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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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Safety assessment of a short span railway bridge for high-speed traffic using simulation techniques
Rocha, J., Henriques, A. A., & Calçada, R. (2012) · Engineering Structures · doi:10.1016/j.engstruct.2012.02.024 · Cited by 64
Survey of reliability and availability evaluation of complex networks using Monte Carlo techniques
Wang, H., & Pham, H. (1997) · Microelectronics Reliability · doi:10.1016/s0026-2714(96)00058-3 · Cited by 64
Automated Approach to Negotiations of BOT Contracts with the Consideration of Project Risk
Liou, F., & Huang, C. (2007) · Journal of Construction Engineering and Management · doi:10.1061/(asce)0733-9364(2008)134:1(18 · Cited by 64
Simulated Annealing and Adaptive Search in Global Optimization
Romeijn, H. E., & Smith, R. L. (1994) · Probability in the Engineering and Informational Sciences · doi:10.1017/s0269964800003624 · Cited by 64
“Following Pincus [15], Rubinstein [19] suggested for approximating the global optimum that we generate points from the Boltzmann distribution ir T with density I where 7 is a "small" positive number, referred to as the temperature parameter This is appropriate because for small T the distribution ir r will "concentrat…”
MethodBenefits and Costs of Interventions to Improve Breast Cancer Outcomes in African American Women
Mandelblatt, J. S., Schechter, C. B., Yabroff, K. R., Lawrence, W., Dignam, J. J., Muennig, P. A., Chavez, Y., Cullen, J. C., & Fahs, M. C. (2004) · Journal of Clinical Oncology · doi:10.1200/jco.2004.05.009 · Cited by 65
“We used a matched simulation approach to maximize computer resource efficiency and maximize the precision of our effect estimates.(27) Briefly, in the analyses of screening interventions as an example, each simulated woman is simulated twice: once with screening and the other time without.”
MethodAlosairi, Y., Al-Salem, S. M., & Ragum, A. A. (2020) · Marine Pollution Bulletin · doi:10.1016/j.marpolbul.2020.111723 · Cited by 62
Combining Generative and Discriminative Models in a Framework for Articulated Pose Estimation
Rosales, R., & Sclaroff, S. (2006) · International Journal of Computer Vision · doi:10.1007/s11263-006-5165-4 · Cited by 61
“The optimal proposal distribution is given by a result in (Rubinstein, 1981; Cheng and Druzdzel, 2000):”
BackgroundEbeed, M., Mostafa, A., Aly, M. M., et al. (2023) · International Journal of Electrical Power & Energy Systems · doi:10.1016/j.ijepes.2023.109250 · Cited by 62
A review of smoothed particle hydrodynamics
Bagheri, M., Mohammadi, M., & Riazi, M. (2023) · Computational Particle Mechanics · doi:10.1007/s40571-023-00679-7 · Cited by 71
Nagem, N. A., Ebeed, M., AlQahtani, D., Jurado, F., Khan, N. H., & Hafez, W. A. (2024) · International Journal of Hydrogen Energy · doi:10.1016/j.ijhydene.2024.08.415 · Cited by 66
Autonomous reinforcement learning with experience replay
Wawrzyński, P., & Tanwani, A. K. (2012) · Neural Networks · doi:10.1016/j.neunet.2012.11.007 · Cited by 61
“Application of the importance sampling technique (Rubinstein, 1981)made it possible to optimize a parametric control policywith the use of experience gainedwith other policies 0893-6080/$ – see front matter© 2012 Elsevier Ltd.”
MethodSchell, J. S. U., Guilleminot, J., Binétruy, C., & Krawczak, P. (2009) · Journal of Materials Processing Technology · doi:10.1016/j.jmatprotec.2009.03.008 · Cited by 63
“…sections can be carried out within a reaonably short time (say, a few seconds), Monte-Carlo numerical imulations are used as the stochastic solver (Rubinstein, 1981). he methodology that is used to study the statistical properties of he interface temperature is as follows: 1) Randomly generate N…”
Hazard identification and scenario selection of ship grounding accidents
Youssef, S. A. M., & Paik, J. K. (2018) · Ocean Engineering · doi:10.1016/j.oceaneng.2018.01.110 · Cited by 62
Reliability analysis of tunnels using an adaptive RBF and a first-order reliability method
Wang, Q., & Fang, H. (2018) · Computers and Geotechnics · doi:10.1016/j.compgeo.2018.02.011 · Cited by 62
Robert, C. P., & Titterington, D. M. (1998) · Statistics and Computing · doi:10.1023/a:1008938201645 · Cited by 62
“The method we consider in this paper is based on a remark, recurrent in the literature (Pincus, 1968; Rubinstein, 1981; Aitkin, 1991), that the eAect of the prior distribution fades away when the likelihood function is taken to a high enough power.”
