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Добірка наукової літератури з теми "Monte Carlo method"

Автор: Grafiati
Опубліковано: 4 червня 2021
Оновлено: 29 липня 2024

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Статті в журналах з теми "Monte Carlo method"

1

Caflisch, Russel E. "Monte Carlo and quasi-Monte Carlo methods." Acta Numerica 7 (January 1998): 1–49. http://dx.doi.org/10.1017/s0962492900002804.

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Monte Carlo is one of the most versatile and widely used numerical methods. Its convergence rate, O(N−1/2), is independent of dimension, which shows Monte Carlo to be very robust but also slow. This article presents an introduction to Monte Carlo methods for integration problems, including convergence theory, sampling methods and variance reduction techniques. Accelerated convergence for Monte Carlo quadrature is attained using quasi-random (also called low-discrepancy) sequences, which are a deterministic alternative to random or pseudo-random sequences. The points in a quasi-random sequence are correlated to provide greater uniformity. The resulting quadrature method, called quasi-Monte Carlo, has a convergence rate of approximately O((logN)kN−1). For quasi-Monte Carlo, both theoretical error estimates and practical limitations are presented. Although the emphasis in this article is on integration, Monte Carlo simulation of rarefied gas dynamics is also discussed. In the limit of small mean free path (that is, the fluid dynamic limit), Monte Carlo loses its effectiveness because the collisional distance is much less than the fluid dynamic length scale. Computational examples are presented throughout the text to illustrate the theory. A number of open problems are described.
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2

Makarova, K. V., A. G. Makarov, M. A. Padalko, V. S. Strongin, and K. V. Nefedev. "Multispin Monte Carlo Method." Dal'nevostochnyi Matematicheskii Zhurnal 20, no. 2 (November 25, 2020): 212–20. http://dx.doi.org/10.47910/femj202020.

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The article offers a Monte Carlo cluster method for numerically calculating a statistical sample of the state space of vector models. The statistical equivalence of subsystems in the Ising model and quasi-Markov random walks can be used to increase the efficiency of the algorithm for calculating thermodynamic means. The cluster multispin approach extends the computational capabilities of the Metropolis algorithm and allows one to find configurations of the ground and low-energy states.
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3

Rajabalinejad, M. "Bayesian Monte Carlo method." Reliability Engineering & System Safety 95, no. 10 (October 2010): 1050–60. http://dx.doi.org/10.1016/j.ress.2010.04.014.

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4

The Lam, Nguyen. "QUANTUM DIFFUSION MONTE CARLO METHOD FOR LOW-DIMENTIONAL SYSTEMS." Journal of Science, Natural Science 60, no. 7 (2015): 81–87. http://dx.doi.org/10.18173/2354-1059.2015-0036.

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5

Siyamah, Imroatus, Endah RM Putri, and Chairul Imron. "Cat bond valuation using Monte Carlo and quasi Monte Carlo method." Journal of Physics: Conference Series 1821, no. 1 (March 1, 2021): 012053. http://dx.doi.org/10.1088/1742-6596/1821/1/012053.

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6

Kandidov, V. P. "Monte Carlo method in nonlinear statistical optics." Uspekhi Fizicheskih Nauk 166, no. 12 (1996): 1309. http://dx.doi.org/10.3367/ufnr.0166.199612c.1309.

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7

Rashki, Mohsen. "The soft Monte Carlo method." Applied Mathematical Modelling 94 (June 2021): 558–75. http://dx.doi.org/10.1016/j.apm.2021.01.022.

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8

Aboughantous, Charles H. "A Contributorn Monte Carlo Method." Nuclear Science and Engineering 118, no. 3 (November 1994): 160–77. http://dx.doi.org/10.13182/nse94-a19382.

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9

Bruce, A. D., A. N. Jackson, G. J. Ackland, and N. B. Wilding. "Lattice-switch Monte Carlo method." Physical Review E 61, no. 1 (January 1, 2000): 906–19. http://dx.doi.org/10.1103/physreve.61.906.

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10

Gubernatis, Jim, and Naomichi Hatano. "The multicanonical Monte Carlo method." Computing in Science & Engineering 2, no. 2 (March 2000): 95–102. http://dx.doi.org/10.1109/mcise.2000.5427643.

