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Volumn 42, Issue 5, 2014, Pages 1850-1878

The Bernstein-von Mises theorem and nonregular models

Author keywords

Approximate posterior; Bayesian inference; Bernstein von Mises theorem; Boundary; Nonregular; Posterior concentration; Spect; Tomography; Total variation distance; Variance estimation in mixed models

Indexed keywords


EID: 84908258625     PISSN: 00905364     EISSN: None     Source Type: Journal    
DOI: 10.1214/14-AOS1239     Document Type: Article
Times cited : (34)

References (28)
  • 1
    • 0033438067 scopus 로고    scopus 로고
    • The consistency of posterior distributions in nonparametric problems
    • MR1714718
    • Barron, A., Schervish, M. J. and Wasserman, L. (1999). The consistency of posterior distributions in nonparametric problems. Ann. Statist. 27 536-561. MR1714718
    • (1999) Ann. Statist , vol.27 , pp. 536-561
    • Barron, A.1    Schervish, M.J.2    Wasserman, L.3
  • 2
    • 85041776740 scopus 로고    scopus 로고
    • Bertsekas, D. P. (2003). Convex Analysis and Optimization. Athena Scientific and Tsinghua Univ. Press, Belmont, MA.
    • Bertsekas, D. P. (2003). Convex Analysis and Optimization. Athena Scientific and Tsinghua Univ. Press, Belmont, MA.
  • 3
    • 0000013152 scopus 로고
    • On the statistical analysis of dirty pictures
    • MR0876840
    • Besag, J. (1986). On the statistical analysis of dirty pictures. J. Roy. Statist. Soc. Ser. B 48 259-302. MR0876840
    • (1986) J. Roy. Statist. Soc. Ser. B , vol.48 , pp. 259-302
    • Besag, J.1
  • 4
    • 84884129834 scopus 로고    scopus 로고
    • Consistency of the posterior distribution in generalized linear inverse problems
    • 43, MR3094485
    • Bochkina, N. (2013). Consistency of the posterior distribution in generalized linear inverse problems. Inverse Problems 29 095010, 43. MR3094485
    • (2013) Inverse Problems , vol.29 , pp. 095010
    • Bochkina, N.1
  • 5
    • 4444268259 scopus 로고    scopus 로고
    • Likelihood estimation and inference in a class of nonregular econometric models
    • MR2077489
    • Chernozhukov, V. and Hong, H. (2004). Likelihood estimation and inference in a class of nonregular econometric models. Econometrica 72 1445-1480. MR2077489
    • (2004) Econometrica , vol.72 , pp. 1445-1480
    • Chernozhukov, V.1    Hong, H.2
  • 6
    • 80052902328 scopus 로고    scopus 로고
    • Consistency of the maximum likelihood estimator for general hidden Markov models
    • MR2797854
    • Douc, R., Moulines, E., Olsson, J. and van Handel, R. (2011). Consistency of the maximum likelihood estimator for general hidden Markov models. Ann. Statist. 39 474-513. MR2797854
    • (2011) Ann. Statist , vol.39 , pp. 474-513
    • Douc, R.1    Moulines, E.2    Olsson, J.3    Van Handel, R.4
  • 7
    • 0036429906 scopus 로고    scopus 로고
    • Asymptotic normality with small relative errors of posterior probabilities of half-spaces
    • MR1936321
    • Dudley, R. M. and Haughton, D. (2002). Asymptotic normality with small relative errors of posterior probabilities of half-spaces. Ann. Statist. 30 1311-1344. MR1936321
    • (2002) Ann. Statist , vol.30 , pp. 1311-1344
    • Dudley, R.M.1    Haughton, D.2
  • 8
    • 84950942481 scopus 로고
    • Laplace approximations for posterior expectations when the mode occurs at the boundary of the parameter space
    • MR1266297
