메뉴 건너뛰기




Volumn 29, Issue 4, 2014, Pages 619-639

The Bayesian analysis of complex, high-dimensional models: Can it be CODA?

Author keywords

Bayesian inference; CODA; Foundations; Functional estimation; Partial linear model; Semiparametrics; Stopping time; White noise models

Indexed keywords


EID: 84921476405     PISSN: 08834237     EISSN: None     Source Type: Journal    
DOI: 10.1214/14-STS483     Document Type: Article
Times cited : (29)

References (49)
  • 1
    • 4043150795 scopus 로고    scopus 로고
    • The interplay of Bayesian and frequentist analysis
    • MR2082147
    • BAYARRI, M. J. and BERGER, J. O. (2004). The interplay of Bayesian and frequentist analysis. Statist. Sci. 19 58-80. MR2082147
    • (2004) Statist. Sci. , vol.19 , pp. 58-80
    • Bayarri, M.J.1    Berger, J.O.2
  • 2
    • 84867176040 scopus 로고    scopus 로고
    • The case for objective Bayesian analysis
    • MR2221271
    • BERGER, J. (2006a). The case for objective Bayesian analysis. Bayesian Anal. 1 385-402. MR2221271
    • (2006) Bayesian Anal. , vol.1 , pp. 385-402
    • Berger, J.1
  • 6
    • 0001073033 scopus 로고
    • Minimax estimation of the mean of a normal distribution when the parameter space is restricted
    • MR0630112
    • BICKEL, P. J. (1981). Minimax estimation of the mean of a normal distribution when the parameter space is restricted. Ann. Statist. 9 1301-1309. MR0630112
    • (1981) Ann. Statist. , vol.9 , pp. 1301-1309
    • Bickel, P.J.1
  • 7
    • 84871232166 scopus 로고    scopus 로고
    • The semiparametric Bernstein-von Mises theorem
    • MR3013185
    • BICKEL, P. J. and KLEIJN, B. J. K. (2012). The semiparametric Bernstein-von Mises theorem. Ann. Statist. 40 206-237. MR3013185
    • (2012) Ann. Statist. , vol.40 , pp. 206-237
    • Bickel, P.J.1    Kleijn, B.J.K.2
  • 8
    • 0001667487 scopus 로고
    • Estimating integrated squared density derivatives: Sharp best order of convergence estimates
    • MR1065550
    • BICKEL, P. J. and RITOV, Y. (1988). Estimating integrated squared density derivatives: Sharp best order of convergence estimates. Sankhya Ser. A 50 381-393. MR1065550
    • (1988) Sankhya Ser. A , vol.50 , pp. 381-393
    • Bickel, P.J.1    Ritov, Y.2
  • 9
    • 0041857920 scopus 로고    scopus 로고
    • Nonparametric estimators which can be "plugged-in"
    • MR2001641
    • BICKEL, P. J. and RITOV, Y. (2003). Nonparametric estimators which can be "plugged-in". Ann. Statist. 31 1033-1053. MR2001641
    • (2003) Ann. Statist. , vol.31 , pp. 1033-1053
    • Bickel, P.J.1    Ritov, Y.2
  • 12
    • 0030335402 scopus 로고    scopus 로고
    • Asymptotic equivalence of nonparametric regression and white noise
    • MR1425958
    • BROWN, L. D. and LOW, M. G. (1996). Asymptotic equivalence of nonparametric regression and white noise. Ann. Statist. 24 2384-2398. MR1425958
    • (1996) Ann. Statist. , vol.24 , pp. 2384-2398
    • Brown, L.D.1    Low, M.G.2
  • 13
    • 21344493554 scopus 로고
    • Data-driven efficient estimators for a partially linear model
    • MR1272081
    • CHEN, H. and SHIAU, J. J. H. (1994). Data-driven efficient estimators for a partially linear model. Ann. Statist. 22 211-237. MR1272081
    • (1994) Ann. Statist. , vol.22 , pp. 211-237
    • Chen, H.1    Shiau, J.J.H.2
  • 14
  • 15
    • 21144475432 scopus 로고
