Generalized Modes in Bayesian Inverse Problems

Uncertainty quantification requires efficient summarization of high- or even infinite-dimensional (i.e., nonparametric) distributions based on, e.g., suitable point estimates (modes) for posterior ...

[1]  Peng Chen,et al.  Hessian-based adaptive sparse quadrature for infinite-dimensional Bayesian inverse problems☆ , 2017, 1706.06692.

[2]  V. Kolehmainen,et al.  Sparsity-promoting Bayesian inversion , 2012 .

[3]  Joel Franklin,et al.  Well-posed stochastic extensions of ill-posed linear problems☆ , 1970 .

[4]  Martin Burger,et al.  Maximum a posteriori probability estimates in infinite-dimensional Bayesian inverse problems , 2014, 1412.5816.

[5]  Nicholas Zabaras,et al.  Hierarchical Bayesian models for inverse problems in heat conduction , 2005 .

[6]  Habib N. Najm,et al.  Stochastic spectral methods for efficient Bayesian solution of inverse problems , 2005 .

[7]  Andrew M. Stuart,et al.  MAP estimators for piecewise continuous inversion , 2015, 1509.03136.

[8]  Juha Lehrback,et al.  The annular decay property and capacity estimates for thin annuli , 2015, 1512.06577.

[9]  Andrew M. Stuart,et al.  Inverse problems: A Bayesian perspective , 2010, Acta Numerica.

[10]  L. Tierney,et al.  Accurate Approximations for Posterior Moments and Marginal Densities , 1986 .

[11]  Habib N. Najm,et al.  Dimensionality reduction and polynomial chaos acceleration of Bayesian inference in inverse problems , 2008, J. Comput. Phys..

[12]  A. Peirce.  Computer Methods in Applied Mechanics and Engineering , 2010 .

[13]  Daniela Calvetti,et al.  Hypermodels in the Bayesian imaging framework , 2008 .

[14]  Matti Lassas. Eero Saksman,et al.  Discretization-invariant Bayesian inversion and Besov space priors , 2009, 0901.4220.

[15]  Barbara Kaltenbacher,et al.  On convergence and convergence rates for Ivanov and Morozov regularization and application to some parameter identification problems in elliptic PDEs , 2018, 1801.10181.

[16]  Andrew M. Stuart,et al.  Gaussian Approximations for Probability Measures on Rd , 2017, SIAM/ASA J. Uncertain. Quantification.

[17]  Raul Tempone,et al.  Fast Bayesian experimental design: Laplace-based importance sampling for the expected information gain , 2017, Computer Methods in Applied Mechanics and Engineering.

[18]  Christian Clason,et al.  Quasi-solution of linear inverse problems in non-reflexive Banach spaces , 2018, Journal of Inverse and Ill-posed Problems.

[19]  A. M. Stuart,et al.  Sparse deterministic approximation of Bayesian inverse problems , 2011, 1103.4522.

[20]  D. Lorenz,et al.  Necessary conditions for variational regularization schemes , 2012, 1204.0649.

[21]  E. Somersalo,et al.  Inverse problems with structural prior information , 1999 .

[22]  Roel Snieder,et al.  Linear and Nonlinear Inverse Problems , 2000 .

[23]  C. Schwab,et al.  Scaling limits in computational Bayesian inversion , 2014 .

[24]  A. Stuart,et al.  MAP estimators and their consistency in Bayesian nonparametric inverse problems , 2013, 1303.4795.

[25]  M. Burger,et al.  Maximum a posteriori estimates in linear inverse problems with log-concave priors are proper Bayes estimators , 2014, 1402.5297.

[26]  Martin Burger,et al.  Sparsity-promoting and edge-preserving maximum a posteriori estimators in non-parametric Bayesian inverse problems , 2017, 1705.03286.

[27]  A. Stuart,et al.  The Bayesian Approach to Inverse Problems , 2013, 1302.6989.

[28]  Andrew M. Stuart,et al.  Approximation of Bayesian Inverse Problems for PDEs , 2009, SIAM J. Numer. Anal..