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Latz, Jonas Bayesian inverse problems are usually well-posed. (English) Zbl 07725072 SIAM Rev. 65, No. 3, 831-865 (2023). MSC: 62F15 49K40 65C60 65N21 68Q32 68T05 PDFBibTeX XMLCite \textit{J. Latz}, SIAM Rev. 65, No. 3, 831--865 (2023; Zbl 07725072) Full Text: DOI
de Hoop, Maarten V.; Kovachki, Nikola B.; Nelsen, Nicholas H.; Stuart, Andrew M. Convergence rates for learning linear operators from noisy data. (English) Zbl 1514.62075 SIAM/ASA J. Uncertain. Quantif. 11, 480-513 (2023). MSC: 62G20 62C10 68T05 47A62 PDFBibTeX XMLCite \textit{M. V. de Hoop} et al., SIAM/ASA J. Uncertain. Quantif. 11, 480--513 (2023; Zbl 1514.62075) Full Text: DOI arXiv
Agapiou, Sergios; Mathé, Peter Designing truncated priors for direct and inverse Bayesian problems. (English) Zbl 1493.62238 Electron. J. Stat. 16, No. 1, 158-200 (2022). MSC: 62G20 62C10 62F15 45Q05 PDFBibTeX XMLCite \textit{S. Agapiou} and \textit{P. Mathé}, Electron. J. Stat. 16, No. 1, 158--200 (2022; Zbl 1493.62238) Full Text: DOI arXiv Link
Tuan, Nguyen Huy; Nane, Erkan; Trong, Dang Duc Analysis of a quasi-reversibility method for nonlinear parabolic equations with uncertainty data. (English) Zbl 1482.35278 Ill. J. Math. 65, No. 4, 793-845 (2021). MSC: 35R30 35K20 35K59 35R60 47H10 47J06 PDFBibTeX XMLCite \textit{N. H. Tuan} et al., Ill. J. Math. 65, No. 4, 793--845 (2021; Zbl 1482.35278) Full Text: DOI Link
Nguyen Huy Tuan; Vo Anh Khoa; Phan Thi Khanh Van; Vo Van Au An improved quasi-reversibility method for a terminal-boundary value multi-species model with white Gaussian noise. (English) Zbl 1466.65108 J. Comput. Appl. Math. 384, Article ID 113176, 14 p. (2021). MSC: 65M32 65M30 65M22 65M15 60H35 60H40 35B35 35B65 35K51 35R25 35R60 92C37 35Q92 PDFBibTeX XMLCite \textit{Nguyen Huy Tuan} et al., J. Comput. Appl. Math. 384, Article ID 113176, 14 p. (2021; Zbl 1466.65108) Full Text: DOI arXiv
Dunlop, Matthew M.; Helin, Tapio; Stuart, Andrew M. Hyperparameter estimation in Bayesian MAP estimation: parameterizations and consistency. (English) Zbl 1441.62084 SMAI J. Comput. Math. 6, 69-100 (2020). MSC: 62G05 62C10 62G20 45Q05 PDFBibTeX XMLCite \textit{M. M. Dunlop} et al., SMAI J. Comput. Math. 6, 69--100 (2020; Zbl 1441.62084) Full Text: DOI arXiv
Latz, Jonas On the well-posedness of Bayesian inverse problems. (English) Zbl 1437.49050 SIAM/ASA J. Uncertain. Quantif. 8, 451-482 (2020). MSC: 49N45 49K40 62F15 65N21 68Q32 68T05 PDFBibTeX XMLCite \textit{J. Latz}, SIAM/ASA J. Uncertain. Quantif. 8, 451--482 (2020; Zbl 1437.49050) Full Text: DOI arXiv
Giordano, Matteo; Kekkonen, Hanne Bernstein-von Mises theorems and uncertainty quantification for linear inverse problems. (English) Zbl 1436.62161 SIAM/ASA J. Uncertain. Quantif. 8, 342-373 (2020). MSC: 62G20 65N21 35J25 35K05 46E22 PDFBibTeX XMLCite \textit{M. Giordano} and \textit{H. Kekkonen}, SIAM/ASA J. Uncertain. Quantif. 8, 342--373 (2020; Zbl 1436.62161) Full Text: DOI arXiv
