
    • Richardson, S.1    Green, P.J.2
  • 38
    • 0000198157 scopus 로고
    • Semiparametric estimation of normal mixture densities
    • Roeder, K. (1992). Semiparametric estimation of normal mixture densities. Ann. Statist. 20, 929-943.
    • (1992) Ann. Statist. , vol.20 , pp. 929-943
    • Roeder, K.1
  • 39
    • 21744460005 scopus 로고    scopus 로고
    • Practical Bayesian density estimation using mixtures of normals
    • Roeder, K. and Wasserman, L. (1997). Practical Bayesian density estimation using mixtures of normals. J. Amer. Statist. Assoc. 92, 894-902.
    • (1997) J. Amer. Statist. Assoc. , vol.92 , pp. 894-902
    • Roeder, K.1    Wasserman, L.2
  • 40
    • 21844489169 scopus 로고
    • Convergence rate of sieve estimates
    • Shen, X. and Wong, W.H. (1994). Convergence rate of sieve estimates. Ann. Statist. 22, 580-615.
    • (1994) Ann. Statist. , vol.22 , pp. 580-615
    • Shen, X.1    Wong, W.H.2
  • 41
    • 0011013254 scopus 로고
    • On the mixture of distributions
    • Teicher H. (1960). On the mixture of distributions. Ann. Math. Statist. 31, 55-73.
    • (1960) Ann. Math. Statist. , vol.31 , pp. 55-73
    • Teicher, H.1
  • 42
    • 0000607206 scopus 로고
    • Identifiability of finite mixtures
    • Teicher H. (1963). Identifiability of finite mixtures. Ann. Math. Statist. 32, 1265-1269.
    • (1963) Ann. Math. Statist. , vol.32 , pp. 1265-1269
    • Teicher, H.1
  • 43
    • 21844517288 scopus 로고
    • Probability inequalities for likelihood ratios and convergence rates of sieve MLEs
    • Wong, W.H. and Shen, X. (1995). Probability inequalities for likelihood ratios and convergence rates of sieve MLEs. Ann. Statist. 23, 339-363.
    • (1995) Ann. Statist. , vol.23 , pp. 339-363
    • Wong, W.H.1    Shen, X.2
  • 44
    • 0002055609 scopus 로고
    • Fourier methods for estimating mixing densities and distributions
    • Zhang, C.H. (1990). Fourier methods for estimating mixing densities and distributions. Ann. Statist. 18, 806-831.
    • (1990) Ann. Statist. , vol.18 , pp. 806-831
    • Zhang, C.H.1


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