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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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Projection Pursuit Density Estimation
Friedman, J. H., Stuetzle, W., & Schroeder, A. (1984) · Journal of the American Statistical Association · doi:10.1080/01621459.1984.10478086 · Cited by 223
“For many choices of PO(X) there exist special algorithms that allow efficient direct sampling (see for example Rubinstein, 1981).”
BackgroundMonte Carlo Studies in Item Response Theory
Harwell, M. R., Stone, C. A., Hsu, T.-C., et al. (1996) · Applied Psychological Measurement · doi:10.1177/014662169602000201 · Cited by 221
Life-cycle reliability-based optimization of civil and aerospace structures
Frangopol, D. M., & Maute, K. K. (2003) · Computers & Structures · doi:10.1016/s0045-7949(03)00020-8 · Cited by 217
A comparison of techniques for the estimation of model prediction uncertainty
Omlin, M., & Reichert, P. (1999) · Ecological Modelling · doi:10.1016/s0304-3800(98)00174-4 · Cited by 215
“Instead the distribution of model results is calculated with Monte Carlo Simulation techniques (Rubinstein, 1981; Sobol, 1994).”
MethodMixtures of Truncated Exponentials in Hybrid Bayesian Networks
Moral, S., Rumí, R., & Salmerón, A. (2001) · Lecture notes in computer science · doi:10.1007/3-540-44652-4_15 · Cited by 208
Bayesian computation: a summary of the current state, and samples backwards and forwards
Green, P., Łatuszyński, K., Pereyra, M., & Robert, C. (2015) · Statistics and computing · doi:10.1007/s11222-015-9574-5 · Cited by 202
“This method can be seen as a particular and efficient instance of auxiliary variables (see, e.g., Besag and Green 1993; Rubinstein 1981), in which we apply a deterministicproposal Metropolis method to the augmented target.”
MethodSHADOW: A synchrotron radiation ray tracing program
Lai, B. C. H., & Cerrina, F. (1986) · Nuclear Instruments and Methods in Physics Research Section A Accelerators Spectrometers Detectors and Associated Equipment · doi:10.1016/0168-9002(86)90101-4 · Cited by 206
Antithetic acceleration of Monte Carlo integration in Bayesian inference
Geweke, J. F. (1988) · Journal of Econometrics · doi:10.1016/0304-4076(88)90027-9 · Cited by 244
Death, taxes and failing chips
Visweswariah, C. (2003) · Proceedings - ACM IEEE Design Automation Conference · doi:10.1145/775832.775921 · Cited by 204
Distribution circuit state estimation using a probabilistic approach
Ghosh, A. K., Lubkeman, D. L., Downey, M., & Jones, R. H. (1997) · IEEE Transactions on Power Systems · doi:10.1109/59.574922 · Cited by 201
Harrison, J. A., Schall, J. D., Maskey, S., Mikulski, P. T., Knippenberg, M. T., & Morrow, B. H. (2018) · Applied Physics Reviews · doi:10.1063/1.5020808 · Cited by 211
Measurement of deeply virtual Compton scattering at HERA
Chekanov, S. V., Derrick, M., Krakauer, D. A., et al. (2003) · Physics Letters B · doi:10.1016/j.physletb.2003.08.048 · Cited by 200
Benefit distribution and equity in road network design
Meng, Q., & Yang, H. (2002) · Transportation Research Part B Methodological · doi:10.1016/s0191-2615(00)00036-9 · Cited by 199
Cheng, J., & Druzdzel, M. J. (2000) · Cited by 198
Stephenson, M. T., & Holbert, R. L. (2003) · Communication Research · doi:10.1177/0093650203030003004 · Cited by 197
“However, Paxton et al. (2001) stated that works providing general overviews of this technique only indirectly apply to SEM (e.g., Mooney, 1997; Robert & Casella, 1999; Rubenstein, 1981).”
BackgroundDimension reduction method for reliability-based robust design optimization
Lee, I., Choi, K. K., Du, L., et al. (2007) · Computers & Structures · doi:10.1016/j.compstruc.2007.05.020 · Cited by 195
“Hence, there have been various numerical attempts to estimate the moments more efficiently: experimental design [10], first order Taylor series expansion [1,2,11], Monte Carlo simulation (MCS) [12], importance sampling method [13], and Latin hyper cube sampling method [14].”
