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In this paper, we consider the inverse problem of determining the permeability of the subsurface from hydraulic head measurements, within the framework of a steady Darcy model of groundwater flow.
Well-posed stochastic extensions of ill-posed linear problems
J. N. Franklin · 1970
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Linear estimators and measurable linear transformations on a Hilbert space
A. Mandelbaum · 1984
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Linear inverse problems for generalised random variables
M. S. Lehtinen, L. Päivärinta, and E. Somersalo · 1989
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Reversible jump markov chain monte carlo computation and bayesian model determination
P. J. Green · 1995
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A procedure to integrate well test data, reservoir performance history and 4-d seismic information into a reservoir description
J. Landa and R. Horne · 1997
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General methods for monitoring convergence of iterative simulations
S. P. Brooks and A. Gelman · 1998
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Inverse problems with structural prior information
J. P. Kaipio, V. Kolehmainen, M. Vauhkonen, and E. Somersalo · 1999
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Conditioning 3d stochastic channels to pressure data
B. Zhuoxin, D. S. Oliver, and A. C. Reynolds · 2000
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Discretizations of generalized random variables with applications to inverse problems
S. Lasanen · 2002
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Evaluation of Monte Carlo methods for assessing uncertainty
N. Liu and D. S. Oliver · 2003
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Ensemble Kalman filter for automatic history matching of geologic facies
N. Liu and D. S. Oliver · 2005
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Statistical inverse problems: discretization, model reduction and inverse crimes
J. P. Kaipio and E. Somersalo · 2007
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MCMC methods for diffusion bridges
A. Beskos, G. Roberts, A. M. Stuart, and J. Voss · 2008
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History matching of petroleum reservoirs using a level set technique
O. Dorn and R. Villegas · 2008
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Inverse Theory for Petroleum Reservoir Characterization and History Matching
D. S. Oliver, A. C. Reynolds, and N. Liu · 2008
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Bayesian inverse problems for functions and applications to fluid mechanics
S. L. Cotter, M. Dashti, J. C. Robinson, and A. M. Stuart · 2009
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Level set methods for inverse scattering-some recent developments
O. Dorn and D. Lesselier · 2009
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Efficient sampling techniques for uncertainty quantification in history matching using nonlinear error models and ensemble level upscaling techniques
Y. Efendiev, A. Datta-Gupta, X. Ma, and B. Mallick · 2009
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Discretization-invariant Bayesian inversion and Besov space priors
M. Lassas, E. Saksman, and S. Siltanen · 2009
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A stochastic collocation approach to Bayesian inference in inverse problems
Riemann manifold langevin and hamiltonian monte carlo methods
M. Girolami and B. Calderhead · 2011
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Level-set techniques for facies identification in reservoir modeling
M. A. Iglesias and D. McLaughlin · 2011
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Recent progress on reservoir history matching: a review
D. Oliver and Y. Chen · 2011
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Uncertainty quantification in history matching of channelized reservoirs using Markov chain level set approaches
J. Xie, Y. Efendiev, and A. Datta-Gupta · 2011
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Variational data assimilation using targetted random walks
S. L. Cotter, M. Dashti, and A. M. Stuart · 2012
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Besov priors for Bayesian inverse problems
M. Dashti, S. Harris, and A. M. Stuart · 2012
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Y. Marzouk and D. Xiu · 2009
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History matching of facies distribution with the enkf and level set parameterization
H. Chang, D. Zhang, and Z. Lu · 2010
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Approximation of Bayesian inverse problems for PDEs
S. L. Cotter, M. Dashti, and A. M. Stuart · 2010
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Bayesian uncertainty quantification for flows in heterogeneous porous media using reversible jump Markov chain Monte Carlo methods
A. Mondal, Y. Efendiev, B. Mallick, and A. Datta-Gupta · 2010
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Regression and classification using Gaussian process priors
R. Neal · 2010
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Inverse problems: a Bayesian perspective
A. M. Stuart · 2010
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Bayesian calibration of a large-scale geothermal reservoir model by a new adaptive delayed acceptance metropolis hastings algorithm
T Cui, C Fox, and MJ O’Sullivan · 2011
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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 convergence for approximated unknowns
S. Lasanen · 2012
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History matching on the Imperial College fault model using parallel tempering
J. N. Carter and D. A. White · 2013
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MCMC methods for functions: Modifying old algorithms to make them faster
S. L. Cotter, G. O. Roberts, A. M. Stuart, and D. White · 2013
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Investigation of the sampling performance of ensemble-based methods with a simple reservoir model
A. A. Emerick and A. C. Reynolds · 2013
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Evaluation of Gaussian approximations for data assimilation in reservoir models
M. A. Iglesias, K. J. H. Law, and A. M. Stuart · 2013
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Dimension-independent MCMC sampling for elliptic inverse problems with non-Gaussian priors
S. Vollmer · 2013
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