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We provide a clear and concise introduction to the subjects of inverse problems and data assimilation, and their inter-relations.
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The iterated Kalman smoother as a Gauss–Newton method
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Multilevel Sequential Monte Carlo Samplers
A. Beskos, A. Jasra, K. J. H. Law, R. Tempone, and Y. Zhou · 1994
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Sequential data assimilation with a nonlinear quasi-geostrophic model using Monte Carlo methods to forecast error statistics
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Numerical Methods for Unconstrained Optimization and Nonlinear Equations
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Regularization of Inverse Problems
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Assimilation of Geosat altimeter data for the Agulhas current using the ensemble Kalman filter with a quasigeostrophic model
G. Evensen and P. V. Leeuwen · 1996
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A regularizing Levenberg-Marquardt scheme, with applications to inverse groundwater filtration problems
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Monte Carlo and quasi-Monte Carlo methods
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Discrete filtering using branching and interacting particle systems
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Asymptotic Statistics
A. V. der Vaart · 1998
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Data assimilation using an ensemble Kalman filter technique
P. L. Houtekamer and H. Mitchell · 1998
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When are quasi-Monte Carlo algorithms efficient for high dimensional integrals?
I. H. Sloan and H. Woźniakowski · 1998
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Dynamical Systems and Numerical Analysis , volume 2
A. M. Stuart and A. R. Humphries · 1998
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An introduction to variational methods for graphical models
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Beneath the noise, chaos
S. P. Lalley · 1999
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Filtering via simulation: Auxiliary particle filters
M. Pitt and N. Shephard · 1999
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On sequential Monte Carlo sampling methods for Bayesian filtering
A. Doucet, S. Godsill, and C. Andrieu · 2000
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An ensemble Kalman smoother for nonlinear dynamics
G. Evensen and P. J. Van Leeuwen · 2000
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The Met. Office global three-dimensional variational data assimilation scheme
A. C. Lorenc, S. P. Ballard, R. S. Bell, N. B. Ingleby, P. L. F. Andrews, D. M. Barker, J. R. Bray, A. M. Clayton, T. Dalby, D. Li, et al · 2000
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An ensemble adjustment Kalman filter for data assimilation
J. L. Anderson · 2001
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Adaptive sampling with the ensemble transform Kalman filter. Part I: Theoretical aspects
C. H. Bishop, B. J. Etherton, and S. J. Majumdar · 2001
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An introduction to sequential Monte Carlo methods
A. Doucet, N. d. Freitas, and N. Gordon · 2001
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Underbalanced and low-head drilling operations: Real time interpretation of measured data and operational support
R. Lorentzen, R. Fjelde, J. FrØyen, A. Lage, G. Naevdal, and E. Vefring · 2001
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Optimal scaling for various Metropolis-Hastings algorithms
G. O. Roberts, J. S. Rosenthal, et al · 2001
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Ensemble randomized maximum likelihood method as an iterative ensemble smoother
Y. Chen and D. Oliver · 2002
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A survey of convergence results on particle filtering methods for practitioners
D. Crisan and A. Doucet · 2002
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On choosing and bounding probability metrics
A. Gibbs and F. Su · 2002
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Lectures on the Coupling Method
T. Lindvall · 2002
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Ergodicity for PDE’s and approximations: locally Lipschitz vector fields and degenerate noise
J. Mattingly, A. Stuart, and D. Higham · 2002
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Computational Methods for Inverse Problems
C. R. Vogel · 2002
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Atmospheric Modeling, Data Assimilation and Predictability
E. Kalnay · 2003
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Information Theory, Inference and Learning Algorithms
D. MacKay · 2003
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Fundamentals of Inverse Problems
E. L. Miller and W. C. Karl · 2003
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Ensemble square root filters
M. K. Tippett, J. L. Anderson, C. H. Bishop, T. M. Hamill, and J. S. Whitaker · 2003
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Convex Optimization
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Feynman-Kac Formulae: Genealogical and Interacting Particle Systems with Applications
P. Del Moral · 2004
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Pattern Recognition and Machine Learning , volume 128
C. M. Bishop · 2006
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Sequential Monte Carlo samplers
P. Del Moral, A. Doucet, and A. Jasra · 2006
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When did Bayesian inference become “Bayesian"?