BackgroundMethodInfluentialFinding Confidence Limits on Population Growth Rates: Monte Carlo Test of a Simple Analytic Method
Alvarez-Buylla, E. R., & Slatkin, M. (1993) · Oikos · doi:10.2307/3544840 · Cited by 62
Hierarchical statistical characterization of mixed-signal circuits using behavioral modeling
Felt, E., Zanella, S., Guardiani, C., et al. (1996) · doi:10.5555/244522.244835 · Cited by 62
“The most widely used technique for performing statistical characterization is Monte Carlo analysis [1, 2].”
MethodOptimal adaptive inspection and maintenance planning for deteriorating structural systems
Bismut, E., & Straub, D. (2021) · Reliability Engineering & System Safety · doi:10.1016/j.ress.2021.107891 · Cited by 66
Random unitaries in extremely low depth
Schuster, T., Haferkamp, J., & Huang, H.-Y. (2025) · Science · doi:10.1126/science.adv8590 · Cited by 181
Stochastic mobility-based path planning in uncertain environments
Kewlani, G., Ishigami, G., & Iagnemma, K. D. (2009) · IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS) · doi:10.1109/iros.2009.5354418 · Cited by 61
“A traditional method for estimating the probability density function of a system’s output response while considering uncertainty is the Monte Carlo method [10].”
MethodPan, H., Tian, L., Fu, X., et al. (2020) · Journal of Constructional Steel Research · doi:10.1016/j.jcsr.2020.105941 · Cited by 61
An Information Theory Framework for the Analysis of Scene Complexity
Feixas, M., del Acebo, E., Bekaert, P., et al. (1999) · Computer Graphics Forum · doi:10.1111/1467-8659.00331 · Cited by 61
“= 1 N N ∑ k=1 log( ATcosθxcosθy πd(x;y)2 ) (27)”
On randomization in sequential and distributed algorithms
Gupta, R., Smolka, S. A., & Bhaskar, S. (1994) · ACM Computing Surveys · doi:10.1145/174666.174667 · Cited by 60
“…Oand c, for a s x s b, this is accomplished by first randomly choosing a set of points that lie within ACM Computing Surveys,Vol 26, No 1, March 1994 . integration becomes attractive if the Y function fails to be regular, which is often the case for multidimensional integrals [Rubinstein 1981].”
MethodKim, J. H., Wang, J.-J., & Ebner, T. J. (1988) · Neuroscience · doi:10.1016/0306-4522(88)90252-7 · Cited by 61
Olivares, A., & Staffetti, E. (2021) · Chaos Solitons & Fractals · doi:10.1016/j.chaos.2021.110895 · Cited by 60
Çelikbilek, K., Saleem, Z., Ferré, R. M., Praks, J., & Lohan, E. S. (2022) · Sensors · doi:10.3390/s22041421 · Cited by 68
“For detailed explanations regarding MC, we advise dedicated sources such as [64,65].”
Machine learning assisted multi-objective design optimization for battery thermal management system
Zhou, X., Zhou, X., Guo, W., et al. (2024) · Applied Thermal Engineering · doi:10.1016/j.applthermaleng.2024.123826 · Cited by 60
Blind source separation using Renyi's α-marginal entropies
Erdoğmuş, D., Hild, K. E., & Príncipe, J. C. (2002) · Neurocomputing · doi:10.1016/s0925-2312(02)00526-x · Cited by 60
“In that work, we also proved that there is a correspondence with the kernel function in this estimator for information potential and the smoothing function in the global optimization method of convolution smoothing [6] [13].”
MethodTwo ways to quantify uncertainty in geophysical inverse problems
Malinverno, A., & Parker, R. L. (2006) · Geophysics · doi:10.1190/1.2194516 · Cited by 60
A comparative study of probability estimation methods for reliability analysis
Xi, Z., Hu, C. K., & Youn, B. D. (2011) · Structural and Multidisciplinary Optimization · doi:10.1007/s00158-011-0656-5 · Cited by 60
“For examples 1, 2 and 3, PDFs derived from MCSs with 1,000,000 samples are treated as true PDFs.”
