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Simulation and the Monte Carlo Method
Abstract
Simulation and the Monte Carlo Method, Second Edition reflects the latest developments in the field and presents a fully updated and comprehensive account of the major topics that have emerged in Monte Carlo simulation since the publication of the classic First Edition over twenty-five years ago. While maintaining its accessible and intuitive approach, this revised edition features a wealth of up-to-date information that facilitates a deeper understanding of problem solving across a wide array of subject areas, such as engineering, statistics, computer science, mathematics, and the physical and life sciences." "Requiring only a basic, introductory knowledge of probability and statistics, Simulation and the Monte Carlo Method, Second Edition is an excellent text for upper-undergraduate and beginning graduate courses in simulation and Monte Carlo techniques. The book also serves as a valuable reference for professionals who would like to achieve a more formal understanding of the Monte Carlo method.
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“Convergence to low variability in terms of mean and standard deviations is reached at M=103, where both metrics stabilized with minimal variation beyond that point and correspond to the plateau of the coefficient of variation [40].”
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Reliability-based design optimization of structural systems under stochastic excitation: An overview
Jerez, D. J., Jensen, H. A., & Beer, M. (2021) · Mechanical Systems and Signal Processing · doi:10.1016/j.ymssp.2021.108397 · Cited by 83
“The use of simulation methods [18, 19, 20], however, is the most widely accepted approach for the evaluation of high-dimensional reliability integrals due to their generality and ability to obtain accurate and robust estimates.”
MethodA New Version of the Price's Algorithm for Global Optimization
Brachetti, P., Ciccoli, M. D. F., Pillo, G. D., & Lucidi, S. (1997) · Journal of Global Optimization · doi:10.1023/a:1008250020656 · Cited by 84
“The only requirement is that the noise is distributed with zero mean ([3]).”
BackgroundReliability based analysis of the crosswind stability of railway vehicles
Carrarini, A. (2006) · Journal of Wind Engineering and Industrial Aerodynamics · doi:10.1016/j.jweia.2006.10.001 · Cited by 84
Post, J., Hattermann, F. F., Krysanova, V., & Suckow, F. (2007) · Environmental Modelling & Software · doi:10.1016/j.envsoft.2007.05.010 · Cited by 84
“The method employed here uses Monte Carlo analysis (Rubinstein, 1981), whereas other methods like analytical (e.g. variance propagation, Morgan and Henrion, 1990) or numerical methods can be used as well (e.g. differential uncertainty analysis, Worley, 1987; non probabilistic methods like fuzzy…”
MethodPreece, R., & Milanović, J. V. (2015) · IEEE Transactions on Power Systems · doi:10.1109/tpwrs.2015.2417204 · Cited by 84
“The traditional numerical MC approach, which relies on extensive and repeated random sampling of system uncertainties [16], provides the benchmark which the proposed methodology is (and other similar approaches have previously been) assessed against in terms of both accuracy and computational burden.”
MethodHigh-order Stochastic Simulation of Complex Spatially Distributed Natural Phenomena
Mustapha, H., & Dimitrakopoulos, R. G. (2010) · Mathematical Geosciences · doi:10.1007/s11004-010-9291-8 · Cited by 84
“…fZ can be decomposed, based on the Bayes relation, into the product of univariate conditional distributions functions (Ripley 1987; Rosenblatt 1985; Rubinstein 1981; Law and Kelton 1999) fZ(z/Λ0) = fZ(z0, z1, z2, . . . , zN/Λ0) = fZ0(z0/Λ0)fZ1(z1/Λ1) · · ·fZN (zN/ΛN), (1) where fZi (zi/Λi) is the…”
BackgroundCollaborative production planning of supply chain under price and demand uncertainty
Zhang, G., Shang, J. S., & Li, W. (2011) · European Journal of Operational Research · doi:10.1016/j.ejor.2011.07.007 · Cited by 84
Measurement of deeply virtual Compton scattering at HERA
The H1 Collaboration (2005) · The European Physical Journal C · doi:10.1140/epjc/s2005-02345-3 · Cited by 84
Statistical circuit modeling and optimization
Duvall, S. G. (2002) · doi:10.1109/iwstm.2000.869312 · Cited by 84
Using lognormal distributions and lognormal probability plots in probabilistic risk assessments
Burmaster, D. E., & Hull, D. A. (1997) · Human and Ecological Risk Assessment An International Journal · doi:10.1080/10807039709383683 · Cited by 83
“Computer algorithms are beyond the scope of this review (Morgan, 1984; Knuth, 1981; Rubinstein, 1981).”
