Monte Carlo Methods

Hammersley, J. M.; Handscomb, D. C.

doi:10.1007/978-94-009-5819-7

Cited by 2,263 publications

(978 citation statements)

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“…We denote by p l i 1 ≤ l ≤ q i the evaluation points and w l i 1 ≤ l ≤ q i the associated weights. The points are the roots of the polynomial ψ q i (y) of order q introduced in (11). A multidimensional quadrature can be obtained by tensorizing the monodimensional gauss quadratures along each random dimension.…”

Section: A Non-intrusive Methods : Projection Methodsmentioning

confidence: 99%

“…The functions u j i [p j (θ )] are the unknowns of the problem and are sought in a one dimensional space for example the space generated by the polynomials ψ l i [p i (θ )] (see (11)). The calculation of the optimal low rank approximation (the value of T as smaller as possible) is a difficult task.…”

Section: Non-intrusive Methodsmentioning

confidence: 99%

“…Monte Carlo Simulation methods or perturbation methods are available to solve stochastic problems since early 50 s [11,12]. In the 90 s, researches on quantification of uncertainties in numerical models using approximation methods first began in the field of mechanical and civil engineering [31].…”

Section: Introductionmentioning

confidence: 99%

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Approximation Methods to Solve Stochastic Problems in Computational Electromagnetics

Clénet

2016

Scientific Computing in Electrical Engineering

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is an open access repository that collects the work of Arts et Métiers ParisTech researchers and makes it freely available over the web where possible. To cite this version :Stephane CLÉNET -Approximation Methods to Solve Stochastic Problems in Computational Electromagnetics -2016Any correspondence concerning this service should be sent to the repository Administrator : archiveouverte@ensam.eu Approximation Methods to solve Stochastic Problems in Computational ElectromagneticsStéphane ClénetAbstract To account for uncertainties on model parameters, the stochastic approach can be used. The model parameters as well as the outputs are then random fields or variables. Several methods are available in the literature to solve stochastic models like sampling methods, perturbation methods or approximation methods. In this paper, we propose an overview on the solution of stochastic problems in computational electromagnetics using approximation methods. Some applications will be presented in order to illustrate the possibilities offered by the approximation methods but also their current limitations due to the curse of dimensionality. Finally, recent numerical techniques proposed in the literature to face the curse of dimensionality are presented for non-intrusive and intrusive approaches.

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Section: A Non-intrusive Methods : Projection Methodsmentioning

confidence: 99%

Section: Non-intrusive Methodsmentioning

confidence: 99%

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Approximation Methods to Solve Stochastic Problems in Computational Electromagnetics

Clénet

2016

Scientific Computing in Electrical Engineering

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“…In CTmod, random quantities with known theoretical distributions are sampled using the inverse transform or acceptance-rejection methods, see for instance [18,19]. In the inverse transform method, a random number γ is sampled from a uniform distribution in the interval (0,1) and the sample x of a random variablex is calculated as…”

Section: The Monte Carlo Methodsmentioning

confidence: 99%

CTmod—A toolkit for Monte Carlo simulation of projections including scatter in computed tomography

Sandborg

Carlsson

2008

Computer Methods and Programs in Biomedicine

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The CTmod toolkit is a set of C++ class libraries based on the CERN's application development framework ROOT. It uses the Monte Carlo method to simulate energy imparted to a CT-scanner detector array. Photons with a given angle-energy distribution are emitted from the X-ray tube approximated by a point source, transported through a phantom, and their contribution to the energy imparted per unit surface area of each detector element is scored. Alternatively, the scored quantity may be the fluence, energy fluence, plane fluence, plane energy fluence, or kerma to air in the center of each detector element. Phantoms are constructed from homogenous solids or voxel arrays via overlapping. Implemented photon interactions (photoelectric effect, coherent scattering, and incoherent scattering) are restricted to the energy range from 10 keV to 200 keV. Variance reduction techniques include the collision density estimator and survival biasing combined with the Russian roulette. The toolkit has been used to estimate the amount of scatter in cone beam computed tomography and planar radiography.

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“…A disadvantage of deterministic predictions is that the influence of uncertainty and variability on exposure remains obscured. To overcome this problem, probabilistic techniques such as Monte Carlo simulation were introduced (Hammersley and Handscomb, 1964;NRC, 1975;McKone and Ryan, 1989). Monte Carlo simulation allows users to define uncertain or variable input parameters as probability distributions and propagates these input distributions into an output distribution of the predicted exposure.…”

Section: Introductionmentioning

confidence: 99%

Separation of uncertainty and interindividual variability in human exposure modeling

Ragas

Brouwer

Büchner

et al. 2008

J Expo Sci Environ Epidemiol

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The NORMTOX model predicts the lifetime-averaged exposure to contaminants through multiple environmental media, that is, food, air, soil, drinking and surface water. The model was developed to test the coherence of Dutch environmental quality objectives (EQOs). A set of EQOs is called coherent if simultaneous exposure to different environmental media that are all polluted up to their respective EQOs does not result in exceeding the acceptable or tolerable daily intake (ADI or TDI). Aim of the present study is to separate the impact of uncertainty and interindividual variability in coherence predictions with the NORMTOX model. The method is illustrated in a case study for chlorfenvinphos, mercury and nitrate. First, ANOVA was used to calculate interindividual variability in input parameters. Second, nested Monte Carlo simulation was used to propagate uncertainty and interindividual variability separately. Lifetime-averaged exposure to chlorfenvinphos, mercury and nitrate was modeled for the Dutch population. Output distributions specified the population fraction at risk, due to a particular exposure, and the reliability of this risk. From the case study, it was obtained that at lifelong exposure to all media polluted up to their standard, 100% of the Dutch population exceeds the ADI for chlorfenvinphos, 15% for mercury and 0% for nitrate. Variance in exposure to chlorfenvinphos, mercury and nitrate is mostly caused by interindividual variability instead of true uncertainty. It is concluded that the likelihood that ADIs of chlorfenvinphos and mercury will be exceeded should be further explored. If exceeding is likely, decision makers should focus on identification of high-risk subpopulations, rather than on additional research to obtain more accurate estimates for particular parameters.

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Monte Carlo Methods

Cited by 2,263 publications

References 0 publications

Approximation Methods to Solve Stochastic Problems in Computational Electromagnetics

Approximation Methods to Solve Stochastic Problems in Computational Electromagnetics

CTmod—A toolkit for Monte Carlo simulation of projections including scatter in computed tomography

Separation of uncertainty and interindividual variability in human exposure modeling

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