MethodInfluentialMaiti, S., Erram, V. C., Gupta, G., et al. (2012) · Journal of Hydrology · doi:10.1016/j.jhydrol.2012.07.020 · Cited by 60
A surrogate based multi-fidelity approach for robust design optimization
Chakraborty, S., Chatterjee, T., Chowdhury, R., & Adhikari, S. (2017) · Applied Mathematical Modelling · doi:10.1016/j.apm.2017.03.040 · Cited by 61
Moustafa, N., Misra, G., & Slay, J. (2018) · IEEE Transactions on Sustainable Computing · doi:10.1109/tsusc.2018.2808430 · Cited by 63
“Data simulation can enable the creation of large numbers of random samples that follow a specific distribution [48].”
BackgroundUncertainty in intraevent spatial correlation of elastic pseudo-acceleration spectral ordinates
Heresi, P., & Miranda, E. (2018) · Bulletin of Earthquake Engineering · doi:10.1007/s10518-018-0506-6 · Cited by 61
“This procedure can also be used with efficient sampling schemes, such as importance sampling (Rubinstein 1981), as the standard Monte Carlo simulation method is not computationally efficient for estimating low-probability high-consequence risks (Au and Beck 2003).”
MethodMethods for assessing uncertainty of growth and yield predictions
Kangas, A. S. (1999) · Canadian Journal of Forest Research · doi:10.1139/x99-100 · Cited by 60
Analytical cross sections for Monte Carlo simulation of photon transport
Baró, J., Roteta, M., Fernández‐Varea, J. M., et al. (1994) · Radiation Physics and Chemistry · doi:10.1016/0969-806x(94)90053-1 · Cited by 60
Random Field Representation and Synthesis Using Wavelet Bases
Zeldin, B. A., & Spanos, P. D. (1996) · Journal of Applied Mechanics · doi:10.1115/1.2787251 · Cited by 60
Response Surface Method for Time-Variant Reliability Analysis
Yao, T., & Wen, Y. K. (1996) · Journal of Structural Engineering · doi:10.1061/(asce)0733-9445(1996)122:2(193 · Cited by 60
Borghetti, A., Nucci, C. A., & Paolone, M. (2004) · IEEE Transactions on Power Delivery · doi:10.1109/tpwrd.2004.829116 · Cited by 60
“Correlation coefficients between the lightning parameters are taken into account by applying the inverse transform method [31], as shown in [32].”
MethodPeng, Y., Zhou, T., & Li, J. (2020) · Mechanical Systems and Signal Processing · doi:10.1016/j.ymssp.2020.107366 · Cited by 60
Predictive Precoder Design for OTFS-Enabled URLLC: A Deep Learning Approach
Liu, C., Li, S., Yuan, W., Liu, X., & Ng, D. W. K. (2023) · IEEE Journal on Selected Areas in Communications · doi:10.1109/jsac.2023.3280984 · Cited by 62
“a Monte Carlo method [40] to approximate the simulation result via averaging sufficient large numbers of theoretical FER results calculated based on various channel realizations.”
A support vector density-based importance sampling for reliability assessment
Dai, H., Zhang, H., & Wang, W. (2012) · Reliability Engineering & System Safety · doi:10.1016/j.ress.2012.04.011 · Cited by 59
Value of information for water quality management
Borisova, T., Shortle, J. S., Horan, R. D., et al. (2005) · Water Resources Research · doi:10.1029/2004wr003576 · Cited by 59
“A Monte Carlo procedure is used to estimate the expected net benefits as a sample mean [Rubinstein, 1981].”
MethodWang, Q., Fang, H., & Shen, L. Y. (2016) · Tunnelling and Underground Space Technology · doi:10.1016/j.tust.2016.02.007 · Cited by 59
Quantum approximate optimization with Gaussian boson sampling
Arrazola, J. M., Bromley, T. R., & Rebentrost, P. (2018) · Physical Review A · doi:10.1103/physreva.98.012322 · Cited by 61
Current trends in disaster management simulation modelling research
Mishra, D. B., Kumar, S., & Hassini, E. (2018) · Annals of Operations Research · doi:10.1007/s10479-018-2985-x · Cited by 61
“The interested readers may refer to Rubinstein (1981) for MCS, Robinson (2005) for DES, Sterman (2001) for SD and Katsaliaki andMustafee (2011) for ABS.”