BackgroundMethodAn Importance Sampling Algorithm Based on Evidence Pre-propagationPreprint
Yuan, C., & Drużdżel, M. J. (2012) · arXiv (Cornell University) · doi:10.48550/arxiv.1212.2507 · Cited by 84
“Rubinstein [22] points out that if f(X) > 0, the optimal importance function is”
BackgroundMay, N., & Guenther, E. (2019) · Journal of Cleaner Production · doi:10.1016/j.jclepro.2019.118946 · Cited by 82
Modeling granular phosphor screens by Monte Carlo methods
Liaparinos, P. F., Kandarakis, I. S., Cavouras, D. A., et al. (2006) · Medical Physics · doi:10.1118/1.2372217 · Cited by 83
A Bayesian Approach for Multiple Response Surface Optimization in the Presence of Noise Variables
Miró-Quesada, G., Castillo, E. D., & Peterson, J. J. (2004) · Journal of Applied Statistics · doi:10.1080/0266476042000184019 · Cited by 83
“Fixing the seed of the random number generator is a common variance reduction technique used in Monte Carlo integration, especially when the interest relies on comparing two different values of p(x), as it does during the search procedures of most NLP algorithms (Rubinstein, 1981, p. 125).”
MethodIdentification of subpopulations from connectivity matrices
Jacobi, M. N., André, C., Döös, K., & Jonsson, P. R. (2012) · Ecography · doi:10.1111/j.1600-0587.2012.07281.x · Cited by 83
“The non-standard optimization approach we use in this paper shows surprisingly good performance when compared to both spectral methods (Fiedler 1973, Newman 2006, Nilsson Jacobi 2010) and simulated annealing (Rubenstein 1981).”
MethodNeural Learning from Unbalanced Data
Murphey, Y. L., Guo, H., & Feldkamp, L. A. (2004) · Applied Intelligence · doi:10.1023/b:apin.0000033632.42843.17 · Cited by 82
“According to [ 14 ], if covariance matrix � is positive definite and symmetric, there exists a unique lower triangular matrix C such that � = CC T . The random vector Z can be represented as:”
Hybrid High Dimensional Model Representation for reliability analysis
Chowdhury, R., & ., B. N. R. (2008) · Computer Methods in Applied Mechanics and Engineering · doi:10.1016/j.cma.2008.10.006 · Cited by 82
The Complexity of Large-scale Convex Programming under a Linear Optimization OraclePreprint
Lan, G. (2013) · arXiv (Cornell University) · doi:10.48550/arxiv.1309.5550 · Cited by 82
“The above convolution-based smoothing technique has been extensively studied in stochastic optimization, e.g., [7,16,31,43,45].”
MethodA new approach of point estimate method for probabilistic load flow
Mohammadi, M., Shayegani, A., & Adaminejad, H. (2013) · International Journal of Electrical Power & Energy Systems · doi:10.1016/j.ijepes.2013.02.019 · Cited by 81
Deniz Erdogmus, B., & Príncipe, J. C. (2003) · IEEE Transactions on Signal Processing · doi:10.1109/tsp.2003.812843 · Cited by 79
“Illustration of supervised adaptive system training using MEE criterion. broadly defined areas are endless; however, our main concern is using these measures and their nonparametric estimators in filter and system adaptation.”
MethodDeep learning of contagion dynamics on complex networks
Murphy, C., Laurence, E., & Allard, A. (2021) · Nature Communications · doi:10.1038/s41467-021-24732-2 · Cited by 85
“In the main paper, we considered the idea that the configurations should be weighted by an importance sampling (IS) scheme [1] where the target distribution is assumed uniform over all possible configurations.”
BackgroundMonte Carlo evaluation of multivariate normal probabilities
Vijverberg, W. P. M. (1997) · Journal of Econometrics · doi:10.1016/0304-4076(95)01792-5 · Cited by 75
Some New Perspectives on the Method of Control Variates
Glynn, P. W., & Szechtman, R. (2002) · Springer eBooks · doi:10.1007/978-3-642-56046-0_3 · Cited by 79
“See, for example, [12] for one means of inducing such a correlation.”