    • An analysis of Bayesian inference for nonparametric regression
    • MR1232525
    • COX, D. D. (1993). An analysis of Bayesian inference for nonparametric regression. Ann. Statist. 21 903-923. MR1232525
    • (1993) Ann. Statist. , vol.21 , pp. 903-923
    • Cox, D.D.1
  • 16
    • 21344494224 scopus 로고
    • Nonparametric binary regression: A Bayesian approach
    • MR1245784
    • DIACONIS, P. and FREEDMAN, D. A. (1993). Nonparametric binary regression: A Bayesian approach. Ann. Statist. 21 2108- 2137. MR1245784
    • (1993) Ann. Statist. , vol.21 , pp. 2108- 2137
    • Diaconis, P.1    Freedman, D.A.2
  • 17
    • 0001928221 scopus 로고    scopus 로고
    • Consistency of Bayes estimates for nonparametric regression: Normal theory
    • MR1679791
    • DIACONIS, P. W. and FREEDMAN, D. (1998). Consistency of Bayes estimates for nonparametric regression: Normal theory. Bernoulli 4 411-444. MR1679791
    • (1998) Bernoulli , vol.4 , pp. 411-444
    • Diaconis, P.W.1    Freedman, D.2
  • 19
    • 84950459514 scopus 로고
    • Adapting to unknown smoothness via wavelet shrinkage
    • MR1379464
    • DONOHO, D. L. and JOHNSTONE, I. M. (1995). Adapting to unknown smoothness via wavelet shrinkage. J. Amer. Statist. Assoc. 90 1200-1224. MR1379464
    • (1995) J. Amer. Statist. Assoc. , vol.90 , pp. 1200-1224
    • Donoho, D.L.1    Johnstone, I.M.2
  • 20
    • 0012921755 scopus 로고
    • Nonparametric estimates of the relation between weather and electricity sales
    • ENGLE, R. F., GRANGER, C. W. J., RICE, J. and WEISS, A. (1986). Nonparametric estimates of the relation between weather and electricity sales. J. Amer. Statist. Assoc. 81 310- 320.
    • (1986) J. Amer. Statist. Assoc. , vol.81 , pp. 310-320
    • Engle, R.F.1    Granger, C.W.J.2    Rice, J.3    Weiss, A.4
  • 21
    • 0034354971 scopus 로고    scopus 로고
    • Inference for multivariate normal hierarchical models
    • MR1749547
    • EVERSON, P. J. and MORRIS, C. N. (2000). Inference for multivariate normal hierarchical models. J. R. Stat. Soc. Ser. B Stat. Methodol. 62 399-412. MR1749547
    • (2000) J. R. Stat. Soc. Ser. B Stat. Methodol. , vol.62 , pp. 399-412
    • Everson, P.J.1    Morris, C.N.2
  • 22
    • 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
  • 23
    • 0000202123 scopus 로고
    • On the asymptotic behavior of Bayes' estimates in the discrete case
    • MR0158483
    • FREEDMAN, D. A. (1963). On the asymptotic behavior of Bayes' estimates in the discrete case. Ann. Math. Statist. 34 1386-1403. MR0158483
    • (1963) Ann. Math. Statist. , vol.34 , pp. 1386-1403
    • Freedman, D.A.1
  • 24
    • 0001446581 scopus 로고
    • On the asymptotic behavior of Bayes estimates in the discrete case
    • MR0174146
    • FREEDMAN, D. A. (1965). On the asymptotic behavior of Bayes estimates in the discrete case. II. Ann. Math. Statist. 36 454- 456. MR0174146
    • (1965) II. Ann. Math. Statist. , vol.36 , pp. 454- 456
    • Freedman, D.A.1
  • 25
    • 0033236897 scopus 로고    scopus 로고
    • On the Bernstein-von Mises theorem with infinite-dimensional parameters
    • MR1740119
    • FREEDMAN, D. (1999). On the Bernstein-von Mises theorem with infinite-dimensional parameters. Ann. Statist. 27 1119-1140. MR1740119
    • (1999) Ann. Statist. , vol.27 , pp. 1119-1140
    • Freedman, D.1
  • 26