    • Erkanli, A. (1994). Laplace approximations for posterior expectations when the mode occurs at the boundary of the parameter space. J. Amer. Statist. Assoc. 89 250-258. MR1266297
    • (1994) J. Amer. Statist. Assoc , vol.89 , pp. 250-258
    • Erkanli, A.1
  • 9
    • 0021518209 scopus 로고
    • Stochastic relaxation, gibbs distributions, and the Bayesian restoration of images
    • Geman, S. and Geman, D. (1984). Stochastic relaxation, gibbs distributions, and the Bayesian restoration of images. IEEE Trans. Pattern Anal. Mach. Intell. 6 721-741.
    • (1984) IEEE Trans. Pattern Anal. Mach. Intell , vol.6 , pp. 721-741
    • Geman, S.1    Geman, D.2
  • 10
    • 3142739880 scopus 로고
    • On convergence of posterior distributions
    • MR1389869
    • Ghosal, S., Ghosh, J. K. and Samanta, T. (1995). On convergence of posterior distributions. Ann. Statist. 23 2145-2152. MR1389869
    • (1995) Ann. Statist , vol.23 , pp. 2145-2152
    • Ghosal, S.1    Ghosh, J.K.2    Samanta, T.3
  • 11
    • 0141947045 scopus 로고
    • Asymptotic behaviour of Bayes estimates and posterior distributions in multiparameter nonregular cases
    • MR1372011
    • Ghosal, S. and Samanta, T. (1995). Asymptotic behaviour of Bayes estimates and posterior distributions in multiparameter nonregular cases. Math. Methods Statist. 4 361-388. MR1372011
    • (1995) Math. Methods Statist , vol.4 , pp. 361-388
    • Ghosal, S.1    Samanta, T.2
  • 12
    • 0012347244 scopus 로고
    • Stability and convergence of the posterior in non-regular problems
    • West Lafayette, IN, S. S. Gupta and J. O. Berger, eds., Springer, New York, MR1286304
    • Ghosh, J. K., Ghosal, S. and Samanta, T. (1994). Stability and convergence of the posterior in non-regular problems. In Statistical Decision Theory and Related Topics, V (West Lafayette, IN, 1992) (S. S. Gupta and J. O. Berger, eds.) 183-199. Springer, New York. MR1286304
    • (1992) Statistical Decision Theory and Related Topics, V , pp. 183-199
    • Ghosh, J.K.1    Ghosal, S.2    Samanta, T.3
  • 13
    • 0025404969 scopus 로고
    • Bayesian reconstructions from emission tomography data using a modified EM algorithm
    • Green, P. J. (1990). Bayesian reconstructions from emission tomography data using a modified EM algorithm. IEEE Trans. Med. Imag. 9 84-93.
    • (1990) IEEE Trans. Med. Imag , vol.9 , pp. 84-93
    • Green, P.J.1
  • 14
    • 0142007875 scopus 로고    scopus 로고
    • Asymptotic efficiency in parametric structural models with parameter-dependent support
    • MR2000249
    • Hirano, K. and Porter, J. R. (2003). Asymptotic efficiency in parametric structural models with parameter-dependent support. Econometrica 71 1307-1338. MR2000249
    • (2003) Econometrica , vol.71 , pp. 1307-1338
    • Hirano, K.1    Porter, J.R.2
  • 15
    • 85041787260 scopus 로고    scopus 로고
    • Ibragimov, I. A. and Has'minskiѤ R. Z. (1981). Statistical Estimation: Asymptotic Theory. Springer, New York. MR0620321
    • Ibragimov, I. A. and Has'minskiѤ R. Z. (1981). Statistical Estimation: Asymptotic Theory. Springer, New York. MR0620321
  • 16
    • 0000319983 scopus 로고
    • Speed of estimation in positron emission tomography and related inverse problems
    • MR1041393
    • Johnstone, I. M. and Silverman, B. W. (1990). Speed of estimation in positron emission tomography and related inverse problems. Ann. Statist. 18 251-280. MR1041393
    • (1990) Ann. Statist , vol.18 , pp. 251-280
    • Johnstone, I.M.1    Silverman, B.W.2