Reliability of uncertain dynamical systems with multiple design points
Au, S., Papadimitriou, C., & Beck, J. L. (1999) · Structural Safety · doi:10.1016/s0167-4730(99)00009-0 · Cited by 79
“It is interesting to note that these results are analogous to those derived for strati®ed sampling [6].”
MethodResultChapter 15 Monte carlo simulation and numerical integration
Geweke, J. F. (1996) · Handbook of computational economics · doi:10.1016/s1574-0021(96)01017-9 · Cited by 215
Huang, X., Sui, L., Xing, F., et al. (2018) · Composites Part B Engineering · doi:10.1016/j.compositesb.2018.09.002 · Cited by 78
Zhou, T., & Peng, Y. (2021) · Reliability Engineering & System Safety · doi:10.1016/j.ress.2021.108283 · Cited by 78
Compartment fire risk analysis by advanced Monte Carlo simulation
Au, S., Wang, Z., & Lo, S. (2007) · Engineering Structures · doi:10.1016/j.engstruct.2006.11.024 · Cited by 78
Statistical methods for the estimation of process variation effects on circuit operation
Mutlu, A. A., & Rahman, M. (2005) · IEEE Transactions on Electronics Packaging Manufacturing · doi:10.1109/tepm.2005.856534 · Cited by 78
“lated annealing, genetic algorithms, or Monte Carlo methods, can be found in the literature [32]–[34].”
MethodStochastic finite element analysis of shells
Argyris, J., Papadrakakis, M., & Stefanou, G. (2002) · Computer Methods in Applied Mechanics and Engineering · doi:10.1016/s0045-7825(02)00404-8 · Cited by 77
Toward optimal screening strategies for older women
Mandelblatt, J. S., Schechter, C. B., Yabroff, K. R., Lawrence, W., Dignam, J. J., Extermann, M., Fox, S., Orosz, G. M., Silliman, R. A., Cullen, J. C., et al. (2005) · Journal of General Internal Medicine · doi:10.1111/j.1525-1497.2005.0116.x · Cited by 74
Structural reliability analysis: A Bayesian perspective
Dang, C., Valdebenito, M. A., Faes, M. G. R., et al. (2022) · Structural Safety · doi:10.1016/j.strusafe.2022.102259 · Cited by 76
“Such uncertainty can be measured by the variance of the estimator [2]: where V [ · ] denotes the variance operator.”
BackgroundAnt Algorithm for Grid Scheduling Problem
Fidanova, S. S., & Durchova, M. K. (2006) · Lecture notes in computer science · doi:10.1007/11666806_46 · Cited by 80
“MC systems [ 9 ] are general stochastic simulation systems, that is, techniques performing repeated sampling experiments on the model of the system under consideration by making use of a stochastic component in the state sampling and/or transition rules.”
BackgroundIntegration of Multimodal Functions by Monte Carlo Importance Sampling
Oh, M., & Berger, J. O. (1993) · Journal of the American Statistical Association · doi:10.1080/01621459.1993.10476295 · Cited by 76
Assessment of high dimensional model representation techniques for reliability analysis
Chowdhury, R., & ., B. N. R. (2008) · Probabilistic Engineering Mechanics · doi:10.1016/j.probengmech.2008.02.001 · Cited by 76
Modeling of uncertainties in biochemical reactions
Mišković, L., & Vassily Hatzimanikatis, A. (2010) · Biotechnology and Bioengineering · doi:10.1002/bit.22932 · Cited by 74
Efficiency, error and yield in light-directed maskless synthesis of DNA microarrays
Agbavwe, C., Kim, C.-H., Hong, D., Heinrich, K., Wang, T., & Somoza, M. M. (2011) · Journal of Nanobiotechnology · doi:10.1186/1477-3155-9-57 · Cited by 76
On the prediction bias and variance in long-term growth projections
Kangas, A. S. (1997) · Forest Ecology and Management · doi:10.1016/s0378-1127(97)00056-x · Cited by 76
Monte Carlo simulation of bremsstrahlung emission by electrons
Salvat, F., Fernández‐Varea, J. M., Sempau, J., et al. (2005) · Radiation Physics and Chemistry · doi:10.1016/j.radphyschem.2005.05.008 · Cited by 75
Accurate Estimation of SRAM Dynamic Stability
Khalil, D. A. M., Khellah, M. M., Kim, N.-S., et al. (2008) · IEEE Transactions on Very Large Scale Integration (VLSI) Systems · doi:10.1109/tvlsi.2008.2001941 · Cited by 75
“The most popular scheme is quasi-Monte Carlo (Quasi MC) [16], [17], which is a Monte Carlo sampling technique.”
