메뉴 건너뛰기




Volumn 28, Issue 3, 2013, Pages 313-334

Modeling with normalized random measure mixture models

Author keywords

Bayesian nonparametrics; Clustering; Completely random measure; Density estimation; Dirichlet process; Increasing additive process; Latent variables; Mixture model; Normalized generalized gamma process; Normalized inverse Gaussian process; Normalized random measure; Normalized stable process.

Indexed keywords


EID: 84878550348     PISSN: 08834237     EISSN: None     Source Type: Journal    
DOI: 10.1214/13-STS416     Document Type: Article
Times cited : (64)

References (49)
  • 1
    • 73149115734 scopus 로고    scopus 로고
    • Bayesian density estimation and model selection using nonparametric hierarchical mixtures
    • MR2580918
    • ARGIENTO, R., GUGLIELMI, A. and PIEVATOLO, A. (2010). Bayesian density estimation and model selection using nonparametric hierarchical mixtures. Comput. Statist. Data Anal. 54 816-832. MR2580918
    • (2010) Comput. Statist. Data Anal. , vol.54 , pp. 816-832
    • Argiento, R.1    Guglielmi, A.2    Pievatolo, A.3
  • 2
    • 0000257224 scopus 로고
    • Empirical Bayes estimation of a binomial parameter via mixtures of Dirichlet processes
    • MR0527491
    • BERRY, D. A. and CHRISTENSEN, R. (1979). Empirical Bayes estimation of a binomial parameter via mixtures of Dirichlet processes. Ann. Statist. 7 558-568. MR0527491
    • (1979) Ann. Statist. , vol.7 , pp. 558-568
    • Berry, D.A.1    Christensen, R.2
  • 3
    • 0001203039 scopus 로고
    • Discreteness of Ferguson selections
    • MR0348905
    • BLACKWELL, D. (1973). Discreteness of Ferguson selections. Ann. Statist. 1 356-358. MR0348905
    • (1973) Ann. Statist. , vol.1 , pp. 356-358
    • Blackwell, D.1
  • 4
    • 0033333437 scopus 로고    scopus 로고
    • Generalized gamma measures and shot-noise Cox processes
    • MR1747450
    • BRIX, A. (1999). Generalized gamma measures and shot-noise Cox processes. Adv. in Appl. Probab. 31 929-953. MR1747450
    • (1999) Adv. in Appl. Probab. , vol.31 , pp. 929-953
    • Brix, A.1
  • 5
    • 0004045887 scopus 로고
    • Numerical Analysis
    • PWS Publishing Company, Boston.
    • BURDEN, R. L. and FAIRES, J. D. (1993). Numerical Analysis. PWS Publishing Company, Boston.
    • (1993)
    • Burden, R.L.1    Faires, J.D.2
  • 6
    • 0000904732 scopus 로고    scopus 로고
    • A semiparametric Bayesian model for randomised block designs
    • BUSH, C. A. andMACEACHERN, S. N. (1996). A semiparametric Bayesian model for randomised block designs. Biometrika 83 275-285.
    • (1996) Biometrika , vol.83 , pp. 275-285
    • Bush, C.A.1    Maceachern, S.N.2
  • 7
    • 0003508387 scopus 로고    scopus 로고
    • An Introduction to the Theory of Point Processes
    • General Theory and Structure, 2nd ed. Springer, New York. MR2371524
    • DALEY, D. J. andVERE-JONES, D. (2008). An Introduction to the Theory of Point Processes. Vol. II, General Theory and Structure, 2nd ed. Springer, New York. MR2371524
    • (2008) , vol.2
    • Daley, D.J.1    Vere-Jones, D.2
  • 8
    • 0033481108 scopus 로고    scopus 로고
    • Gibbs sampling for Bayesian non-conjugate and hierarchical models by using auxiliary variables
    • MR1680334
    • DAMIEN, P.,WAKEFIELD, J. andWALKER, S. (1999). Gibbs sampling for Bayesian non-conjugate and hierarchical models by using auxiliary variables. J. R. Stat. Soc. Ser. B Stat. Methodol. 61 331-344. MR1680334
    • (1999) J. R. Stat. Soc. Ser. B Stat. Methodol. , vol.61 , pp. 331-344
    • Damien, P.1    Wakefield, J.2    Walker, S.3
  • 10
    • 84950937290 scopus 로고
    • Bayesian density estimation and inference using mixtures
    • MR1340510
    • ESCOBAR, M. D. and WEST, M. (1995). Bayesian density estimation and inference using mixtures. J. Amer. Statist. Assoc. 90 577-588. MR1340510
    • (1995) J. Amer. Statist. Assoc. , vol.90 , pp. 577-588
    • Escobar, M.D.1    West, M.2
  • 11
    • 84865452997 scopus 로고    scopus 로고
    • On the stickbreaking representation of normalized inverse Gaussian priors
    • MR2966776
    • FAVARO, S., LIJOI, A. and PRÜNSTER, I. (2012). On the stickbreaking representation of normalized inverse Gaussian priors. Biometrika 99 663-674. MR2966776
    • (2012) Biometrika , vol.99 , pp. 663-674
    • Favaro, S.1    Lijoi, A.2    Prünster, I.3
  • 12
    • 84878592020 scopus 로고    scopus 로고
    • MCMC for normalized random measure mixture models
    • FAVARO, S. and TEH, Y. W. (2013). MCMC for normalized random measure mixture models. Statist. Sci. 28 335-359.