S. E. Fienberg · 2006
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Markov chain Monte Carlo: stochastic simulation for Bayesian inference
D. Gamerman and H. Lopes · 2006
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Statistical and Computational Inverse Problems
J. Kaipio and E. Somersalo · 2006
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Numerical Optimization
J. Nocedal and S. Wright · 2006
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Iterative forms of the ensemble Kalman filter
A. C. Reynolds, M. Zafari, and G. Li · 2006
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An Introduction to Bayesian Scientific Computing: Ten Lectures on Subjective Computing , volume 2
D. Calvetti and E. Somersalo · 2007
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An iterative ensemble Kalman filter for multiphase fluid flow data assimilation
Y. Gu and D. S. Oliver · 2007
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Stochastic Processes and Filtering Theory
A. Jazwinski · 2007
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An iterative ensemble Kalman filter for data assimilation
G. Li and A. C. Reynolds · 2007
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The Met Office global four-dimensional variational data assimilation scheme
F. Rawlins, S. P. Ballard, K. J. Bovis, A. M. Clayton, D. Li, G. W. Inverarity, A. C. Lorenc, and T. J. Payne · 2007
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Fundamentals of Stochastic Filtering , volume 60
A. Bain and D. Crisan · 2008
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Sharp failure rates for the bootstrap particle filter in high dimensions
P. Bickel, B. Li, and T. Bengtsson · 2008
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A note on auxiliary particle filters
A. Johansen and A. Doucet · 2008
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Monte Carlo Strategies in Scientific Computing
J. S. Liu · 2008
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Inverse Theory for Petroleum Reservoir Characterization and History Matching
D. Oliver, A. Reynolds, and N. Liu · 2008
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The matrix cookbook
K. Petersen and M. Pedersen · 2008
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Graphical Models, Exponential Families, and Variational Inference
M. J. Wainwright and M. I. Jordan · 2008
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The ensemble Kalman filter in reservoir engineering–a review
S. I. Aanonsen, G. Nævdal, D. S. Oliver, A. C. Reynolds, and B. Vallès · 2009
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Data Assimilation: the Ensemble Kalman Filter
G. Evensen · 2009
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Data assimilation in weather forecasting: a case study in PDE-constrained optimization
M. Fisher, J. Nocedal, Y. Trémolet, and S. Wright · 2009
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Large sample asymptotics for the ensemble Kalman filter
F. Gland, V. Monbet, and V. Tran · 2009
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A stochastic collocation approach to Bayesian inference in inverse problems
Y. Marzouk and D. Xiu · 2009
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Bayesian approach to inverse problems
M. Dashti and A. M. Stuart · 2017
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Theory of Probability: A Critical Introductory Treatment , volume 6
B. De Finetti · 2017
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The Bayesian formulation and well-posedness of fractional elliptic inverse problems
N. Garcia Trillos and D. Sanz-Alonso · 2017
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Well-posed Bayesian inverse problems with infinitely divisible and heavy-tailed prior measures
B. Hosseini · 2017
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Well-posed Bayesian inverse problems: Priors with exponential tails
B. Hosseini and N. Nigam · 2017
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Adaptive importance sampling Monte Carlo simulation for general multivariate probability laws
R. Kawai · 2017
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Statistical exponential families: A digest with flash cards
F. Nielsen and V. Garcia · 2009
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Approximation of Bayesian inverse problems for PDE’s
S. Cotter, M. Dashti, and A. M. Stuart · 2010
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Ensemble samplers with affine invariance
J. Goodman and J. Weare · 2010
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Parameter and state model reduction for large-scale statistical inverse problems
C. Lieberman, K. Willcox, and O. Ghattas · 2010
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Inverse problems: a Bayesian perspective
A. M. Stuart · 2010
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Importance sampling: a review
S. Tokdar, S. Kass, and R. Kass · 2010
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Structured inference networks for nonlinear state space models
R. Krishnan, U. Shalit, and D. Sontag · 2017
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Gaussian approximations for probability measures on ℝ d \mathbb{R}^{d}
Y. Lu, A. M. Stuart, and H. Weber · 2017
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Effective sample size for importance sampling based on discrepancy measures
L. Martino, V. Elvira, and F. Louzada · 2017
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What the collapse of the ensemble Kalman filter tells us about particle filters
M. Morzfeld, D. Hodyss, and C. Snyder · 2017
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A dynamical systems framework for intermittent data assimilation
S. Reich · 2017
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Gaussian approximations of small noise diffusions in Kullback-Leibler divergence
D. Sanz-Alonso and A. M. Stuart · 2017
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Analysis of the ensemble Kalman filter for inverse problems
C. Schillings and A. M. Stuart · 2017
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A strongly convergent numerical scheme from ensemble Kalman inversion
D. Blömker, C. Schillings, and P. Wacker · 2018
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Optimization methods for large-scale machine learning
L. Bottou, F. E. Curtis, and J. Nocedal · 2018
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Accuracy of some approximate Gaussian filters for the Navier–Stokes equation in the presence of model error
M. Branicki, A. J. Majda, and K. J. H. Law · 2018
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Data assimilation in the geosciences: An overview of methods, issues, and perspectives
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Analysis of hierarchical ensemble Kalman inversion
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Parameterizations for ensemble Kalman inversion
N. K. Chada, M. A. Iglesias, L. Roininen, and A. M. Stuart · 2018
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The sample size required in importance sampling
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Comparison of local particle filters and new implementations
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Continuum limits of posteriors in graph Bayesian inverse problems
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E. Haber, F. Lucka, and L. Ruthotto · 2018
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Almost sure error bounds for data assimilation in dissipative systems with unbounded observation noise
L. Oljaca, J. Brocker, and T. Kuna · 2018
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On concentration properties of partially observed chaotic systems
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