MethodMonte Carlo Simulation and Numerical IntegrationPreprint
Geweke, J. F. (1994) · doi:10.21034/sr.192 · Cited by 195
New Metrics for Assessing the Reliability and Economics of Microgrids in Distribution System
Wang, S., Li, Z., Wu, L., et al. (2013) · IEEE Transactions on Power Systems · doi:10.1109/tpwrs.2013.2249539 · Cited by 193
“6) Convergence Criteria: The coefficient of variation [20] given in (35) is used in this paper as convergence criterion for the MCS simulation:”
MethodSeasonal and long‐term dynamics of the upper ocean carbon cycle at Station ALOHA near Hawaii
Keeling, C. D., Brix, H., & Gruber, N. (2004) · Global Biogeochemical Cycles · doi:10.1029/2004gb002227 · Cited by 192
“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 the parameter set shown in Table C4 for each simulation.”
MethodA de-noising scheme for enhancing wavelet-based power quality monitoring system
Yang, H., & Liao, C.-C. (2001) · IEEE Transactions on Power Delivery · doi:10.1109/61.924810 · Cited by 192
Cooper, B. A., Holekamp, N. M., Bohigian, G. M., et al. (2003) · American Journal of Ophthalmology · doi:10.1016/s0002-9394(03)00202-2 · Cited by 189
A fast approximate method for parameter sensitivity estimation in Monte Carlo structural reliability
Melchers, R. E., & Ahammed, M. (2003) · Computers & Structures · doi:10.1016/j.compstruc.2003.08.003 · Cited by 188
Modeling Multibody Systems with Uncertainties. Part I: Theoretical and Computational Aspects
Sandu, A., Sandu, C., & Ahmadian, M. (2006) · Multibody System Dynamics · doi:10.1007/s11044-006-9007-5 · Cited by 194
“An ensemble of runs is performed with each member using a different set of parameters drawn from the corresponding uncertainty distribution [7-9].”
MethodSoize, C. (2005) · Computer Methods in Applied Mechanics and Engineering · doi:10.1016/j.cma.2004.12.014 · Cited by 183
“(123)) can be solved by several methods, in particular by using the Monte Carlo numerical method [61].”
MethodHu, C. K., & Youn, B. D. (2010) · Structural and Multidisciplinary Optimization · doi:10.1007/s00158-010-0568-9 · Cited by 184
“Direct or smart MCS provides an alternative means of multi-dimensional integration ( Rubinstein 1981 ; F u and Moses1988 ;A u and Beck 2001).”
BackgroundMethodModelling and simulation of non-Rayleigh radar clutter
Conte, E., Longo, M., & Lops, M. (1991) · IEE Proceedings F Radar and Signal Processing · doi:10.1049/ip-f-2.1991.0018 · Cited by 184
Efficient Evaluation of Reliability for Slopes with Circular Slip Surfaces Using Importance Sampling
Ching, J., Phoon, K., & Hu, Y.-G. (2009) · Journal of Geotechnical and Geoenvironmental Engineering · doi:10.1061/(asce)gt.1943-5606.0000035 · Cited by 183
Sampling methods for solving Bayesian model updating problems: A tutorial
Lye, A., Cicirello, A., & Patelli, E. (2021) · Mechanical Systems and Signal Processing · doi:10.1016/j.ymssp.2021.107760 · Cited by 169
Adaptive importance sampling in monte carlo integration
Oh, M., & Berger, J. O. (1992) · Journal of Statistical Computation and Simulation · doi:10.1080/00949659208810398 · Cited by 180
ESC: an efficient error-based stopping criterion for kriging-based reliability analysis methods
Wang, Z., & Shafieezadeh, A. (2018) · Structural and Multidisciplinary Optimization · doi:10.1007/s00158-018-2150-9 · Cited by 179
Randomized smoothing for stochastic optimizationPreprint
Duchi, J. C., & Wainwright, M. J. (2016) · Cited by 179
Evolution of alluvial mudrock forced by early land plants
McMahon, W. J., & Davies, N. S. (2018) · Science · doi:10.1126/science.aan4660 · Cited by 178
Direction Choice for Accelerated Convergence in Hit-and-Run Sampling
Kaufman, D. E., & Smith, R. L. (1998) · Operations Research · doi:10.1287/opre.46.1.84 · Cited by 178
“Dixon and Szegö [7, 8], Rubinstein [21]).”
BackgroundInfluentialEntropy-based criterion in categorical clustering
Li, T., Ma, S., & Ogihara, M. (2004) · doi:10.1145/1015330.1015404 · Cited by 176
“The convergence property of the Monte-Carlo optimization is shown in (Rubinstein, 1981).”
