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Volumn 2, Issue , 2008, Pages 1281-1299

Lower bounds for posterior rates with Gaussian process priors

Author keywords

Bayesian nonparametrics; Gaussian process priors; Lower bounds

Indexed keywords


EID: 78650708410     PISSN: 19357524     EISSN: None     Source Type: Journal    
DOI: 10.1214/08-EJS273     Document Type: Article
Times cited : (83)

References (17)
  • 1
    • 0033438067 scopus 로고    scopus 로고
    • The consistency of posterior distributions in nonparametric problems
    • Barron, A., Schervish, M. J., and Wasserman, L. The consistency of posterior distributions in nonparametric problems. Ann. Statist. 27, 2 (1999), 536-561.
    • (1999) Ann. Statist , vol.27 , Issue.2 , pp. 536-561
    • Barron, A.1    Schervish, M.J.2    Wasserman, L.3
  • 2
    • 0038702584 scopus 로고    scopus 로고
    • Adaptive Bayesian inference on the mean of an infinite-dimensional normal distribution
    • Dedicated to the memory of Herbert E. Robbins
    • Belitser, E., and Ghosal, S. Adaptive Bayesian inference on the mean of an infinite-dimensional normal distribution. Ann. Statist. 31, 2 (2003), 536-559. Dedicated to the memory of Herbert E. Robbins.
    • (2003) Ann. Statist , vol.31 , Issue.2 , pp. 536-559
    • Belitser, E.1    Ghosal, S.2
  • 3
    • 0001639899 scopus 로고
    • The Brunn-Minkowski inequality in Gauss space
    • Borell, C. The Brunn-Minkowski inequality in Gauss space. Invent. Math. 30, 2 (1975), 207-216.
    • (1975) Invent. Math , vol.30 , Issue.2 , pp. 207-216
    • Borell, C.1
  • 4
    • 38849086628 scopus 로고    scopus 로고
    • On continuity and strict increase of the CDF for the sup-functional of a Gaussian process with applications to statistics
    • Gaenssler, P., Molnár, P., and Rost, D. On continuity and strict increase of the CDF for the sup-functional of a Gaussian process with applications to statistics. Results Math. 51, 1-2 (2007), 51-60.
    • (2007) Results Math , vol.51 , Issue.1-2 , pp. 51-60
    • Gaenssler, P.1    Molnár, P.2    Rost, D.3
  • 5
    • 0034164796 scopus 로고    scopus 로고
    • A. W. Convergence rates of posterior distributions
    • Ghosal, S., Ghosh, J. K., and Van der Vaart, A. W. Convergence rates of posterior distributions. Ann. Statist. 28, 2 (2000), 500-531.
    • (2000) Ann. Statist , vol.28 , Issue.2 , pp. 500-531
    • Ghosal, S.1    Ghosh, J.K.2    Vaart, V.D.3
  • 6
    • 49449093584 scopus 로고    scopus 로고
    • A. W. Convergence rates of posterior distributions for noniid observations
    • Ghosal, S., and Van der Vaart, A. W. Convergence rates of posterior distributions for noniid observations. Ann. Statist. 35, 1 (2007).
    • (2007) Ann. Statist , vol.35 , Issue.1
    • Ghosal, S.1    Vaart, V.D.2
  • 7
    • 0001655260 scopus 로고
    • Some properties of fractional integrals
    • Hardy, G. H., and Littlewood, J. E. Some properties of fractional integrals. I. Math. Z. 27, 1 (1928), 565-606.
    • (1928) I. Math. Z , vol.27 , Issue.1 , pp. 565-606
    • Hardy, G.H.1    Littlewood, J.E.2
  • 8
    • 0001461506 scopus 로고
    • Metric entropy and the small ball problem for Gaussian measures
    • Kuelbs, J., and Li, W. V. Metric entropy and the small ball problem for Gaussian measures. J. Funct. Anal. 116, 1 (1993), 133-157.
    • (1993) J. Funct. Anal , vol.116 , Issue.1 , pp. 133-157
    • Kuelbs, J.1    Li, W.V.2
  • 10
    • 0032092875 scopus 로고    scopus 로고
    • Existence of small ball constants for fractional Brownian motions
    • Li, W. V., and Linde, W. Existence of small ball constants for fractional Brownian motions. C. R. Acad. Sci. Paris Sér. I Math. 326, 11 (1998), 1329-1334.
    • (1998) C. R. Acad. Sci. Paris Sér. I Math , vol.326 , Issue.11 , pp. 1329-1334
    • Li, W.V.1    Linde, W.2
  • 11
    • 70350344396 scopus 로고    scopus 로고
    • Gaussian processes: Inequalities, small ball probabilities and applications
    • Handbook of Statist. North-Holland, Amsterdam
    • Li, W. V., and Shao, Q.-M. Gaussian processes: inequalities, small ball probabilities and applications. In Stochastic processes: theory and methods, vol. 19 of Handbook of Statist. North-Holland, Amsterdam, 2001, pp. 533-597.
    • (2001) In Stochastic Processes: Theory and Methods , vol.19 , pp. 533-597
    • Li, W.V.1    Shao, Q.-M.2
  • 13
    • 0035539848 scopus 로고    scopus 로고
    • Rates of convergence of posterior distributions
    • Shen, X., and Wasserman, L. Rates of convergence of posterior distributions. Ann. Statist. 29, 3 (2001), 687-714.
    • (2001) Ann. Statist , vol.29 , Issue.3 , pp. 687-714
    • Shen, X.1    Wasserman, L.2
  • 14
    • 51049088387 scopus 로고    scopus 로고
    • Rates of contraction of posterior distributions based on Gaussian process priors
    • Van der Vaart, A. W., and Van Zanten, J. H. Rates of contraction of posterior distributions based on Gaussian process priors. Ann. Statist. 36, 3 (2008), 1435-1463.
    • (2008) Ann. Statist. , vol.36 , Issue.3 , pp. 1435-1463
    • Van Der Vaart, A.W.1    Van Zanten, J.H.2
  • 15
    • 69049100661 scopus 로고    scopus 로고
    • Reproducing kernel Hilbert spaces of Gaussian priors
    • Van der Vaart, A. W., and van Zanten, J. H. Reproducing kernel Hilbert spaces of Gaussian priors. IMS Collections 3 (2008), 200-222.
    • (2008) IMS Collections , vol.3 , pp. 200-222
    • Van Der Vaart, A.W.1    Van Zanten, J.H.2
  • 17
    • 0034347381 scopus 로고    scopus 로고
    • Bayesian aspects of some nonparametric problems
    • Zhao, L. H. Bayesian aspects of some nonparametric problems. Ann. Statist. 28, 2 (2000), 532-552.
    • (2000) Ann. Statist , vol.28 , Issue.2 , pp. 532-552
    • Zhao, L.H.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.