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In this paper we address the problem of the prohibitively large computational cost of existing Markov chain Monte Carlo methods for large--scale applications with high dimensional parameter spaces, e.g.
Equation of state calculations by fast computing machines
N. Metropolis, A.W. Rosenbluth, M.N. Rosenbluth, A.H. Teller, and E. Teller · 1953
Earlier work this paper cites.
Monte-Carlo sampling methods using Markov chains and their applications
W.K. Hastings · 1970
Earlier work this paper cites.
The Finite Element Method for Elliptic Problems
P. G. Ciarlet · 1978
Earlier work this paper cites.
A spectral method for confidence interval generation and run length control in simulations
P. Heidelberger and P. D. Welch · 1981
Earlier work this paper cites.
Analysis of the spatial structure of properties of selected aquifers
R.J. Hoeksema and P.K. Kitanidis · 1985
Earlier work this paper cites.
Quantitative Hydrogeology
G. de Marsily · 1986
Earlier work this paper cites.
Stochastic finite elements: a spectral approach
R.G. Ghanem and P.D. Spanos · 1991
Earlier work this paper cites.
Stochastic equations in infinite dimensions
G. Da Prato and J. Zabczyk · 1992
Earlier work this paper cites.
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A. Brandt, M. Galun, and D. Ron · 1994
Earlier work this paper cites.
Monte Carlo Statistical Methods
C. Robert and G. Casella · 1999
Earlier work this paper cites.
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Earlier work this paper cites.
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