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Volumn 23, Issue 6, 2007, Pages 2469-2484

Convergence rate for the Bayesian approach to linear inverse problems

Author keywords

[No Author keywords available]

Indexed keywords

BAYESIAN NETWORKS; CONVERGENCE OF NUMERICAL METHODS; COVARIANCE MATRIX; PROBLEM SOLVING;

EID: 36749089116     PISSN: 02665611     EISSN: 13616420     Source Type: Journal    
DOI: 10.1088/0266-5611/23/6/012     Document Type: Article
Times cited : (22)

References (33)
  • 1
    • 13744251469 scopus 로고
    • On probabilistic methods for the solution of improperly posed problems
    • Bertero M and Viano G A 1978 On probabilistic methods for the solution of improperly posed problems Boll. Un. Mat. Ital. B 15 453-508
    • (1978) Boll. Un. Mat. Ital. , vol.15 , pp. 453-508
    • Bertero, M.1    Viano, G.A.2
  • 3
    • 10844236506 scopus 로고    scopus 로고
    • Consistency and rates of convergence of nonlinear Tikhonov regularization with random noise
    • Bissantz N, Hohage T and Munk A 2004 Consistency and rates of convergence of nonlinear Tikhonov regularization with random noise Inverse Problems 20 1773-89
    • (2004) Inverse Problems , vol.20 , Issue.6 , pp. 1773-1789
    • Bissantz, N.1    Hohage, T.2    Munk, A.3
  • 4
    • 41549168778 scopus 로고    scopus 로고
    • Convergence rates of general regularization methods for statistical inverse problems and applications
    • Bissantz N, Hohage T, Munk A and Ruymgaart F Convergence rates of general regularization methods for statistical inverse problems and applications SIAM J. Numer. Anal. accepted
    • SIAM J. Numer. Anal.
    • Bissantz, N.1    Hohage, T.2    Munk, A.3    Ruymgaart, F.4
  • 5
    • 21344492321 scopus 로고
    • Statistical estimation and optimal recovery
    • Donoho D L 1994 Statistical estimation and optimal recovery Ann. Stat. 22 238-70
    • (1994) Ann. Stat. , vol.22 , pp. 238-270
    • Donoho, D.L.1
  • 6
    • 0001346514 scopus 로고
    • Distances of probability measures and random variables
    • Dudley R M 1968 Distances of probability measures and random variables Ann. Math. Stat. 39 1563-72
    • (1968) Ann. Math. Stat. , vol.39 , pp. 1563-1572
    • Dudley, R.M.1
  • 9
    • 13744252042 scopus 로고    scopus 로고
    • Convergence rates in the Prokhorov metric for assessing uncertainty in ill-posed problems
    • Engl H W, Hofinger A and Kindermann S 2005 Convergence rates in the Prokhorov metric for assessing uncertainty in ill-posed problems Inverse Problems 21 399-412
    • (2005) Inverse Problems , vol.21 , Issue.1 , pp. 399-412
    • Engl, H.W.1    Hofinger, A.2    Kindermann, S.3
  • 10
    • 13744255231 scopus 로고
    • Continuity properties of the extension of a locally Lipschitz continuous map to the space of probability measures
    • Engl H W and Wakolbinger A 1995 Continuity properties of the extension of a locally Lipschitz continuous map to the space of probability measures Mon.hefte Math. 100 85-103
    • (1995) Mon.hefte Math. , vol.100 , Issue.2 , pp. 85-103
    • Engl, H.W.1    Wakolbinger, A.2
  • 11
    • 0038629779 scopus 로고
    • Entfernung zweier zufälliger Gröen und die Konvergenz nach Wahrscheinlichkeit
    • Fan K 1944 Entfernung zweier zufälliger Gröen und die Konvergenz nach Wahrscheinlichkeit Mat. Z. 49 681-3
    • (1944) Mat. Z. , vol.49 , Issue.1 , pp. 681-683
    • Fan, K.1
  • 13
    • 0034561754 scopus 로고    scopus 로고
    • Adaptive estimation of linear functionals in Hilbert scales from indirect white noise observations
    • Goldenshluger A and Pereverzev S V 2000 Adaptive estimation of linear functionals in Hilbert scales from indirect white noise observations Probab. Theory Relat. Fields 118 169-86
    • (2000) Probab. Theory Relat. Fields , vol.118 , Issue.2 , pp. 169-186
    • Goldenshluger, A.1    Pereverzev, S.V.2
  • 14
    • 84966255914 scopus 로고
    • Asymptotic theory of filtering for linear operator equations with discrete noisy data
    • Groetsch C W and Vogel C R 1987 Asymptotic theory of filtering for linear operator equations with discrete noisy data Math. Comput. 49 499-506