Arridge, Simon; Maass, Peter; Öktem, Ozan; Schönlieb, Carola-Bibiane Solving inverse problems using data-driven models. (English) Zbl 1429.65116 Acta Numerica 28, 1-174 (2019). MSC: 65J20 65J22 94A08 65-02 PDFBibTeX XMLCite \textit{S. Arridge} et al., Acta Numerica 28, 1--174 (2019; Zbl 1429.65116) Full Text: DOI
Agapiou, Sergios; Mathé, Peter Posterior contraction in Bayesian inverse problems under Gaussian priors. (English) Zbl 1405.62051 Hofmann, Bernd (ed.) et al., New trends in parameter identification for mathematical models. Proceedings of the conference, Rio de Janeiro, Brazil, October 30 – November 3, 2017. Cham: Birkhäuser (ISBN 978-3-319-70823-2/hbk; 978-3-319-70824-9/ebook). Trends in Mathematics, 1-29 (2018). MSC: 62G99 62F15 PDFBibTeX XMLCite \textit{S. Agapiou} and \textit{P. Mathé}, in: New trends in parameter identification for mathematical models. Proceedings of the conference, Rio de Janeiro, Brazil, October 30 -- November 3, 2017. Cham: Birkhäuser. 1--29 (2018; Zbl 1405.62051) Full Text: DOI
Trabs, Mathias Bayesian inverse problems with unknown operators. (English) Zbl 1394.62036 Inverse Probl. 34, No. 8, Article ID 085001, 27 p. (2018). MSC: 62G05 62F15 62G20 PDFBibTeX XMLCite \textit{M. Trabs}, Inverse Probl. 34, No. 8, Article ID 085001, 27 p. (2018; Zbl 1394.62036) Full Text: DOI arXiv
Agapiou, Sergios; Burger, Martin; Dashti, Masoumeh; Helin, Tapio Sparsity-promoting and edge-preserving maximum a posteriori estimators in non-parametric Bayesian inverse problems. (English) Zbl 06866427 Inverse Probl. 34, No. 4, Article ID 045002, 37 p. (2018). MSC: 65J22 62G07 62F15 PDFBibTeX XMLCite \textit{S. Agapiou} et al., Inverse Probl. 34, No. 4, Article ID 045002, 37 p. (2018; Zbl 06866427) Full Text: DOI arXiv
Ding, Litao; Lu, Shuai; Cheng, Jin Weak-norm posterior contraction rate of the 4DVAR method for linear severely ill-posed problems. (English) Zbl 1516.65079 J. Complexity 46, 1-18 (2018). MSC: 65M32 65M30 35R30 62P30 62F15 26A33 35R11 PDFBibTeX XMLCite \textit{L. Ding} et al., J. Complexity 46, 1--18 (2018; Zbl 1516.65079) Full Text: DOI
Agapiou, S.; Papaspiliopoulos, O.; Sanz-Alonso, D.; Stuart, A. M. Importance sampling: intrinsic dimension and computational cost. (English) Zbl 1442.62026 Stat. Sci. 32, No. 3, 405-431 (2017). MSC: 62D05 62-08 PDFBibTeX XMLCite \textit{S. Agapiou} et al., Stat. Sci. 32, No. 3, 405--431 (2017; Zbl 1442.62026) Full Text: DOI arXiv Euclid
De Micheli, Enrico; Viano, Giovanni Alberto Probabilistic regularization of Fredholm integral equations of the first kind. (English) Zbl 1334.45002 J. Integral Equations Appl. 28, No. 1, 31-74 (2016). MSC: 45B05 47A52 65C20 94A05 PDFBibTeX XMLCite \textit{E. De Micheli} and \textit{G. A. Viano}, J. Integral Equations Appl. 28, No. 1, 31--74 (2016; Zbl 1334.45002) Full Text: DOI Euclid