MethodSeismic demand sensitivity of reinforced concrete shear‐wall building using FOSM method
Lee, T., & Mosalam, K. M. (2005) · Earthquake Engineering & Structural Dynamics · doi:10.1002/eqe.506 · Cited by 174
“One way of considering GMP uncertainty in probabilistic evaluation of structures is to employ MCS using a set of ground motions for a given IM to obtain a set of outputs.”
BackgroundInfluentialChapter 40 Classical estimation methods for LDV models using simulation
Hajivassiliou, V. A., & Ruud, P. A. (1994) · Handbook of econometrics · doi:10.1016/s1573-4412(05)80009-1 · Cited by 168
Improved importance sampling technique for efficient simulation of digital communication systems
Lu, D., & Yao, K. (1988) · IEEE Journal on Selected Areas in Communications · doi:10.1109/49.192731 · Cited by 172
On the usefulness of overparameterized ecological models
Reichert, P., & Omlin, M. (1997) · Ecological Modelling · doi:10.1016/s0304-3800(96)00043-9 · Cited by 171
Validation and error estimation of computational models
Rebba, R., Mahadevan, S., & Huang, S. (2006) · Reliability Engineering & System Safety · doi:10.1016/j.ress.2005.11.035 · Cited by 164
“For example, sampling error could be assumed to be a Gaussian random variable with zero mean and variance given by s(2)=N where N is the number of Monte Carlo runs and s(2) is the original variance of the model output [21].”
BackgroundRandomized algorithms for probabilistic robustness with real and complex structured uncertainty
Calafiore, G. C., Dabbene, F., & Tempo, R. (2000) · IEEE Transactions on Automatic Control · doi:10.1109/9.895560 · Cited by 164
“Among these techniques we recall the classical inversion method [17], [ 34 ].”
MethodProbabilistic load flow for photovoltaic distributed generation using the Cornish–Fisher expansion
Ruiz-Rodriguez, F. J., Hernández, J. C., & Jurado, F. (2012) · Electric Power Systems Research · doi:10.1016/j.epsr.2012.03.009 · Cited by 163
An introduction to mathematical models in sexually transmitted disease epidemiology
Garnett, G. P. (2002) · Sexually Transmitted Infections · doi:10.1136/sti.78.1.7 · Cited by 163
A state-of-the-art review on uncertainty analysis of rotor systems
Fu, C., Sinou, J.-J., Zhu, W. D., et al. (2022) · Mechanical Systems and Signal Processing · doi:10.1016/j.ymssp.2022.109619 · Cited by 162
REAK: Reliability analysis through Error rate-based Adaptive Kriging
Wang, Z., & Shafieezadeh, A. (2018) · Reliability Engineering & System Safety · doi:10.1016/j.ress.2018.10.004 · Cited by 163
“d the limit state. Thus, the probability of failure can be defined as: 𝑃Ù𝑃:𝑔:𝑿; Q0; :1; Several methodologies have been de veloped in order to calculate 𝑃Ù. Crude Monte Carlo simulation (MCS) [1], [2], First and Second Order Reliability Methods (FORM & SORM) [3], [4], Importance Sampling [5] and Subset Simulation…”
MethodDecomposition methods for structural reliability analysis
Xu, H. J., & Rahman, S. (2005) · Probabilistic Engineering Mechanics · doi:10.1016/j.probengmech.2005.05.005 · Cited by 160
“Direct Monte Carlo simulation [9] is the most widely used simulation method and involves the generation of independent samples of all input random variables, repeated deterministic trials (analyses) to obtain corresponding simulated samples of response variables, and standard statistical analysis to estimate probabili…”
MethodSampling-based RBDO using the stochastic sensitivity analysis and Dynamic Kriging method
Lee, I., Choi, K. K., & Zhao, L. (2011) · Structural and Multidisciplinary Optimization · doi:10.1007/s00158-011-0659-2 · Cited by 158
“Once an accurate surrogate model is available for the design optimization, the Monte Carlo simulation (MCS) (Rubinstein 1981) can be directly applied to the accurate surrogate model to estimate the reliability of the system without intensive computational burden.”