MethodQuasi-Monte Carlo simulation of the light environment of plants
Cieslak, M., Lemieux, C., Hanan, J., & Prusinkiewicz, P. (2008) · Functional Plant Biology · doi:10.1071/fp08082 · Cited by 75
“First, importance sampling (Rubinstein 1981) is used to generate rays preferentially in the direction from which (or towards which) most energy propagates, as opposed to generating them with a uniform distribution.”
BackgroundMethodInfluentialBalasubramanian, K., & Ghadimi, S. (2021) · Foundations of Computational Mathematics · doi:10.1007/s10208-021-09499-8 · Cited by 85
Bayesian post-processing of Monte Carlo simulation in reliability analysis
Betz, W., Papaioannou, I., & Straub, D. (2022) · Reliability Engineering & System Safety · doi:10.1016/j.ress.2022.108731 · Cited by 75
Seismic Potential of the Main Active Faults in the Granada Basin (Southern Spain)
de Galdeano, C. S., Montilla, J. A. P., & Casado, C. L. (2003) · Pure and Applied Geophysics · doi:10.1007/s00024-003-2359-3 · Cited by 74
“For this, given that the parameters appearing in the different proposed lineal relationships are accompanied by their respective variance, simulations were performed using the Monte Carlo method (RUBINSTEIN, 1981) when determining the variance (uncertainty) of the estimated result.”
MethodAssessment of large transport infrastructure projects: The CBA-DK model
Salling, K. B., & Banister, D. (2009) · Transportation Research Part A Policy and Practice · doi:10.1016/j.tra.2009.08.001 · Cited by 78
Statistical theory of edge detection
Huang, J. S., & Tseng, D. H. (1988) · Computer Vision Graphics and Image Processing · doi:10.1016/0734-189x(88)90087-4 · Cited by 74
Risk quantification combining geostatistical realizations and discretized Latin Hypercube
Schiozer, D. J., Avansi, G. D., & dos Santos, A. A. D. S. (2016) · Journal of the Brazilian Society of Mechanical Sciences and Engineering · doi:10.1007/s40430-016-0576-9 · Cited by 73
Lee, U., Park, S.-D., & Lee, I. (2020) · Energy · doi:10.1016/j.energy.2020.117090 · Cited by 73
Review of atomic layer deposition process, application and modeling tools
Kunene, T. J., Tartibu, L. K., Ukoba, K. O., & Jen, T. (2022) · Materials Today Proceedings · doi:10.1016/j.matpr.2022.02.094 · Cited by 76
Zhao, Y., & Wang, Z. (2022) · Structural and Multidisciplinary Optimization · doi:10.1007/s00158-022-03260-7 · Cited by 73
“…such as the first- and second-order reliability methods (FORM and SORM) (Rackwitz and Flessler 1978; Kiureghian Armen Der and Stefano Mario De 1991), sampling-based methods such as crude Monte Carlo Simulation(MCS) (Rubinstein and Kroese 2016; Fishman 2013), importance sampling(IS) (Echard et al.”