    • (2013) Statist. Sci. , vol.28 , pp. 335-359
    • Favaro, S.1    Teh, Y.W.2
  • 13
    • 0001120413 scopus 로고
    • A Bayesian analysis of some nonparametric problems
    • MR0350949
    • FERGUSON, T. S. (1973). A Bayesian analysis of some nonparametric problems. Ann. Statist. 1 209-230. MR0350949
    • (1973) Ann. Statist. , vol.1 , pp. 209-230
    • Ferguson, T.S.1
  • 14
    • 0000780135 scopus 로고
    • Prior distributions on spaces of probability measures
    • MR0438568
    • FERGUSON, T. S. (1974). Prior distributions on spaces of probability measures. Ann. Statist. 2 615-629. MR0438568
    • (1974) Ann. Statist. , vol.2 , pp. 615-629
    • Ferguson, T.S.1
  • 15
    • 0001787029 scopus 로고
    • Bayesian density estimation by mixtures of normal distributions
    • In Recent Advances in Statistics 287- 302. Academic Press, New York. MR0736538
    • FERGUSON, T. S. (1983). Bayesian density estimation by mixtures of normal distributions. In Recent Advances in Statistics 287- 302. Academic Press, New York. MR0736538
    • (1983)
    • Ferguson, T.S.1
  • 16
    • 0001411887 scopus 로고
    • A representation of independent increment processes without Gaussian components
    • MR0373022
    • FERGUSON, T. S. and KLASS, M. J. (1972). A representation of independent increment processes without Gaussian components. Ann. Math. Statist. 43 1634-1643. MR0373022
    • (1972) Ann. Math. Statist. , vol.43 , pp. 1634-1643
    • Ferguson, T.S.1    Klass, M.J.2
  • 17
    • 0000079228 scopus 로고
    • Model determination using predictive distributions with implementation via sampling-based methods
    • Oxford Univ. Press, New York. MR1380275
    • GELFAND, A. E., DEY, D. K. and CHANG, H. (1992). Model determination using predictive distributions with implementation via sampling-based methods. In Bayesian Statistics 4 147-167. Oxford Univ. Press, New York. MR1380275
    • (1992) In Bayesian Statistics , vol.4 , pp. 147-167
    • Gelfand, A.E.1    Dey, D.K.2    Chang, H.3
  • 18
    • 1842816362 scopus 로고    scopus 로고
    • Gibbs sampling methods for stick-breaking priors
    • MR1952729
    • ISHWARAN, H. and JAMES, L. F. (2001). Gibbs sampling methods for stick-breaking priors. J. Amer. Statist. Assoc. 96 161-173. MR1952729
    • (2001) J. Amer. Statist. Assoc. , vol.96 , pp. 161-173
    • Ishwaran, H.1    James, L.F.2
  • 19
    • 33645066123 scopus 로고    scopus 로고
    • Conjugacy as a distinctive feature of the Dirichlet process
    • MR2255112
    • JAMES, L. F., LIJOI, A. and PRÜNSTER, I. (2006). Conjugacy as a distinctive feature of the Dirichlet process. Scand. J. Stat. 33 105-120. MR2255112
    • (2006) Scand. J. Stat. , vol.33 , pp. 105-120
    • James, L.F.1    Lijoi, A.2    Prünster, I.3
  • 20
    • 60249093564 scopus 로고    scopus 로고
    • Posterior analysis for normalized random measures with independent increments
    • MR2508332
    • JAMES, L. F., LIJOI, A. and PRÜNSTER, I. (2009). Posterior analysis for normalized random measures with independent increments. Scand. J. Stat. 36 76-97. MR2508332