  • 17
    • 0000678581 scopus 로고
    • On some asymptotic properties of maximum likelihood estimates and related Bayes' estimates
    • MR0054913
    • Le Cam, L. (1953). On some asymptotic properties of maximum likelihood estimates and related Bayes' estimates. Univ. California Publ. Statist. 1 277-329. MR0054913
    • (1953) Univ. California Publ. Statist , vol.1 , pp. 277-329
    • Le Cam, L.1
  • 18
    • 85041757239 scopus 로고    scopus 로고
    • Le Cam, L. and Yang, G. L. (1990). Asymptotics in Statistics: Some Basic Concepts. Springer, New York. MR1066869
    • Le Cam, L. and Yang, G. L. (1990). Asymptotics in Statistics: Some Basic Concepts. Springer, New York. MR1066869
  • 19
    • 84976156472 scopus 로고
    • Maximum-likelihood estimation in non-standard conditions
    • MR0290493
    • Moran, P. A. P. (1971). Maximum-likelihood estimation in non-standard conditions. Proc. Cambridge Philos. Soc. 70 441-450. MR0290493
    • (1971) Proc. Cambridge Philos. Soc , vol.70 , pp. 441-450
    • Moran, P.A.P.1
  • 21
    • 84908241445 scopus 로고    scopus 로고
    • Bayes and empirical Bayes: Do they merge?
    • Petrone, S., Rousseau, J. and Scricciolo, C. (2012). Bayes and empirical Bayes: Do they merge? Biometrika 99 1-21.
    • (2012) Biometrika , vol.99 , pp. 1-21
    • Petrone, S.1    Rousseau, J.2    Scricciolo, C.3
  • 22
    • 85041791626 scopus 로고    scopus 로고
    • Polyak, B. T. (1983). Introduction to Optimization (Vvedenie v Optimizatsiyu, in Russian). Nauka, Moscow. MR0719196
    • Polyak, B. T. (1983). Introduction to Optimization (Vvedenie v Optimizatsiyu, in Russian). Nauka, Moscow. MR0719196
  • 23
    • 84907319426 scopus 로고
    • Asymptotic properties of maximum likelihood estimators and likelihood ratio tests under nonstandard conditions
    • MR0898365
    • Self, S. G. and Liang, K.-Y. (1987). Asymptotic properties of maximum likelihood estimators and likelihood ratio tests under nonstandard conditions. J. Amer. Statist. Assoc. 82 605-610. MR0898365
    • (1987) J. Amer. Statist. Assoc , vol.82 , pp. 605-610
    • Self, S.G.1    Liang, K.-Y.2
  • 24
    • 0034356976 scopus 로고    scopus 로고
    • On the asymptotics of constrained local M-estimators
    • MR1792795
    • Shapiro, A. (2000). On the asymptotics of constrained local M-estimators. Ann. Statist. 28 948-960. MR1792795
    • (2000) Ann. Statist , vol.28 , pp. 948-960
    • Shapiro, A.1
  • 26
    • 85041762033 scopus 로고    scopus 로고
    • van der Vaart, A. W. (1998). Asymptotic Statistics. Cambridge Univ. Press, Cambridge. MR1652247
    • van der Vaart, A. W. (1998). Asymptotic Statistics. Cambridge Univ. Press, Cambridge. MR1652247
  • 27
    • 0031497559 scopus 로고    scopus 로고
    • Generalization of likelihood ratio tests under nonstandard conditions
    • MR1439327
    • Vu, H. T. V. and Zhou, S. (1997). Generalization of likelihood ratio tests under nonstandard conditions. Ann. Statist. 25 897-916. MR1439327
    • (1997) Ann. Statist , vol.25 , pp. 897-916
    • Vu, H.T.V.1    Zhou, S.2
  • 28
    • 0031503760 scopus 로고    scopus 로고
    • Fully Bayesian reconstructions from single-photon emission computed tomography data
    • Weir, I. S. (1997). Fully Bayesian reconstructions from single-photon emission computed tomography data. J. Amer. Statist. Assoc. 92 49-60.
    • (1997) J. Amer. Statist. Assoc , vol.92 , pp. 49-60
    • Weir, I.S.1


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