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Дисертації з теми "Monte Carlo method"

1

Janzon, Krister. "Monte Carlo Path Simulation and the Multilevel Monte Carlo Method." Thesis, Umeå universitet, Institutionen för fysik, 2018. http://urn.kb.se/resolve?urn=urn:nbn:se:umu:diva-151975.

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Анотація:
A standard problem in the field of computational finance is that of pricing derivative securities. This is often accomplished by estimating an expected value of a functional of a stochastic process, defined by a stochastic differential equation (SDE). In such a setting the random sampling algorithm Monte Carlo (MC) is useful, where paths of the process are sampled. However, MC in its standard form (SMC) is inherently slow. Additionally, if the analytical solution to the underlying SDE is not available, a numerical approximation of the process is necessary, adding another layer of computational complexity to the SMC algorithm. Thus, the computational cost of achieving a certain level of accuracy of the estimation using SMC may be relatively high. In this thesis we introduce and review the theory of the SMC method, with and without the need of numerical approximation for path simulation. Two numerical methods for path approximation are introduced: the Euler–Maruyama method and Milstein's method. Moreover, we also introduce and review the theory of a relatively new (2008) MC method – the multilevel Monte Carlo (MLMC) method – which is only applicable when paths are approximated. This method boldly claims that it can – under certain conditions – eradicate the additional complexity stemming from the approximation of paths. With this in mind, we wish to see whether this claim holds when pricing a European call option, where the underlying stock process is modelled by geometric Brownian motion. We also want to compare the performance of MLMC in this scenario to that of SMC, with and without path approximation. Two numerical experiments are performed. The first to determine the optimal implementation of MLMC, a static or adaptive approach. The second to illustrate the difference in performance of adaptive MLMC and SMC – depending on the used numerical method and whether the analytical solution is available. The results show that SMC is inferior to adaptive MLMC if numerical approximation of paths is needed, and that adaptive MLMC seems to meet the complexity of SMC with an analytical solution. However, while the complexity of adaptive MLMC is impressive, it cannot quite compensate for the additional cost of approximating paths, ending up roughly ten times slower than SMC with an analytical solution.
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2

Lacasse, Martin Daniel. "New dynamical Monte Carlo renormalization group method." Thesis, McGill University, 1990. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=60062.

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The kinetics of a phase transition has been studied by using a new dynamical Monte Carlo renormalization group method. Using a majority rule block-spin transformation in both space and contiguous times, we numerically renormalized the evolving configurations during the phase separation of a kinetic Ising model with spin-flip dynamics. We find that, in the scaling regime, the average domain size R(t) grows in time consistently with the $R sim t sp{1/2}$ Allen-Cahn antiphase boundary motion theory, although some correcting factors may exist. The same procedure has also been applied to the corresponding equilibrium critical system in order to find the critical exponent z. Our method yields values that are consistent with the ones obtained from a finite-size scaling analysis applied on the same data, thus showing that, in principle, this method can be successfully used to determine z in a more precise and consistent way.
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3

Zhang, Yichuan. "Scalable geometric Markov chain Monte Carlo." Thesis, University of Edinburgh, 2016. http://hdl.handle.net/1842/20978.

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Markov chain Monte Carlo (MCMC) is one of the most popular statistical inference methods in machine learning. Recent work shows that a significant improvement of the statistical efficiency of MCMC on complex distributions can be achieved by exploiting geometric properties of the target distribution. This is known as geometric MCMC. However, many such methods, like Riemannian manifold Hamiltonian Monte Carlo (RMHMC), are computationally challenging to scale up to high dimensional distributions. The primary goal of this thesis is to develop novel geometric MCMC methods applicable to large-scale problems. To overcome the computational bottleneck of computing second order derivatives in geometric MCMC, I propose an adaptive MCMC algorithm using an efficient approximation based on Limited memory BFGS. I also propose a simplified variant of RMHMC that is able to work effectively on larger scale than the previous methods. Finally, I address an important limitation of geometric MCMC, namely that is only available for continuous distributions. I investigate a relaxation of discrete variables to continuous variables that allows us to apply the geometric methods. This is a new direction of MCMC research which is of potential interest to many applications. The effectiveness of the proposed methods is demonstrated on a wide range of popular models, including generalised linear models, conditional random fields (CRFs), hierarchical models and Boltzmann machines.
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4

Veld, Pieter Jacob in 't. "Monte Carlo studies of liquid structure /." Digital version:, 2000. http://wwwlib.umi.com/cr/utexas/fullcit?p9992826.