    • 0034164796 scopus 로고    scopus 로고
    • Convergence rates of posterior distributions
    • MR1790007
    • GHOSAL, S., GHOSH, J. K. and VAN DER VAART, A. W. (2000). Convergence rates of posterior distributions. Ann. Statist. 28 500-531. MR1790007
    • (2000) Ann. Statist. , vol.28 , pp. 500-531
    • Ghosal, S.1    Ghosh, J.K.2    Van Der Vaart, A.W.3
  • 27
    • 33845455708 scopus 로고    scopus 로고
    • Subjective Bayesian analysis: Principles and practice
    • MR2221272 (electronic)
    • GOLDSTEIN, M. (2006). Subjective Bayesian analysis: Principles and practice. Bayesian Anal. 1 403-420 (electronic). MR2221272
    • (2006) Bayesian Anal. , vol.1 , pp. 403-420
    • Goldstein, M.1
  • 28
    • 85008827350 scopus 로고    scopus 로고
    • Estimating the mean of high valued observations in high dimensions
    • MR2528789
    • GREENSHTEIN, E., PARK, J. andRITOV, Y. (2008). Estimating the mean of high valued observations in high dimensions. J. Stat. Theory Pract. 2 407-418. MR2528789
    • (2008) J. Stat. Theory Pract. , vol.2 , pp. 407-418
    • Greenshtein, E.1    Park, J.2    Ritov, Y.3
  • 30
    • 0002282584 scopus 로고
    • On nonparametric estimation of a linear functional in Gaussian white noise
    • IBRAGIMOV, I. A. and HASMINSKII, R. Z. (1984). On nonparametric estimation of a linear functional in Gaussian white noise. Theory Probab. Appl. 29 19-32.
    • (1984) Theory Probab. Appl. , vol.29 , pp. 19-32
    • Ibragimov, I.A.1    Hasminskii, R.Z.2
  • 31
    • 33746227433 scopus 로고    scopus 로고
    • Misspecification in infinite-dimensional Bayesian statistics
    • MR2283395
    • KLEIJN, B. J. K. and VAN DER VAART, A. W. (2006). Misspecification in infinite-dimensional Bayesian statistics. Ann. Statist. 34 837-877. MR2283395
    • (2006) Ann. Statist. , vol.34 , pp. 837-877
    • Kleijn, B.J.K.1    Van Der Vaart, A.W.2
  • 34
    • 0033407245 scopus 로고    scopus 로고
    • Testing symmetry and proportionality in ppp
    • LI, K. (1999). Testing symmetry and proportionality in ppp. J. Bus. Econom. Statist. 17 409-418.
    • (1999) J. Bus. Econom. Statist. , vol.17 , pp. 409-418
    • Li, K.1
  • 35
    • 77349117025 scopus 로고    scopus 로고
    • Are Bayesian inferences weak for Wasserman's example?
    • MR2784548
    • LI, L. (2010). Are Bayesian inferences weak for Wasserman's example? Comm. Statist. Simulation Comput. 39 655-667. MR2784548
    • (2010) Comm. Statist. Simulation Comput. , vol.39 , pp. 655-667
    • Li, L.1
  • 36
    • 77955162849 scopus 로고
    • Statistical inference
    • discussion 65-76. MR0057522
    • LINDLEY, D. V. (1953). Statistical inference. J. R. Stat. Soc. Ser. B Stat. Methodol. 15 30-65; discussion 65-76. MR0057522
    • (1953) J. R. Stat. Soc. Ser. B Stat. Methodol. , vol.15 , pp. 30-65
    • Lindley, D.V.1
  • 38
    • 83855165448 scopus 로고    scopus 로고
    • A statistical analysis of multiple temperature proxies: Are reconstructions of surface temperatures over the last 1000 years reliable?
    • MR2810377
    • MCSHANE, B. B. andWYNER, A. J. (2011). A statistical analysis of multiple temperature proxies: Are reconstructions of surface temperatures over the last 1000 years reliable? Ann. Appl. Stat. 5 5-44. MR2810377
    • (2011) Ann. Appl. Stat. , vol.5 , pp. 5-44
    • Mcshane, B.B.1    Wyner, A.J.2
  • 39
    • 0030328670 scopus 로고    scopus 로고