Gorman, D., Gutiérrez, A. R., Turra, A., Manzano, A. B., Balthazar-Silva, D., Oliveira, N. R. D., & Harari, J. (2020) · Frontiers in Environmental Science · doi:10.3389/fenvs.2020.559405 · Cited by 56
“Particle diffusion was simulated using the well-known random walk method (Rubinstein and Kroese, 2016), considering a function of uniform probability density, with zero mean and unitary standard deviation which meant that the maximum displacement of each particle, for each time interval, is about…”
Methodde Gelder, E., Hof, J. P., Cator, E., et al. (2022) · IEEE Transactions on Intelligent Transportation Systems · doi:10.1109/tits.2022.3154774 · Cited by 58
“To get unbiased results, the result of a test with scenario parameters x is weighted by the ratio of the original probability density, ˆ f H ( x ) , and the probability density of the pdf used for importance sampling, g ( x ) [10, 52–54].”
BackgroundMethodInfluentialAdhikari, A., Jurado, F., Naetiladdanon, S., et al. (2023) · International Journal of Electrical Power & Energy Systems · doi:10.1016/j.ijepes.2023.109314 · Cited by 58
Kim, Y.-K., Hong, J., & Hur, J. (2003) · IEEE Transactions on Industry Applications · doi:10.1109/tia.2003.811777 · Cited by 58
Mathematical Models for Air Traffic Conflict and Collision Probability Estimation
Mitici, M., & Blom, H. A. P. (2018) · IEEE Transactions on Intelligent Transportation Systems · doi:10.1109/tits.2018.2839344 · Cited by 60
“H. Importance Sampling and Splitting Application of straightforward MC simulation may lead to computer runs that are very costly in computer time.”
MethodInfluentialHyperspace Division Method for Structural Reliability
Katsuki, S., & Frangopol, D. M. (1994) · Journal of Engineering Mechanics · doi:10.1061/(asce)0733-9399(1994)120:11(2405 · Cited by 58
Monte Carlo method for solving Fredholm integral equations of the second kind
Farnoosh, R., & Ebrahimi, M. (2007) · Applied Mathematics and Computation · doi:10.1016/j.amc.2007.04.097 · Cited by 58
Probabilistic Seismic Evaluation of Reinforced Concrete Structural Components and Systems
Lee, T., & Mosalam, K. M. (2006) · Cited by 58
A survey on the global optimization problem: General theory and computational approaches
Archetti, F., & Schoen, F. (1984) · Annals of Operations Research · doi:10.1007/bf01876141 · Cited by 58
Hierarchical Refinement of Latin Hypercube Samples
Vořechovský, M. (2014) · Computer-Aided Civil and Infrastructure Engineering · doi:10.1111/mice.12088 · Cited by 57
Uncertainty in seismic slope deformation model predictions
Strenk, P. M., & Wartman, J. (2011) · Engineering Geology · doi:10.1016/j.enggeo.2011.03.003 · Cited by 57
Uncertainty in Seismic Capacity of Masonry Buildings
Parisi, F., & Augenti, N. (2012) · Buildings · doi:10.3390/buildings2030218 · Cited by 57
“Based on the use of Monte Carlo methods and response surface analysis [8,9], a response surface has been derived to describe each median collapse capacity parameter as a multivariate function of modeling random variables.”
MethodProbabilistic Failure Analysis by Importance Sampling Markov Chain Simulation
Au, S. (2004) · Journal of Engineering Mechanics · doi:10.1061/(asce)0733-9399(2004)130:3(303 · Cited by 57
Reliability analysis of roof wedges and rockbolt forces in tunnels
Low, B. K., & Einstein, H. H. (2013) · Tunnelling and Underground Space Technology · doi:10.1016/j.tust.2013.04.006 · Cited by 57
Mohanty, S. D. (1998) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.57.630 · Cited by 57
“Another method that can be used [17] is to perform the Cholesky decomposition of CX with the elements of one of the factors chosen in such a way as to give the correct covariances for the components of X.”
MethodWard, R. E., Gheorghiade, M., Young, J. B., & Uretsky, B. F. (1995) · Journal of the American College of Cardiology · doi:10.1016/0735-1097(95)00140-u · Cited by 57
Xu, S., Yi, N., Burke, D., et al. (2003) · Genetics Research · doi:10.1017/s0016672303006414 · Cited by 56
Shi, S., Zhou, K., Zhao, J., Mukherjee, S., & Zhuang, P. (2022) · Physical review. D/Physical review. D. · doi:10.1103/physrevd.105.014017 · Cited by 71
“[60]), which samples {θi} according to a reference distribution P̃ (θ), hence dθi = M P̃(θi), and perform re-weighting on each sample by assigning an extra weight determined by the ratio of the posterior to the reference, wi = Posterior(θi)/P̃ (θi)/M .”