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5

Hazelton, Martin Luke. "Method of density estimation with application to Monte Carlo methods." Thesis, University of Oxford, 1993. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.334850.

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6

Lefebvre, Geneviève 1978. "Practical issues in modern Monte Carlo integration." Thesis, McGill University, 2007. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=103209.

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Анотація:
Computing marginal likelihoods to perform Bayesian model selection is a challenging task, particularly when the models considered involve a large number of parameters. In this thesis, we propose the use of an adaptive quadrature algorithm to automate the selection of the grid in path sampling, an integration technique recognized as one of the most powerful Monte Carlo integration statistical methods for marginal likelihood estimation. We begin by examining the impact of two tuning parameters of path sampling, the choice of the importance density and the specification of the grid, which are both shown to be potentially very influential. We then present, in detail, the Grid Selection by Adaptive Quadrature (GSAQ) algorithm for selecting the grid. We perform a comparison between the GSAQ and standard grid implementation of path sampling using two well-studied data sets; the GSAQ approach is found to yield superior results. GSAQ is then successfully applied to a longitudinal hierarchical regression model selection problem in Multiple Sclerosis research.
Using an identity arising in path sampling, we then derive general expressions for the Kullback-Leibler (KL) and Jeffrey (J) divergences between two distributions with common support but from possibly different parametric families. These expressions naturally stem from path sampling when the popular geometric path is used to link the extreme densities. Expressions for the KL and J-divergences are also given for any two intermediate densities lying on the path. Estimates for the KL divergence (up to a constant) and for the J-divergence, between a posterior distribution and a selected importance density, can be obtained directly, prior to path sampling implementation. The J-divergence is shown to be helpful for choosing importance densities that minimize the error of the path sampling estimates.
Finally we present the results of a simulation study devised to investigate whether improvement in performance can be achieved by using the KL and J-divergences to select sequences of distributions in parallel (population-based) simulations, such as in the Sequential Monte Carlo Sampling and the Annealed Importance Sampling algorithms. We compare these choices of sequences to more conventional choices in the context of a mixture example. Unexpected results are obtained, and those for the KL and J-divergences are mixed. More fundamentally, we uncover the need to select the sequence of tempered distributions in accordance with the resampling scheme.
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7

Lee, Ming Ripman, and 李明. "Monte Carlo simulation for confined electrolytes." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 2000. http://hub.hku.hk/bib/B31240513.

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Lee, Ming Ripman. "Monte Carlo simulation for confined electrolytes /." Hong Kong : University of Hong Kong, 2000. http://sunzi.lib.hku.hk/hkuto/record.jsp?B22055009.

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9

Yam, Chiu Yu. "Quasi-Monte Carlo methods for bootstrap." HKBU Institutional Repository, 2000. http://repository.hkbu.edu.hk/etd_ra/272.

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Wong, Ping-yung. "Molecular clusters on surfaces : a Monte Carlo study /." Hong Kong : University of Hong Kong, 1999. http://sunzi.lib.hku.hk/hkuto/record.jsp?B20566694.

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Книги з теми "Monte Carlo method"

1

Lemieux, Christiane. Monte carlo and quasi-monte carlo sampling. New York: Springer, 2009.

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2

Kalos, Malvin H. Monte Carlo methods. New York: J. Wiley & Sons, 1986.

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3

Dunn, William L. Exploring Monte Carlo methods. Amsterdam: Elsevier/Academic Press, 2012.

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4

1957-, Madras Neal Noah, Fields Institute for Research in Mathematical Sciences., and Workshop on Monte Carlo Methods (1998 : Toronto, Ont.), eds. Monte Carlo methods. Providence, RI: American Mathematical Society, 2000.

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5

I, Schueller G., ed. Monte Carlo simulation. Lisse: A.A. Balkema, 2001.

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6

Fox, Bennett L. Strategies for quasi-Monte Carlo. Boston: Kluwer Academic, 1999.

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7

Pierre, L' Ecuyer, and Owen Art B, eds. Monte Carlo and quasi-Monte Carlo methods 2008. Heidelberg: Springer, 2009.