MethodThe multivariate hazard construction
Shaked, M., & Shanthikumar, J. G. (1987) · Stochastic Processes and their Applications · doi:10.1016/0304-4149(87)90015-9 · Cited by 73
Evaluation of Front Detection Methods for Satellite-Derived SST Data Using In Situ Observations
Ullman, D. S., & Cornillon, P. (2000) · Journal of Atmospheric and Oceanic Technology · doi:10.1175/1520-0426(2000)017 · Cited by 103
Niknam, T., Golestaneh, F., & Shafiei, M. (2012) · Energy · doi:10.1016/j.energy.2012.09.055 · Cited by 72
Structural System Reliability: Overview of Theories and Applications to Optimization
Song, J., Kang, W., Lee, Y., & Chun, J. (2021) · ASCE-ASME Journal of Risk and Uncertainty in Engineering Systems Part A Civil Engineering · doi:10.1061/ajrua6.0001122 · Cited by 74
Munck, M. D., Moens, D., Desmet, W., & Vandepitte, D. (2007) · Computers & Structures · doi:10.1016/j.compstruc.2007.07.006 · Cited by 71
Multi-objective capacity allocation of hospital wards combining revenue and equity
Zhou, L., Geng, N., Jiang, Z., et al. (2017) · Omega · doi:10.1016/j.omega.2017.11.005 · Cited by 72
Pure adaptive search in monte carlo optimization
Patel, N. R., Smith, R. L., & Zabinsky, Z. B. (1989) · Mathematical Programming · doi:10.1007/bf01582296 · Cited by 72
Plastic Reliability Analysis By Directional Simulation
Ditlevsen, O., & Bjerager, P. (1989) · Journal of Engineering Mechanics · doi:10.1061/(asce)0733-9399(1989)115:6(1347 · Cited by 72
Kriging based reliability and sensitivity analysis – Application to the stability of an earth dam
Guo, X., & Dias, D. (2020) · Computers and Geotechnics · doi:10.1016/j.compgeo.2019.103411 · Cited by 71
A nonparametric exponentially weighted moving average control scheme
Amin, R., & Searcy, A. J. (1991) · Communications in Statistics - Simulation and Computation · doi:10.1080/03610919108812996 · Cited by 71
Leonard, T., Hsu, J. S. J., & Tsui, K. (1989) · Journal of the American Statistical Association · doi:10.1080/01621459.1989.10478871 · Cited by 71
Simulation study on the degradation process of photovoltaic modules
Huang, C., & Wang, L. (2018) · Energy Conversion and Management · doi:10.1016/j.enconman.2018.03.056 · Cited by 71
Weraikat, D., Zanjani, M. K., & Lehoux, N. (2019) · Operations Research for Health Care · doi:10.1016/j.orhc.2019.04.004 · Cited by 71
Guehring, T., Unglaub, F., Lorenz, H., et al. (2005) · European Spine Journal · doi:10.1007/s00586-005-0953-z · Cited by 71
“Thus, the Monte–Carlo– simulation for the Mann–Whitney U-test is useful in the case of samples with expected cell frequencies smaller than five [19, 31].”
MethodPrediction of muscle force involved in shoulder internal rotation
Chang, Y.-W., Hughes, R. E., Su, F., et al. (2000) · Journal of Shoulder and Elbow Surgery · doi:10.1067/mse.2000.105135 · Cited by 70
Importance sampling for reinforcement learning with multiple objectives
Shelton, C. R., & Poggio, T. (2001) · DSpace@MIT (Massachusetts Institute of Technology) · Cited by 68
Sequential simulation applied to composite system reliability evaluation
Úbeda, J. R., & Allan, R. N. (1992) · IEE Proceedings C Generation Transmission and Distribution · doi:10.1049/ip-c.1992.0014 · Cited by 70
Numerical Solution of Stochastic Differential Equations in Finance
SAUER, T. D. (2011) · Springer eBooks · doi:10.1007/978-3-642-17254-0_19 · Cited by 70
Probabilistic methods for risk assessment of airframe digital twin structures
Millwater, H. R., Ocampo, J., & Crosby, N. (2019) · Engineering Fracture Mechanics · doi:10.1016/j.engfracmech.2019.106674 · Cited by 69
The impact of imperfect maintenance actions on the degradation of buildings’ envelope components
Ferreira, C., Silva, A. R., de Brito, J., et al. (2020) · Journal of Building Engineering · doi:10.1016/j.jobe.2020.101571 · Cited by 70
Simulation of communication systems
Tranter, W. H., & Kosbar, K. L. (1994) · IEEE Communications Magazine · doi:10.1109/35.295942 · Cited by 70
Wang, R., Liu, X., Hu, D., et al. (2017) · Aerospace Science and Technology · doi:10.1016/j.ast.2017.08.011 · Cited by 69
An introduction to second‐order random variables in human health risk assessments
Burmaster, D. E., & Wilson, A. (1996) · Human and Ecological Risk Assessment An International Journal · doi:10.1080/10807039609383655 · Cited by 69
Husmeier, D. (2003) · Molecular Biology and Evolution · doi:10.1093/molbev/msg039 · Cited by 69
“9), from which sampling is straightforward (Rubinstein 1981).”