BackgroundBux, C., & Amicarelli, V. (2022) · Journal of Environmental Management · doi:10.1016/j.jenvman.2022.115001 · Cited by 67
State of the Art Monte Carlo Method Applied to Power System Analysis with Distributed Generation
Abud, T. P., Augusto, A. A., Fortes, M. Z., Maciel, R. S., & Borba, B. (2022) · Energies · doi:10.3390/en16010394 · Cited by 63
Advanced optimization methods for power systems
Panciatici, P., Campi, M. C., Garatti, S., Low, S. H., Molzahn, D. K., Sun, A., & Wehenkel, L. A. (2014) · Power Systems Computation Conference · doi:10.1109/pscc.2014.7038504 · Cited by 58
“the variance) of the function that has to be integrated [81].”
BackgroundEfficient Monte Carlo based incremental statistical timing analysis
Veetil, V., Sylvester, D., & Blaauw, D. T. (2008) · ACM/IEEE Design Automation Conference (DAC) · doi:10.1145/1391469.1391645 · Cited by 56
Analysis of one-dimensional stochastic finite elements using neural networks
Hurtado, J. E. (2002) · Probabilistic Engineering Mechanics · doi:10.1016/s0266-8920(01)00011-x · Cited by 56
Adaptive Newton-based multivariate smoothed functional algorithms for simulation optimization
Bhatnagar, S. (2007) · ACM Transactions on Modeling and Computer Simulation · doi:10.1145/1315575.1315577 · Cited by 52
“Moreover, the above procedure has also been proposed in Spall [2000] for the case of high-dimensional parameters.”
MethodMethods for Structural Reliability Computations
Bjerager, P. (1991) · Springer eBooks · doi:10.1007/978-3-7091-2616-5_3 · Cited by 56
Failure correction techniques for large disk arrays
Gibson, G. A., Hellerstein, L., Karp, R. M., et al. (1989) · ACM SIGARCH Computer Architecture News · doi:10.1145/68182.68194 · Cited by 56
Bridge health monitoring using deflection measurements under random traffic
Martínez, D., Malekjafarian, A., & OBrien, E. J. (2020) · Structural Control and Health Monitoring · doi:10.1002/stc.2593 · Cited by 55
Paradongan, H. T., Hakam, D. F., Wiryono, S. K., et al. (2024) · Heliyon · doi:10.1016/j.heliyon.2024.e27680 · Cited by 55
“According to Kanugrahan ’ s 2050 net-zero carbon scenario, PV power plants are expected to contribute to 56.95% of the total electricity generation output in Indonesia [21].”
BackgroundMethodInfluentialGhofrani, M., Arabali, A., & Ghayekhloo, M. (2014) · Electric Power Systems Research · doi:10.1016/j.epsr.2014.08.007 · Cited by 55
Yang, Z., Iemura, H., Kanae, S., & Wada, K. (2007) · Automatica · doi:10.1016/j.automatica.2006.12.026 · Cited by 56
“This smoothed functional is given by (Rubinstein, 1981) ˇ̆ V N( , ) = ∫ ∞ −∞ ȟ( , )V̆N ( − ) d (23)”
BackgroundInfluentialA general RBDO decoupling approach for different reliability analysis methods
Torii, A. J., Lopez, R. H., & Miguel, L. F. F. (2016) · Structural and Multidisciplinary Optimization · doi:10.1007/s00158-016-1408-3 · Cited by 55
Guo, X., Dias, D., Carvajal, C., et al. (2019) · Engineering Structures · doi:10.1016/j.engstruct.2019.03.056 · Cited by 55
Randomized quasi-Monte Carlo methods in pricing securities
Ökten, G., & Eastman, W. (2004) · Journal of Economic Dynamics and Control · doi:10.1016/j.jedc.2003.11.003 · Cited by 55
Belshan, M., Baccam, P., Oaks, J. L., et al. (2001) · Virology · doi:10.1006/viro.2000.0696 · Cited by 55
“For the Monte Carlo simulation (Rubinstein, 1981) comparing the four primer pairs, the chi-square distance was calculated between the four sets of simulated data.”