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8

Casella, George, and Christian P. Robert. Monte Carlo Statistical Methods. 2nd ed. New York, USA: Springer, 2004.

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9

Kroese, Dirk P., Thomas Taimre, Zdravko I. Botev, and Rueven Y. Rubinstein. Simulation and the Monte Carlo Method. Hoboken, NJ, USA: John Wiley & Sons, Inc., 2007. http://dx.doi.org/10.1002/9780470285312.

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10

Rubinstein, Reuven Y., and Dirk P. Kroese. Simulation and the Monte Carlo Method. Hoboken, NJ, USA: John Wiley & Sons, Inc., 2016. http://dx.doi.org/10.1002/9781118631980.

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Частини книг з теми "Monte Carlo method"

1

Liou, William W. "Monte Carlo Method." In Encyclopedia of Microfluidics and Nanofluidics, 2315–19. New York, NY: Springer New York, 2015. http://dx.doi.org/10.1007/978-1-4614-5491-5_1059.

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2

Liou, William W. "Monte Carlo Method." In Encyclopedia of Microfluidics and Nanofluidics, 1–5. Boston, MA: Springer US, 2013. http://dx.doi.org/10.1007/978-3-642-27758-0_1059-3.

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3

Weik, Martin H. "Monte Carlo method." In Computer Science and Communications Dictionary, 1045. Boston, MA: Springer US, 2000. http://dx.doi.org/10.1007/1-4020-0613-6_11803.

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4

Mosegaard, Klaus. "Monte Carlo Method." In Encyclopedia of Mathematical Geosciences, 1–7. Cham: Springer International Publishing, 2022. http://dx.doi.org/10.1007/978-3-030-26050-7_431-2.

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5

Mosegaard, Klaus. "Monte Carlo Method." In Encyclopedia of Mathematical Geosciences, 1–7. Cham: Springer International Publishing, 2021. http://dx.doi.org/10.1007/978-3-030-26050-7_431-1.

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6

Mosegaard, Klaus. "Monte Carlo Method." In Encyclopedia of Mathematical Geosciences, 890–96. Cham: Springer International Publishing, 2023. http://dx.doi.org/10.1007/978-3-030-85040-1_431.

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7

Choe, Geon Ho. "The Monte Carlo Method for Option Pricing Monte Carlo method." In Universitext, 501–17. Cham: Springer International Publishing, 2016. http://dx.doi.org/10.1007/978-3-319-25589-7_28.

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8

Buckley, James J., and Leonard J. Jowers. "Fuzzy Monte Carlo Method." In Monte Carlo Methods in Fuzzy Optimization, 57–65. Berlin, Heidelberg: Springer Berlin Heidelberg, 2007. http://dx.doi.org/10.1007/978-3-540-76290-4_6.

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9

Rollett, Anthony D., and Priya Manohar. "The Monte Carlo Method." In Continuum Scale Simulation of Engineering Materials, 77–114. Weinheim, FRG: Wiley-VCH Verlag GmbH & Co. KGaA, 2005. http://dx.doi.org/10.1002/3527603786.ch4.

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Tildesley, D. J. "The Monte Carlo Method." In Computer Simulation in Chemical Physics, 1–22. Dordrecht: Springer Netherlands, 1993. http://dx.doi.org/10.1007/978-94-011-1679-4_1.

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Тези доповідей конференцій з теми "Monte Carlo method"

1

Wilding, Nigel B. "Phase Switch Monte Carlo." In THE MONTE CARLO METHOD IN THE PHYSICAL SCIENCES: Celebrating the 50th Anniversary of the Metropolis Algorithm. AIP, 2003. http://dx.doi.org/10.1063/1.1632147.

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2

Frenkel, D. "Biased Monte Carlo Methods." In THE MONTE CARLO METHOD IN THE PHYSICAL SCIENCES: Celebrating the 50th Anniversary of the Metropolis Algorithm. AIP, 2003. http://dx.doi.org/10.1063/1.1632121.

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3

Bilgin, Muhammed, and Tolga Ensari. "Robot localization with Monte Carlo method." In 2017 Electric Electronics, Computer Science, Biomedical Engineerings' Meeting (EBBT). IEEE, 2017. http://dx.doi.org/10.1109/ebbt.2017.7956755.