    • (2009) Scand. J. Stat. , vol.36 , pp. 76-97
    • James, L.F.1    Lijoi, A.2    Prünster, I.3
  • 21
    • 84969653882 scopus 로고
    • Completely random measures
    • MR0210185
    • KINGMAN, J. F. C. (1967). Completely random measures. Pacific J. Math. 21 59-78. MR0210185
    • (1967) Pacific J. Math. , vol.21 , pp. 59-78
    • Kingman, J.F.C.1
  • 23
    • 0003523893 scopus 로고
    • Poisson Processes
    • Oxford Studies in Probability 3. Oxford Univ. Press, New York. MR1207584
    • KINGMAN, J. F. C. (1993). Poisson Processes. Oxford Studies in Probability 3. Oxford Univ. Press, New York. MR1207584
    • (1993)
    • Kingman, J.F.C.1
  • 24
    • 29144511286 scopus 로고    scopus 로고
    • Hierarchical mixture modeling with normalized inverse-Gaussian priors
    • MR2236441
    • LIJOI, A., MENA, R. H. and PRÜNSTER, I. (2005). Hierarchical mixture modeling with normalized inverse-Gaussian priors. J. Amer. Statist. Assoc. 100 1278-1291. MR2236441
    • (2005) J. Amer. Statist. Assoc. , vol.100 , pp. 1278-1291
    • Lijoi, A.1    Mena, R.H.2    Prünster, I.3
  • 25
    • 34547828069 scopus 로고    scopus 로고
    • Controlling the reinforcement in Bayesian non-parametric mixture models
    • MR2370077
    • LIJOI, A., MENA, R. H. and PRÜNSTER, I. (2007). Controlling the reinforcement in Bayesian non-parametric mixture models. J. R. Stat. Soc. Ser. B Stat. Methodol. 69 715-740. MR2370077
    • (2007) J. R. Stat. Soc. Ser. B Stat. Methodol. , vol.69 , pp. 715-740
    • Lijoi, A.1    Mena, R.H.2    Prünster, I.3
  • 26
    • 75749084121 scopus 로고    scopus 로고
    • Models beyond the Dirichlet process
    • In Bayesian Nonparametrics (N. L. Hjort, C. C. Holmes, P. Müller and S. G. Walker, eds.) Cambridge Univ. Press, Cambridge. MR2730661
    • LIJOI, A. and PRÜNSTER, I. (2010). Models beyond the Dirichlet process. In Bayesian Nonparametrics (N. L. Hjort, C. C. Holmes, P. Müller and S. G. Walker, eds.) 80-136. Cambridge Univ. Press, Cambridge. MR2730661
    • (2010) , pp. 80-136
    • Lijoi, A.1    Prünster, I.2
  • 27
    • 84889100973 scopus 로고    scopus 로고
    • Bayesian inference with dependent normalized completely random measures
    • Bernoulli. To appear. DOI:10.3150/13-BEJ521.
    • LIJOI, A., NIPOTI, B. and PRÜNSTER, I. (2013). Bayesian inference with dependent normalized completely random measures. Bernoulli. To appear. DOI:10.3150/13-BEJ521.
    • (2013)
    • Lijoi, A.1    Nipoti, B.2    Prünster, I.3
  • 28
    • 0001876649 scopus 로고
    • On a class of Bayesian nonparametric estimates
    • MR0733519
    • LO, A. Y. (1984). On a class of Bayesian nonparametric estimates. I. Density estimates. Ann. Statist. 12 351-357. MR0733519
    • (1984) I. Density estimates. Ann. Statist. , vol.12 , pp. 351-357
    • Lo, A.Y.1
  • 29
    • 0032221058 scopus 로고    scopus 로고
    • Estimating mixtures of Dirichlet process models
    • MACEACHERN, S. N. and MÜLLER, P. (1998). Estimating mixtures of Dirichlet process models. J. Comput. Graph. Statist. 7 223-238.