BackgroundA Self-Supervised Residual Feature Learning Model for Multifocus Image Fusion
Wang, Z., Li, X., Duan, H., & Zhang, X. (2022) · IEEE Transactions on Image Processing · doi:10.1109/tip.2022.3184250 · Cited by 71
“The Monte Carlo method [26], [27] is a broad class of computational algorithms that rely on repeated random sampling to obtain numerical results.”
MethodModified subset simulation method for reliability analysis of structural systems
Miao, F., & Ghosn, M. (2011) · Structural Safety · doi:10.1016/j.strusafe.2011.02.004 · Cited by 68
Interannual variability of the upper ocean carbon cycle at station ALOHA near Hawaii
Brix, H., Gruber, N., & Keeling, C. D. (2004) · Global Biogeochemical Cycles · doi:10.1029/2004gb002245 · Cited by 84
“[66] To address uncertainties in the model parameters, Monte Carlo experiments [Rubinstein, 1981] were performed (see Gruber et al. [1998] for details), in which a random set of values were chosen from a predefined parameter set (shown in Table C4 of Keeling et al. [2004]) for each simulation.”
MethodPassive Harmonic Filter Planning in a Power System With Considering Probabilistic Constraints
Chang, G. W., Wang, H.-L., Chuang, G. S., et al. (2008) · IEEE Transactions on Power Delivery · doi:10.1109/tpwrd.2008.2005371 · Cited by 68
Statistical transfer learning: A review and some extensions to statistical process control
Tsung, F., Zhang, K., Cheng, L., & Song, Z. (2017) · Quality Engineering · doi:10.1080/08982112.2017.1373810 · Cited by 67
“However, it is also possible to undertake model inference in a full Bayesian manner through Markov chain Monte Carlo methods (Gilks et al. 1995, Rubinstein et al. 2016) or variational inference (Wainwright et al. 2008, Blei et al. 2016).”
MethodExact and randomization distributions of Kolmogorov-Smirnov tests two or three samples
Schröer, G., & Trenkler, D. (1995) · Computational Statistics & Data Analysis · doi:10.1016/0167-9473(94)00040-p · Cited by 67
A survey on deep learning-based Monte Carlo denoising
Huo, Y., & Yoon, S. (2021) · Computational Visual Media · doi:10.1007/s41095-021-0209-9 · Cited by 73
Backward Simulation in Bayesian Networks
Fung, R. M., & Favero, B. D. (1994) · Elsevier eBooks · doi:10.1016/b978-1-55860-332-5.50034-1 · Cited by 67
“3 IMPORTANCE SAMPLING Importance sampling (Rubinstein, 1981) is a well-known technique for improving convergence in Monte Carlo simulation.”
MethodAn empirical approach to modeling inter-AS traffic matrices
Chang, H., Jamin, S., Mao, Z. M., et al. (2005) · doi:10.5555/1251086.1251098 · Cited by 67
Some examples of simulation model validation using hypothesis testing
Balcı, O., & Sargent, R. G. (1982) · Winter Simulation Conference · doi:10.5555/1035909.1035948 · Cited by 67
Unbiased sampling techniques for image synthesis
Kirk, D. B., & Arvo, J. R. (1991) · ACM SIGGRAPH Annual Conference on Computer Graphics and Interactive Techniques (SIGGRAPH) · doi:10.1145/122718.122735 · Cited by 67
Monte Carlo Simulation: The Method
Zio, E. (2012) · Springer series in reliability engineering · doi:10.1007/978-1-4471-4588-2_3 · Cited by 75
Optimal Control for Heterogeneous Node-Based Information Epidemics Over Social Networks
Liu, F., & BUSS, M. J. (2020) · IEEE Transactions on Control of Network Systems · doi:10.1109/tcns.2019.2963488 · Cited by 66
“Since direct simulations cannot be expected due to the massive number of states, we resort to Monte Carlo simulations (MCS) [46].”