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4

Ling*, Yue, Huazhong Wang, and Shaoyong Liu. "Monte Carlo background velocity inversion method." In Beijing 2014 International Geophysical Conference & Exposition, Beijing, China, 21-24 April 2014. Society of Exploration Geophysicists and Chinese Petroleum Society, 2014. http://dx.doi.org/10.1190/igcbeijing2014-188.

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Papp, Zsolt, Janos Kornis, and Balazs Gombkoto. "Monte Carlo method in digital holography." In Speckle Metrology 2003. SPIE, 2003. http://dx.doi.org/10.1117/12.516573.

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6

Gonzalez-Jorge, H., J. L. Valencia, V. Alvarez, F. Rodriguez, and F. J. Yebra. "Monte-Carlo method in AFM calibration." In 2009 Spanish Conference on Electron Devices (CDE). IEEE, 2009. http://dx.doi.org/10.1109/sced.2009.4800526.

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Stoffova, Veronika, and R. Horváth. "MONTE CARLO METHOD IN EDUCATIONAL PRACTICE." In 13th annual International Conference of Education, Research and Innovation. IATED, 2020. http://dx.doi.org/10.21125/iceri.2020.1532.

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Zhu, Juan, Shuai Wang, Da-wei Wang, Yan-ying Liu, and Yan-jie Wang. "Monte Carlo Tracking Method with Threshold Constraint." In 2009 2nd International Congress on Image and Signal Processing (CISP). IEEE, 2009. http://dx.doi.org/10.1109/cisp.2009.5301685.

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Chen, Nanguang. "Controlled Monte Carlo Method for Reflection Geometry." In Biomedical Topical Meeting. Washington, D.C.: OSA, 2006. http://dx.doi.org/10.1364/bio.2006.me9.

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DIMOV, IVAN, and ANETA KARAIVANOVA. "A POWER METHOD WITH MONTE CARLO ITERATIONS." In Proceedings of the Fourth International Conference. WORLD SCIENTIFIC, 1999. http://dx.doi.org/10.1142/9789814291071_0022.

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Звіти організацій з теми "Monte Carlo method"

1

Hill, James Lloyd. Introduction to the Monte Carlo Method. Office of Scientific and Technical Information (OSTI), June 2020. http://dx.doi.org/10.2172/1634920.

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2

Blomquist, R. N., and E. M. Gelbard. Alternative implementations of the Monte Carlo power method. Office of Scientific and Technical Information (OSTI), March 2002. http://dx.doi.org/10.2172/793906.

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3

Svatos, M. The macro response Monte Carlo method for electron transport. Office of Scientific and Technical Information (OSTI), September 1998. http://dx.doi.org/10.2172/3847.

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4

Fishman, George S. Sensitivity Analysis Using the Monte Carlo Acceptance-Rejection Method. Fort Belvoir, VA: Defense Technical Information Center, September 1988. http://dx.doi.org/10.21236/ada201261.

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5

Carlin, Bradley P., and Alan E. Gelfand. An Iterative Monte Carlo Method for Nonconjugate Bayesian Analysis. Fort Belvoir, VA: Defense Technical Information Center, September 1992. http://dx.doi.org/10.21236/ada255991.

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Taro Ueki. A Multivariate Time Series Method for Monte Carlo Reactor Analysis. Office of Scientific and Technical Information (OSTI), August 2008. http://dx.doi.org/10.2172/935876.

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Richie, David A., James A. Ross, Song J. Park, and Dale R. Shires. A Monte Carlo Method for Multi-Objective Correlated Geometric Optimization. Fort Belvoir, VA: Defense Technical Information Center, May 2014. http://dx.doi.org/10.21236/ada603830.

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Acton, Scott T., and Bing Li. A Sequential Monte Carlo Method for Real-time Tracking of Multiple Targets. Fort Belvoir, VA: Defense Technical Information Center, May 2010. http://dx.doi.org/10.21236/ada532576.

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Boyd, Iain D. A Threshold Line Dissociation Model for the Direct Simulation Monte Carlo Method,. Fort Belvoir, VA: Defense Technical Information Center, May 1996. http://dx.doi.org/10.21236/ada324950.

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Politis, Dimitris N., Raffaella Giacomini, and Halbert White. A warp-speed method for conducting Monte Carlo experiments involving bootstrap estimators. Cemmap, May 2012. http://dx.doi.org/10.1920/wp.cem.2012.1112.

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