    • (1987) Math. Comput. , vol.49 , Issue.180 , pp. 499-506
    • Groetsch, C.W.1    Vogel, C.R.2
  • 16
    • 36749062827 scopus 로고    scopus 로고
    • The metrics of Prokhorov and Ky Fan for assessing uncertainty in inverse problems
    • Hofinger A 2006 The metrics of Prokhorov and Ky Fan for assessing uncertainty in inverse problems Sit.ber., Oesterr. Akad. Wiss. Math.-Nat.wiss. Kl. II accepted
    • (2006) Sit.ber., Oesterr. Akad. Wiss. Math.-Nat.wiss. Kl.
    • Hofinger, A.1
  • 18
    • 0034187252 scopus 로고    scopus 로고
    • Regularization of exponentially ill-posed problems
    • Hohage T 2000 Regularization of exponentially ill-posed problems Numer. Funct. Anal. Optim. 21 439-64
    • (2000) Numer. Funct. Anal. Optim. , vol.21 , Issue.3 , pp. 439-464
    • Hohage, T.1
  • 22
    • 0006684185 scopus 로고
    • Linear inverse problems for generalised random variables
    • Lehtinen M S, Päivärinta L and Somersalo E 1989 Linear inverse problems for generalised random variables Inverse Problems 5 599-612
    • (1989) Inverse Problems , vol.5 , Issue.4 , pp. 599-612
    • Lehtinen, M.S.1    Päivärinta, L.2    Somersalo, E.3
  • 24
    • 84966254921 scopus 로고
    • Convergence rates for regularized solutions
    • Lukas M A 1988 Convergence rates for regularized solutions Math. Comput. 51 107-31
    • (1988) Math. Comput. , vol.51 , Issue.183 , pp. 107-131
    • Lukas, M.A.1
  • 25
    • 36749064820 scopus 로고
    • Linear estimators and rodonifying operators
    • Luschgy H 1995 Linear estimators and rodonifying operators Theory Probab. Appl. 40 167-75
    • (1995) Theory Probab. Appl. , vol.40 , Issue.1 , pp. 167-175
    • Luschgy, H.1
  • 26
    • 0030269038 scopus 로고    scopus 로고
    • Statistical inverse estimation in Hilbert scales
    • Mair B A and Ruymgaart F H 1996 Statistical inverse estimation in Hilbert scales SIAM J. Appl. Math. 56 1424-44
    • (1996) SIAM J. Appl. Math. , vol.56 , Issue.5 , pp. 1424-1444
    • Mair, B.A.1    Ruymgaart, F.H.2
  • 27
    • 0038339461 scopus 로고    scopus 로고
    • Geometry of linear ill-posed problems in variable Hilbert scales
    • Mathé P and Pereverzev S V 2003 Geometry of linear ill-posed problems in variable Hilbert scales Inverse Problems 19 789-803
    • (2003) Inverse Problems , vol.19 , Issue.3 , pp. 789-803
    • Mathé, P.1    Pereverzev, S.V.2
  • 28
    • 33744515791 scopus 로고    scopus 로고
    • Regularization of some linear ill-posed problems with discretized random noisy data
    • Mathé P and Pereverzev S V 2006 Regularization of some linear ill-posed problems with discretized random noisy data Math. Comput. 75 1913-29
    • (2006) Math. Comput. , vol.75 , Issue.256 , pp. 1913-1929
    • Mathé, P.1    Pereverzev, S.V.2
  • 29
    • 0037227075 scopus 로고    scopus 로고
    • Morozov's discrepancy principle under general source conditions
    • Nair M T, Schock E and Tautenhahn U 2003 Morozov's discrepancy principle under general source conditions Z. Anal. Anwendungen 22 199-214
    • (2003) Z. Anal. Anwendungen , vol.22 , pp. 199-214
    • Nair, M.T.1    Schock, E.2    Tautenhahn, U.3
  • 31
    • 0000649228 scopus 로고
    • The existence of probability measures with given marginals
    • Strassen V 1965 The existence of probability measures with given marginals Ann. Math. Stat. 36 423-39
    • (1965) Ann. Math. Stat. , vol.36 , pp. 423-439
    • Strassen, V.1
  • 32
    • 0000544453 scopus 로고
    • Practical approximate solutions to linear operator equations when the data are noisy
    • Wahba G 1977 Practical approximate solutions to linear operator equations when the data are noisy SIAM J. Numer. Anal. 14 651-67
    • (1977) SIAM J. Numer. Anal. , vol.14 , Issue.4 , pp. 651-667
    • Wahba, G.1
  • 33
    • 0002555118 scopus 로고
    • Preservation of rates of convergence under mappings
    • Whitt W 1974 Preservation of rates of convergence under mappings Z. Wahrscheinlichkeitstheorie Verwandte Geb. 29 39-44
    • (1974) Z. Wahrscheinlichkeitstheorie Verwandte Geb. , vol.29 , Issue.1 , pp. 39-44
    • Whitt, W.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.