    • Asymptotic equivalence of density estimation and Gaussian white noise
    • MR1425959
    • NUSSBAUM, M. (1996). Asymptotic equivalence of density estimation and Gaussian white noise. Ann. Statist. 24 2399-2430. MR1425959
    • (1996) Ann. Statist. , vol.24 , pp. 2399-2430
    • Nussbaum, M.1
  • 40
    • 0031016404 scopus 로고    scopus 로고
    • Toward a curse of dimensionality appropriate (coda) asymptotic theory for semiparametric models
    • ROBINS, J. M. and RITOV, Y. (1997). Toward a curse of dimensionality appropriate (coda) asymptotic theory for semiparametric models. Stat. Med. 17 285-319.
    • (1997) Stat. Med. , vol.17 , pp. 285-319
    • Robins, J.M.1    Ritov, Y.2
  • 42
    • 0003369804 scopus 로고
    • The foundations of statistics reconsidered
    • Univ. California Press, Berkeley, CA. MR0133898
    • SAVAGE, L. J. (1961). The foundations of statistics reconsidered. In Proc. 4th Berkeley Sympos. Math. Statist. and Prob., Vol. I 575-586. Univ. California Press, Berkeley, CA. MR0133898
    • (1961) Proc. 4th Berkeley Sympos. Math. Statist. and Prob. , vol.1 , pp. 575-586
    • Savage, L.J.1
  • 43
    • 21344489030 scopus 로고
    • On efficient estimation in regression models
    • MR1241276
    • SCHICK, A. (1993). On efficient estimation in regression models. Ann. Statist. 21 1486-1521. MR1241276
    • (1993) Ann. Statist. , vol.21 , pp. 1486-1521
    • Schick, A.1
  • 44
    • 37349095914 scopus 로고
    • Some Bayesian thoughts on modelling and model choice
    • SMITH, A. F. M. (1986). Some Bayesian thoughts on modelling and model choice. J. R. Stat. Soc. Ser. D (The Statistician) 35 97-101.
    • (1986) J. R. Stat. Soc. Ser. D (The Statistician) , vol.35 , pp. 97-101
    • Smith, A.F.M.1
  • 45
    • 84921490446 scopus 로고    scopus 로고
    • The horseshoe estimator: Posterior concentration around nearly black vectors
    • MR3285877
    • VAN DER PAS, S. L. and KLEIJN, B. J. K. (2014). The horseshoe estimator: Posterior concentration around nearly black vectors. Electron. J. Statist. 8 2585-2618. MR3285877
    • (2014) Electron. J. Statist. , vol.8 , pp. 2585-2618
    • Van Der Pas, S.L.1    Kleijn, B.J.K.2
  • 46
    • 79961007790 scopus 로고    scopus 로고
    • A difference based approach to the semiparametric partial linear model
    • MR2813557
    • WANG, L., BROWN, L. D. and CAI, T. T. (2011). A difference based approach to the semiparametric partial linear model. Electron. J. Stat. 5 619-641. MR2813557
    • (2011) Electron. J. Stat. , vol.5 , pp. 619-641
    • Wang, L.1    Brown, L.D.2    Cai, T.T.3
  • 47
    • 0034360396 scopus 로고    scopus 로고
    • Asymptotic inference for mixture models using data-dependent priors
    • MR1747402
    • WASSERMAN, L. (2000). Asymptotic inference for mixture models using data-dependent priors. J. R. Stat. Soc. Ser. B Stat. Methodol. 62 159-180. MR1747402
    • (2000) J. R. Stat. Soc. Ser. B Stat. Methodol. , vol.62 , pp. 159-180
    • Wasserman, L.1
  • 49
    • 0034347381 scopus 로고    scopus 로고
    • Bayesian aspects of some nonparametric problems
    • MR1790008
    • ZHAO, L. H. (2000). Bayesian aspects of some nonparametric problems. Ann. Statist. 28 532-552. MR1790008
    • (2000) Ann. Statist. , vol.28 , pp. 532-552
    • Zhao, L.H.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.