    • (1998) J. Comput. Graph. Statist. , vol.7 , pp. 223-238
    • Maceachern, S.N.1    Müller, P.2
  • 30
    • 0038524824 scopus 로고    scopus 로고
    • Efficient MCMC schemes for robust model extensions using encompassing Dirichlet process mixture models
    • Springer, New York. MR1795222
    • MACEACHERN, S. and MÜLLER, P. (2000). Efficient MCMC schemes for robust model extensions using encompassing Dirichlet process mixture models. In Robust Bayesian Analysis. Lecture Notes in Statist. 152 295-315. Springer, New York. MR1795222
    • (2000) In Robust Bayesian Analysis. Lecture Notes in Statist. , vol.152 , pp. 295-315
    • Maceachern, S.1    Müller, P.2
  • 31
    • 0001366850 scopus 로고
    • Exact mean integrated squared error
    • MR1165589
    • MARRON, J. S. andWAND, M. P. (1992). Exact mean integrated squared error. Ann. Statist. 20 712-736. MR1165589
    • (1992) Ann. Statist. , vol.20 , pp. 712-736
    • Marron, J.S.1    Wand, M.P.2
  • 32
    • 0032091593 scopus 로고    scopus 로고
    • Approximating distributions of random functionals of Ferguson-Dirichlet priors
    • MR1648431
    • MULIERE, P. and TARDELLA, L. (1998). Approximating distributions of random functionals of Ferguson-Dirichlet priors. Canad. J. Statist. 26 283-297. MR1648431
    • (1998) Canad. J. Statist. , vol.26 , pp. 283-297
    • Muliere, P.1    Tardella, L.2
  • 33
    • 4043092820 scopus 로고    scopus 로고
    • Nonparametric Bayesian data analysis
    • MR2082149
    • MÜLLER, P. and QUINTANA, F. A. (2004). Nonparametric Bayesian data analysis. Statist. Sci. 19 95-110. MR2082149
    • (2004) Statist. Sci. , vol.19 , pp. 95-110
    • Müller, P.1    Quintana, F.A.2
  • 34
    • 0032271927 scopus 로고    scopus 로고
    • Bayesian inference with wavelets: Density estimation
    • MÜLLER, P. and VIDAKOVIC, B. (1998). Bayesian inference with wavelets: Density estimation. J. Comput. Graph. Statist. 7 456- 468.
    • (1998) J. Comput. Graph. Statist. , vol.7
    • Müller, P.1    Vidakovic, B.2
  • 35
    • 21644433245 scopus 로고    scopus 로고
    • Normalized random measures driven by increasing additive processes
    • MR2153987
    • NIETO-BARAJAS, L. E., PRÜNSTER, I. and WALKER, S. G. (2004). Normalized random measures driven by increasing additive processes. Ann. Statist. 32 2343-2360. MR2153987
    • (2004) Ann. Statist. , vol.32 , pp. 2343-2360
    • Nieto-Barajas, L.E.1    Prünster, I.2    Walker, S.G.3
  • 36
    • 68149131525 scopus 로고    scopus 로고
    • A sensitivity analysis for Bayesian nonparametric density estimators
    • MR2514182
    • NIETO-BARAJAS, L. E. and PRÜNSTER, I. (2009). A sensitivity analysis for Bayesian nonparametric density estimators. Statist. Sinica 19 685-705. MR2514182
    • (2009) Statist. Sinica , vol.19 , pp. 685-705
    • Nieto-Barajas, L.E.1    Prünster, I.2
  • 37
    • 84885362915 scopus 로고    scopus 로고
    • Unit-rate Poisson representations of completely random measures
    • Technical report.
    • ORBANZ, P. andWILLIAMSON, S. (2011). Unit-rate Poisson representations of completely random measures. Technical report.