MethodMonte Carlo simulation of Markov unreliability models
Lewis, E. E., & Böhm, F. (1984) · Nuclear Engineering and Design · doi:10.1016/0029-5493(84)90060-8 · Cited by 158
Zhang, J., Xiao, M., & Gao, L. (2019) · Reliability Engineering & System Safety · doi:10.1016/j.ress.2019.03.002 · Cited by 156
Elastic scattering of electrons and positrons by atoms. Schrödinger and Dirac partial wave analysis
Salvat, F., & Mayol, R. (1993) · Computer Physics Communications · doi:10.1016/0010-4655(93)90019-9 · Cited by 156
Airspace Encounter Models for Estimating Collision Risk
Kochenderfer, M. J., Edwards, M., Espindle, L. P., Kuchar, J. K., & Griffith, J. (2010) · Journal of Guidance Control and Dynamics · doi:10.2514/1.44867 · Cited by 156
Design of a stand alone system with renewable energy sources using trade off methods
Gavanidous, E. S., & Bakirtzis, A. G. (1992) · IEEE Transactions on Energy Conversion · doi:10.1109/60.124540 · Cited by 154
Equivalent linearization and Monte Carlo simulation in stochastic dynamics
Proppe, C., Pradlwarter, H. J., & Schuëller, G. I. (2003) · Probabilistic Engineering Mechanics · doi:10.1016/s0266-8920(02)00037-1 · Cited by 154
Litaize, O., & Sérot, O. (2010) · Physical Review C · doi:10.1103/physrevc.82.054616 · Cited by 153
Contribution of contaminated sites to the global mercury budget
Kocman, D., Horvat, M., Pirrone, N., & Cinnirella, S. (2013) · Environmental Research · doi:10.1016/j.envres.2012.12.011 · Cited by 151
“, 1966 ; Hammersley and Handscomb , 1976 ; Rubinstein , 1981 ) .”
Novel sizing algorithm for yield improvement under process variation in nanometer technology
Choi, S. H., Paul, B. C., & Roy, K. (2004) · Proceedings - ACM IEEE Design Automation Conference · doi:10.1145/996566.996695 · Cited by 151
Generating Capacity Reliability Evaluation Based on Monte Carlo Simulation and Cross-Entropy Methods
da Silva, A. M. L., Fernandez, R. A. G., & Singh, C. (2010) · IEEE Transactions on Power Systems · doi:10.1109/tpwrs.2009.2036710 · Cited by 149
“In order to improve the performance of MCS tools, various variance reduction techniques are available [13].”
MethodA review on the integration of probabilistic solar forecasting in power systems
Li, B., & Zhang, J. (2020) · Solar Energy · doi:10.1016/j.solener.2020.07.066 · Cited by 156
A Stochastic Model for the Growth of Matrix Cracks in Composite Laminates
Wang, A. S. D., Chou, P. C., & Lei, S. (1984) · Journal of Composite Materials · doi:10.1177/002199838401800304 · Cited by 148
To Peer or Not to Peer: Modeling the Evolution of the Internet's AS-Level Topology
Chang, H., Jamin, S., & Willinger, W. (2006) · doi:10.1109/infocom.2006.236 · Cited by 147
“We use a well-known method for generating multi-variate normal random numbers [17] to ensure that the generated rankings are statistically consistent with the empirically inferred ones (i.e.,. Traffic demand from node i to j is then calculated according to Eq.”
MethodCoding techniques for handling failures in large disk arrays
Hellerstein, L., Gibson, G. A., Karp, R. M., et al. (1994) · Algorithmica · doi:10.1007/bf01185210 · Cited by 147
Proportional sampling strategy: guidelines for software testing practitioners
Chan, F. T., Chen, T. Y., Mak, I. K., et al. (1996) · Information and Software Technology · doi:10.1016/0950-5849(96)01103-2 · Cited by 147
Petkov, J., Harvey, P. W., & Battersby, M. (2010) · Quality of Life Research · doi:10.1007/s11136-010-9661-1 · Cited by 145
“Computationally, this is a Monte-Carlo technique [20] generating random samples with the same sample size and number of items and computing ‘‘expected’’ eigenvalues.”
MethodRadial Importance Sampling for Structural Reliability
Melchers, R. E. (1990) · Journal of Engineering Mechanics · doi:10.1061/(asce)0733-9399(1990)116:1(189 · Cited by 146
Monte Carlo simulation of extreme traffic loading on short and medium span bridges
Enright, B., & OBrien, E. J. (2012) · Structure and Infrastructure Engineering · doi:10.1080/15732479.2012.688753 · Cited by 146
“This is a form of importance sampling (Rubinstein 1981; Townsend, Haraszti, Freebersyser, & Devetsikiotis 1998) and greatly reduces the required processing time.”
BackgroundLoad modeling for distribution circuit state estimation
Ghosh, A. K., Lubkeman, D. L., & Jones, R. H. (1997) · IEEE Transactions on Power Delivery · doi:10.1109/61.584427 · Cited by 146
Moens, D., & Vandepitte, D. (2006) · Archives of Computational Methods in Engineering · doi:10.1007/bf02736398 · Cited by 144
“A comprehensive introduction to the Monte Carlo simulation methodology can be found in [9, 10 ].”
