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Multilevel Monte Carlo path simulation
 OPERATIONS RESEARCH
, 2008
"... We show that multigrid ideas can be used to reduce the computational complexity of estimating an expected value arising from a stochastic differential equation using Monte Carlo path simulations. In the simplest case of a Lipschitz payoff and an Euler discretisation, the computational cost to achiev ..."
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Cited by 190 (22 self)
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to achieve an accuracy of O(É) is reduced from O(É â3) to O(É â2 (log É) 2). The analysis is supported by numerical results showing significant computational savings.
The psychometric function: I. Fitting, sampling, and goodness of fit
, 2001
"... The psychometric function relates an observer’s performance to an independent variable, usually some physical quantity of a stimulus in a psychophysical task. This paper, together with its companion paper (Wichmann & Hill, 2001), describes an integrated approach to (1) fitting psychometric funct ..."
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Cited by 219 (11 self)
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the potential errors of applying traditional c 2 methods to psychophysical data and advocate use of Monte Carlo resampling techniques that do not rely on asymptotic theory. We have made available the software to implement our methods. The performance of an observer on a psychophysical
Monte Carlo Status Report
"... A systematic study of the detector response for various MSW parameters has been completed. Survival probabilities for neutrinos produced at the center of the sun were calculated by integrating the MSW equations [1] for a range of Am^E (109 to 3 x 10"5) and sin ^. Figure 1 shows a typical set o ..."
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.1). Finally in^figures 3 to 7 we show the detector response for sm^O = 0.7, 0.3, 0.1, 0.01 and 0.01 for selected values oflogio(Am2) ranging from 3.0 to 8.5 (the plots are labeled with the mass difference and the mixing angle in the formmmaa). Each figure represents a vertical slice (ranging from
Monte Carlo Simulations of Spin Systems
 In: Computational Physics (Springer, BerlinHeidelberg
, 1996
"... Abstract. This lecture gives a brief introduction to Monte Carlo simulations of classical O(n) spin systems such as the Ising (n = 1), XY (n = 2), and Heisenberg (n = 3) model. In the first part I discuss some aspects of Monte Carlo algorithms to generate the raw data. Here special emphasis is place ..."
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Cited by 10 (7 self)
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Abstract. This lecture gives a brief introduction to Monte Carlo simulations of classical O(n) spin systems such as the Ising (n = 1), XY (n = 2), and Heisenberg (n = 3) model. In the first part I discuss some aspects of Monte Carlo algorithms to generate the raw data. Here special emphasis
QuasiMonte Carlo sampling for stochastic variational problems
"... • Computational methods for solving stochastic variational problems require (first) a discretization of the underlying probability distribution induced by a numerical integration scheme for the approximate computation of expectations and (second) an efficient solver for a (large scale) finitedimen ..."
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• Computational methods for solving stochastic variational problems require (first) a discretization of the underlying probability distribution induced by a numerical integration scheme for the approximate computation of expectations and (second) an efficient solver for a (large scale) finitedimensional
Sequential Monte Carlo Techniques for the Solution of Linear Systems
 Journal of Scientific Computing
, 1994
"... Given a linear system Ax = b, where x is an mvector, direct numerical methods, such as Gaussian elimination, take time O(m 3) to find x. Iterative numerical methods, such as the GaussSeidel method or SOR, reduce the system to the form whence x = a + Hx, x = ∑r=0ּHra; and then apply the iterations ..."
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Cited by 24 (2 self)
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Given a linear system Ax = b, where x is an mvector, direct numerical methods, such as Gaussian elimination, take time O(m 3) to find x. Iterative numerical methods, such as the GaussSeidel method or SOR, reduce the system to the form whence x = a + Hx, x = ∑r=0ּHra; and then apply the iterations
MONTE CARLO SIMULATIONS OF THE ELECTRODEPOSITION OF COPPER
"... Deposition of submicron features by electrodeposition, used for microelectronics interconnects[1], requires trace amounts of organic additives to obtain desired deposit characteristics. A Monte Carlo simulation has been developed to model the growth of Copper electrodeposits with additives and witho ..."
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and without additives. The overall model is a collection of three modules, (a) a Monte Carlo model of nano scale surface growth, (b) a continuum model of the macro scale bulk solution and (c) an overall electrochemical control module for the linked Monte Carlo and continuum model. These modules
Valuation of Mortgage Backed Securities Using Brownian Bridges to Reduce Effective Dimension
, 1997
"... The quasiMonte Carlo method for financial valuation and other integration problems has error bounds of size O((log N) k N \Gamma1 ), or even O((log N) k N \Gamma3=2 ), which suggests significantly better performance than the error size O(N \Gamma1=2 ) for standard Monte Carlo. But in hig ..."
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Cited by 100 (15 self)
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The quasiMonte Carlo method for financial valuation and other integration problems has error bounds of size O((log N) k N \Gamma1 ), or even O((log N) k N \Gamma3=2 ), which suggests significantly better performance than the error size O(N \Gamma1=2 ) for standard Monte Carlo
A Quantum Monte Carlo Study
, 1992
"... The one dimensional Kondo lattice model is investigated using Quantum Monte Carlo and transfer matrix techniques. In the strong coupling region ferromagnetic ordering is found even at large band fillings. In the weak coupling region the system shows an RKKY like behavior. In recent years the Kondo l ..."
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. However, as a typical model of strongly correlated electron systems it could be analyzed by only few approximate treatments[2, 3] and has still 1 resisted to give clear insight into the various possible ground state. It would be of particular interest to understand the phase diagram of the KLM
Markov chain Monte Carlo Inversion
, 2009
"... a b s t r a c t We present an overview of Markov chain Monte Carlo, a sampling method for model inference and uncertainty quantification. We focus on the Bayesian approach to MCMC, which allows us to estimate the posterior distribution of model parameters, without needing to know the normalising con ..."
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a b s t r a c t We present an overview of Markov chain Monte Carlo, a sampling method for model inference and uncertainty quantification. We focus on the Bayesian approach to MCMC, which allows us to estimate the posterior distribution of model parameters, without needing to know the normalising
Results 1  10
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1,146