    • (2011)
    • Orbanz, P.1    Illiamson, S.2
  • 38
    • 40249114903 scopus 로고    scopus 로고
    • Retrospective Markov chain Monte Carlo methods for Dirichlet process hierarchical models
    • MR2409721
    • PAPASPILIOPOULOS, O. and ROBERTS, G. O. (2008). Retrospective Markov chain Monte Carlo methods for Dirichlet process hierarchical models. Biometrika 95 169-186. MR2409721
    • (2008) Biometrika , vol.95 , pp. 169-186
    • Papaspiliopoulos, O.1    Roberts, G.O.2
  • 39
    • 18244380018 scopus 로고    scopus 로고
    • Poisson-Kingman partitions
    • In Statistics and Science: A Festschrift for Terry Speed (D. R. Goldstein, ed.). Institute of Mathematical Statistics Lecture Notes-Monograph Series . IMS, Beachwood, OH. MR2004330
    • PITMAN, J. (2003). Poisson-Kingman partitions. In Statistics and Science: A Festschrift for Terry Speed (D. R. Goldstein, ed.). Institute of Mathematical Statistics Lecture Notes-Monograph Series 40 1-34. IMS, Beachwood, OH. MR2004330
    • (2003) , vol.40 , pp. 1-34
    • Pitman, J.1
  • 40
    • 0038702581 scopus 로고    scopus 로고
    • Distributional results for means of normalized random measures with independent increments
    • MR1983542
    • REGAZZINI, E., LIJOI, A. and PRÜNSTER, I. (2003). Distributional results for means of normalized random measures with independent increments. Ann. Statist. 31 560-585. MR1983542
    • (2003) Ann. Statist. , vol.31 , pp. 560-585
    • Regazzini, E.1    Lijoi, A.2    Prünster, I.3
  • 41
    • 18244378520 scopus 로고    scopus 로고
    • On Bayesian analysis of mixtures with an unknown number of components
    • MR1483213
    • 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. MR1483213
    • (1997) J. Roy. Statist. Soc. Ser. B , vol.59 , pp. 731-792
    • Richardson, S.1    Green, P.J.2
  • 42
    • 21744460005 scopus 로고    scopus 로고
    • Practical Bayesian density estimation using mixtures of normals
    • MR1482121
    • ROEDER, K. and WASSERMAN, L. (1997). Practical Bayesian density estimation using mixtures of normals. J. Amer. Statist. Assoc. 92 894-902. MR1482121
    • (1997) J. Amer. Statist. Assoc. , vol.92 , pp. 894-902
    • Roeder, K.1    Wasserman, L.2
  • 43
    • 0004044683 scopus 로고
    • Lévy Processes and Infinitely Divisible Distributions
    • Cambridge Univ. Press, Cambridge.
    • SATO, K. (1990). Lévy Processes and Infinitely Divisible Distributions. Cambridge Univ. Press, Cambridge.
    • (1990)
    • Sato, K.1
  • 44
    • 0000720609 scopus 로고
    • A constructive definition of Dirichlet priors
    • MR1309433
    • SETHURAMAN, J. (1994). A constructive definition of Dirichlet priors. Statist. Sinica 4 639-650. MR1309433
    • (1994) Statist. Sinica , vol.4 , pp. 639-650
    • Sethuraman, J.1
  • 45
    • 0003443397 scopus 로고
    • Density Estimation for Statistics and Data Analysis
    • Chapman & Hall, London. MR0848134
    • SILVERMAN, B. W. (1986). Density Estimation for Statistics and Data Analysis. Chapman & Hall, London. MR0848134
    • (1986)
    • Silverman, B.W.1
  • 46
    • 0000576595 scopus 로고
    • Markov chains for exploring posterior distributions
    • MR1329166
    • TIERNEY, L. (1994). Markov chains for exploring posterior distributions. Ann. Statist. 22 1701-1762. MR1329166
    • (1994) Ann. Statist. , vol.22 , pp. 1701-1762
    • Tierney, L.1
  • 47
    • 33847707418 scopus 로고    scopus 로고
    • Sampling the Dirichlet mixture model with slices
    • MR2370888
    • WALKER, S. G. (2007). Sampling the Dirichlet mixture model with slices. Comm. Statist. Simulation Comput. 36 45-54. MR2370888
    • (2007) Comm. Statist. Simulation Comput. , vol.36 , pp. 45-54
    • Walker, S.G.1
  • 48
    • 0007247917 scopus 로고    scopus 로고
    • Representations of Lévy processes without Gaussian components
    • MR1782492
    • WALKER, S. and DAMIEN, P. (2000). Representations of Lévy processes without Gaussian components. Biometrika 87 477- 483. MR1782492
    • (2000) Biometrika , vol.87
    • Walker, S.1    Damien, P.2
  • 49
    • 0001121317 scopus 로고    scopus 로고
    • Poisson/gamma random field models for spatial statistics
    • MR1649114
    • WOLPERT, R. L. and ICKSTADT, K. (1998). Poisson/gamma random field models for spatial statistics. Biometrika 85 251-267. MR1649114
    • (1998) Biometrika , vol.85 , pp. 251-267
    • Wolpert, R.L.1    Ickstadt, K.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.