Modelling stochastic decision systems using dependent-chance programming
Liu, B., & Iwamura, K. (1997) · European Journal of Operational Research · doi:10.1016/0377-2217(95)00371-1 · Cited by 55
Water flow modeling in the unsaturated zone with imprecise parameters using a fuzzy approach
Schulz, K., & Huwe, B. (1997) · Journal of Hydrology · doi:10.1016/s0022-1694(97)00038-3 · Cited by 55
Electromagnetic simulation of bonding wires and comparison with wide band measurements
Schuster, C., Leonhardt, G., & Fïchtner, W. (2000) · IEEE Transactions on Advanced Packaging · doi:10.1109/6040.826764 · Cited by 55
“This integral is evaluated with a sample mean Monte Carlo method [ 23 ]”
MethodQuasi-Monte Carlo Methods for Multidimensional Numerical Integration
Niederreiter, H. (1988) · International series of numerical mathematics · doi:10.1007/978-3-0348-6398-8_15 · Cited by 52
Ang, A., & Sherris, M. (1997) · North American Actuarial Journal · doi:10.1080/10920277.1997.10595601 · Cited by 55
Bayesian inference of random fields represented with the Karhunen–Loève expansion
Uribe, F., Papaioannou, I., Betz, W., et al. (2019) · Computer Methods in Applied Mechanics and Engineering · doi:10.1016/j.cma.2019.112632 · Cited by 54
A review of Monte Carlo and quasi‐Monte Carlo sampling techniques
Hung, Y. (2023) · Wiley Interdisciplinary Reviews Computational Statistics · doi:10.1002/wics.1637 · Cited by 58
Timoshenko beam with uncertainty on the boundary conditions
Ritto, T. G., Sampaio, R., & Cataldo, E. (2008) · Journal of the Brazilian Society of Mechanical Sciences and Engineering · doi:10.1590/s1678-58782008000400005 · Cited by 55
“Section 4 presents the numerical simulations where a stochastic Monte Carlo solver (Rubinstein, 1981) is used to generate the independent realizations of the random variables, and, finally, in Section 5 concluding remarks are outlined.”
Evaluating small failure probabilities of multiple limit states by parallel subset simulation
Hsu, W.-C., & Ching, J. (2010) · Probabilistic Engineering Mechanics · doi:10.1016/j.probengmech.2010.01.003 · Cited by 54
Chakraborty, S., Mandal, B., Chowdhury, R., et al. (2015) · Composite Structures · doi:10.1016/j.compstruct.2015.09.044 · Cited by 54
Rahman, S. (1995) · Engineering Fracture Mechanics · doi:10.1016/0013-7944(95)00018-q · Cited by 54
Salvat, F., & Fernández‐Varea, J. M. (1992) · Nuclear Instruments and Methods in Physics Research Section B Beam Interactions with Materials and Atoms · doi:10.1016/0168-583x(92)95108-4 · Cited by 54
Monte Carlo Matrix Inversion and Reinforcement Learning
Barto, A. G., & Duff, M. O. (1993) · Cited by 55
Financial Modeling with Crystal Ball and Excel
Charnes, J. M. (2007) · doi:10.1002/9781119203216 · Cited by 53
Niknam, T., Bornapour, M., & Gheisari, A. (2012) · Energy Conversion and Management · doi:10.1016/j.enconman.2012.08.016 · Cited by 53
Chan, C. L., & Low, B. K. (2012) · Computers and Geotechnics · doi:10.1016/j.compgeo.2012.03.001 · Cited by 53
Approximately bisimilar symbolic models for randomly switched stochastic systems
Zamani, M., & Abate, A. (2014) · Systems & Control Letters · doi:10.1016/j.sysconle.2014.04.003 · Cited by 53
“For instance, one may leverage flow-based techniques [32] or alternatively Monte-Carlo simulations [33].”
MethodMonte Carlo simulation of a planar shoulder model
Hughes, R. E., & An, K. N. (1997) · Medical & Biological Engineering & Computing · doi:10.1007/bf02525538 · Cited by 53
Bi-objective project portfolio selection and staff assignment under uncertainty
Gutjahr, W. J., & Reiter, P. (2010) · Optimization · doi:10.1080/02331931003700699 · Cited by 53
Neumann, L. (1995) · Computing · doi:10.1007/bf02238235 · Cited by 53
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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