BackgroundGascard, E., & Simeu-Abazi, Z. (2018) · Reliability Engineering & System Safety · doi:10.1016/j.ress.2018.07.011 · Cited by 66
Random tunneling by means of acceptance-rejection sampling for global optimization
Lucidl, S., & Piccioni, M. (1989) · Journal of Optimization Theory and Applications · doi:10.1007/bf00941057 · Cited by 66
Assessment of low probability events of dynamical systems by controlled Monte Carlo simulation
Pradlwarter, H. J., & Schuëller, G. I. (1999) · Probabilistic Engineering Mechanics · doi:10.1016/s0266-8920(98)00009-5 · Cited by 66
Influenza and pneumococcal vaccination of HIV-infected patients: A policy analysis
Rose, D. N., Schechter, C. B., & Sacks, H. S. (1993) · The American Journal of Medicine · doi:10.1016/0002-9343(93)90178-r · Cited by 66
Asymptotic importance sampling
Maes, M. A., Breitung, K., & Dupuis, D. J. (1993) · Structural Safety · doi:10.1016/0167-4730(93)90001-h · Cited by 65
Evaluation of mobile ad hoc network reliability using propagation-based link reliability model
Padmavathy, N., & Chaturvedi, S. K. (2013) · Reliability Engineering & System Safety · doi:10.1016/j.ress.2013.01.008 · Cited by 65
Jensen, H. A., Valdebenito, M. A., & Schuëller, G. I. (2008) · Computer Methods in Applied Mechanics and Engineering · doi:10.1016/j.cma.2008.01.003 · Cited by 65
Reliability-based shape optimization of structures undergoing fluid–structure interaction phenomena
Allen, M. S., & Maute, K. K. (2005) · Computer Methods in Applied Mechanics and Engineering · doi:10.1016/j.cma.2004.12.028 · Cited by 65
Unraveling a Clinical Paradox: Why Does Bronchial Thermoplasty Work in Asthma?
Donovan, G. M., Elliot, J., Green, F. H. Y., et al. (2018) · American Journal of Respiratory Cell and Molecular Biology · doi:10.1165/rcmb.2018-0011oc · Cited by 65
A Stochastic Approach to Global Optimization
Kan, A. H. G. R., Boender, C. G. E., & Timmer, G. T. (1985) · Springer eBooks · doi:10.1007/978-3-642-82450-0_10 · Cited by 65
Reliability analysis of H-section steel columns under blast loading
Hadianfard, M. A., Malekpour, S., & Momeni, M. S. (2018) · Structural Safety · doi:10.1016/j.strusafe.2018.06.001 · Cited by 64
Statistical Performance Modeling and Optimization
Li, X., Le, J., & Pileggi, L. (2006) · now publishers, Inc. eBooks · doi:10.1561/9781601980571 · Cited by 64
The state of the art in critical infrastructure protection: a framework for convergence
Ghorbani, A. A., & Bagheri, E. (2008) · International Journal of Critical Infrastructures · doi:10.1504/ijcis.2008.017438 · Cited by 67
“Monte Carlo Simulation Monte Carlo simulation is an approach for repeatedly analyzing a deterministic model through the employment of random input values for the uncertain variables of the model [Rubinstein (1981)].”
Method
Metadata
- Authors
- Rubinstein, R. Y., & Kroese, D. P.
- ORCID
- Kroese, Dirk P.
- Venue
- Wiley Series in Probability and Statistics
- Publisher
- Wiley
- Published
- 2016-11-21
- ISSN
- 1940-6347 (ISSN-L)
- OpenAlex
- W2147632348
- Cited by
- 3,356
- References
- 0
- Citations by year
- 2026: 131 · 2025: 182 · 2024: 168 · 2023: 157 · 2022: 167 · 2021: 162 · 2020: 171 · 2019: 139 · 2018: 118 · 2017: 66 · 2016: 41
- FWCI
- 52.82
- Type
- book
- Language
- en
- Open access
- closed
- Locations
- Wiley series in probability and statistics (publishedVersion)
- CERN Document Server (European Organization for Nuclear Research) (submittedVersion)
- International Linear Collider (submittedVersion)
- Topics
- Social Sciences › Decision Sciences › Management Science and Operations Research › Simulation Techniques and Applications
- Physical Sciences › Mathematics › Statistics and Probability › Markov Chains and Monte Carlo Methods
- Physical Sciences › Mathematics › Numerical Analysis › Mathematical Approximation and Integration
- Keywords
- Monte Carlo simulation, stochastic simulation, random number generation, probability distributions, variance reduction, Markov chain Monte Carlo
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
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