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These lecture notes highlight the mathematical and computational structure relating to the formulation of, and development of algorithms for, the Bayesian approach to inverse problems in differential equations.
Integration von Funktionen, deren Werte die Elemente eines Vektorraumes sind
S. Bochner · 1933
Earlier work this paper cites.
Integration in abstract spaces
T. H. Hildebrandt · 1953
Earlier work this paper cites.
Equations of state calculations by fast computing machines
N. Metropolis · 1953
Earlier work this paper cites.
Equivalence and perpendicularity of Gaussian processes
J. Feldman · 1958
Earlier work this paper cites.
On a property of normal distribution of any stochastic process
Y. Hájek · 1958
Earlier work this paper cites.
Convergence of Probability Measures
P. Billingsley · 1968
Earlier work this paper cites.
Intégrabilité des vecteurs gaussiens
X. Fernique · 1970
Earlier work this paper cites.
Well-posed stochastic extensions of ill-posed linear problems
J. Franklin · 1970
Earlier work this paper cites.
Monte Carlo sampling methods using Markov chains and their applications
W. K. Hastings · 1970
Earlier work this paper cites.
A short proof of the Hájek-Feldman theorem
T. Kühn · 1978
Earlier work this paper cites.
Functional analysis
K. Yosida · 1980
Earlier work this paper cites.
The Geometry of Random Fields
R. Adler · 1981
Earlier work this paper cites.
An inverse problem for the steady state diffusion equation
G. Richter · 1981
Earlier work this paper cites.
Semigroups of Linear Operators and Applications to Partial Differential Equations
A. Pazy · 1983
Earlier work this paper cites.
Theory of function spaces , vol. 38 of Mathematik und ihre Anwendungen in Physik und Technik [Mathematics and its Applications in Physics and Technology]
H. Triebel · 1983
Earlier work this paper cites.
Linear estimators and measurable linear transformations on a Hilbert space
A. Mandelbaum · 1984
Earlier work this paper cites.
Handbook of stochastic methods
C. W. Gardiner · 1985
Earlier work this paper cites.
Some random series of functions , vol. 5 of Cambridge Studies in Advanced Mathematics
J.-P. Kahane · 1985
Earlier work this paper cites.
Real and complex analysis . Third edition
W. Rudin · 1987
Earlier work this paper cites.
Estimation Techniques for Distributed Parameter Systems
H.T. Banks · 1989
Earlier work this paper cites.
Linear inverse problems for generalised random variables
M. S. Lehtinen · 1989
Earlier work this paper cites.
Stochastic equations in infinite dimensions , vol. 44 of Encyclopedia of Mathematics and its Applications
G. DaPrato · 1992
Earlier work this paper cites.
Ten lectures on wavelets. CBMS-NSF Regional Conference Series in Applied Mathematics, 61. Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA, (1992)
I. Daubechies · 1992
Earlier work this paper cites.
Wavelets and operators. Translated from the 1990 French original by D. H. Salinger. Cambridge Studies in Advanced Mathematics, 37. Cambridge University Press, Cambridge, (1992)
Y. Meyer · 1992
Earlier work this paper cites.
Theory of function spaces. II , vol. 84 of Monographs in Mathematics
H. Triebel · 1992
Earlier work this paper cites.
Markov Chains and Stochastic Stability
S. P. Meyn · 1993
Earlier work this paper cites.
Bayesian Theory
J. Bernardo · 1994
Earlier work this paper cites.
H. Niederreiter
1994
Earlier work this paper cites.
Continuous martingales and Brownian motion , vol. 293 of Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences]
D. Revuz · 1994
Earlier work this paper cites.
Gaussian Random Functions , vol. 322 of Mathematics and its Applications
M. Lifshits · 1995
Cited alongside, same era.
Analytic Semigroups and Optimal Regularity in Parabolic Problems
A. Lunardi · 1995
Cited alongside, same era.
Ergodicity for infinite dimensional systems
G. Da Prato · 1996
Cited alongside, same era.
Regularization of Inverse Problems
H. Engl · 1996
Cited alongside, same era.
An Introduction to the Mathematical Theory of Inverse Problems
A. Kirsch · 1996
Cited alongside, same era.
Isoperimetry and Gaussian analysis
M. Ledoux · 1996
Cited alongside, same era.
Gaussian measures , vol. 62 of Mathematical Surveys and Monographs
Partial differential equations. An introduction . Second edition
W. A. Strauss · 2008
Later among the works it cites.
Bayesian inverse problems for functions and applications to fluid mechanics
S. Cotter · 2009
Later among the works it cites.
Introduction to the calculus of variations. Translated from the 1992 French original. Second edition
B. Dacorogna · 2009
Later among the works it cites.
Introduction to Stochastic PDEs
M. Hairer · 2009
Later among the works it cites.
Discretization-invariant Bayesian inversion and Besov space priors
M. Lassas · 2009
Later among the works it cites.
Convergence rates of best n n -term galerkin approximations for a class of elliptic spdes
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V. I. Bogachev · 1998
Cited alongside, same era.
Partial Differential Equations
L. Evans · 1998
Cited alongside, same era.
Regression and classification using Gaussian process priors, (1998)
R. Neal · 1998
Cited alongside, same era.
Markov chains
J. Norris · 1998
Cited alongside, same era.
A note on Metropolis-Hastings kernels for general state spaces
L. Tierney · 1998
Cited alongside, same era.
Continuous-time Markov chains and applications , vol. 37 of Applications of Mathematics (New York)
G. Yin · 1998
Cited alongside, same era.
A. Cohen · 2010
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Approximation of Bayesian inverse problems
S. Cotter · 2010
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F.Y. Kuo, I.H. Sloan, G.W. Wasilikowski
2010
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Transition paths in molecules at finite temperature
F. Pinski · 2010
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Inverse problems: a Bayesian perspective
A. M. Stuart · 2010
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Imre Csiszar · 2011
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Uncertainty quantification and weak approximation of an elliptic inverse problem
M. Dashti · 2011
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Sampling conditioned hypoelliptic diffusions
M. Hairer · 2011
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Bayesian inverse problems with Gaussian priors
B. Knapik · 2011
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F.Y. Kuo, Ch. Schwab
2011
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Besov priors for Bayesian inverse problems
M. Dashti · 2012
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Non-Gaussian statistical inverse problems. Part I: Posterior distributions
S. Lasanen · 2012
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Non-Gaussian statistical inverse problems. Part II: Posterior distributions
S. Lasanen · 2012
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Diffusion limits of the random walk Metropolis algorithm in high dimensions
J. Mattingly · 2012
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Sparse deterministic approximation of bayesian inverse problems
C. Schwab · 2012
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Posterior contraction rates for the Bayesian approach to linear ill-posed inverse problems
S. Agapiou · 2013
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MCMC methods for functions: modifying old algorithms to make them faster
S. Cotter · 2013
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MAP estimators and their consistency in Bayesian nonparametric inverse problems
M. Dashti, KJH.Law, AM Stuart · 2013
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I.G. Graham, F.Y. Kuo, J.A. Nicholls, R. Scheichl, Ch. Schwab
2013
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Sparse, adaptive Smolyak quadratures for Bayesian inverse problems
C. Schillings · 2013
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S.Vollmer · 2013
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Spectral gaps for a Metropolis–Hastings algorithm in infinite dimensions
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