MethodGenealogical particle analysis of rare events
Moral, P. D., & Garnier, J. C. (2005) · The Annals of Applied Probability · doi:10.1214/105051605000000566 · Cited by 144
“The general approach to speeding up such simulations is to accelerate the occurrence of the rare events by using importance sampling (IS) [16, 24].”
BackgroundOutput space sampling for graph patterns
Hasan, M. A., & Zaki, M. J. (2009) · Proceedings of the VLDB Endowment · doi:10.14778/1687627.1687710 · Cited by 144
“The above algorithm is just an adaptation of classical Metropolis-Hastings (MH) algorithm where the proposal distribution is same as the transition probability matrix of a general random walk (each neighbor is chosen uniformly, q(x, y) = 1/dx) and the acceptance probability, as suggested by the MH algorithm, is: αxy =…”
MethodInfluentialOn the theory and simulation of multiple elastic scattering of electrons
Fernández‐Varea, J. M., Mayol, R., Baró, J., et al. (1993) · Nuclear Instruments and Methods in Physics Research Section B Beam Interactions with Materials and Atoms · doi:10.1016/0168-583x(93)95827-r · Cited by 142
Sampling Methods to Estimate Foliage and Other Characteristics of Individual Trees
Grégoire, T. G., Valentine, H. T., & Furnival, G. M. (1995) · Ecology · doi:10.2307/1940925 · Cited by 141
Cross entropy-based importance sampling using Gaussian densities revisited
Geyer, S., Papaioannou, I., & Straub, D. (2018) · Structural Safety · doi:10.1016/j.strusafe.2018.07.001 · Cited by 140
“This equivalence has also been discussed in [4].”
BackgroundRecent Advances in Surrogate Modeling Methods for Uncertainty Quantification and Propagation
Wang, C., Qiang, X., Xu, M., & Wu, T. (2022) · Symmetry · doi:10.3390/sym14061219 · Cited by 143
“Theoretically, MCS requires extensive samplings (usually 106 runs or greater) to procure reliable statistics, which implies that it is often computationally expensive for complex engineering problems [84].”
BackgroundApproaches for performing uncertainty analysis in large-scale energy/economic policy models
Kann, A., & Weyant, J. P. (2000) · Environmental Modeling & Assessment · doi:10.1023/a:1019041023520 · Cited by 137
“The most widespread technique used for this purpose is the Monte Carlo Method [Rubinstein, 1981].”
MethodQuasi-Random Methods for Estimating Integrals Using Relatively Small Samples
Spanier, J., & Maize, E. H. (1994) · SIAM Review · doi:10.1137/1036002 · Cited by 138
“the theory of complexity [28], to a host of simulation problems in engineering [ 29 ], [30], and”
BackgroundReliability-based design optimization strategies based on FORM: a review
Lopez, R. H., & Beck, A. T. (2012) · Journal of the Brazilian Society of Mechanical Sciences and Engineering · doi:10.1590/s1678-58782012000400012 · Cited by 137
“Simulations methods using sampling and estimation are well known in the literature, the most widely used being the Direct Monte Carlo simulation (MCS) method (Rubinstein, 1981).”
MethodChen, J., Ghanem, R., & Li, J. (2007) · Probabilistic Engineering Mechanics · doi:10.1016/j.probengmech.2007.12.017 · Cited by 137
Ching, J., Au, S., & Beck, J. L. (2004) · Computer Methods in Applied Mechanics and Engineering · doi:10.1016/j.cma.2004.05.028 · Cited by 136
Statistical Issues in Toxicokinetic Modeling: A Bayesian Perspective
Bernillon, P., & Bois, F. Y. (2000) · Environmental Health Perspectives · doi:10.1289/ehp.00108s5883 · Cited by 156
Yang, M., Zhang, D., & Han, X. (2020) · Computer Methods in Applied Mechanics and Engineering · doi:10.1016/j.cma.2020.113018 · Cited by 135
Methods of structural systems reliability
Ditlevsen, O., & Bjerager, P. (1986) · Structural Safety · doi:10.1016/0167-4730(86)90004-4 · Cited by 137
Anand, B. N., & Shachar, R. (2002) · The RAND Journal of Economics · doi:10.1111/j.1756-2171.2011.00131.x · Cited by 151
Shayegan‐Rad, A., Badri, A., & Zangeneh, A. (2017) · Energy · doi:10.1016/j.energy.2017.01.006 · Cited by 134
Arhami, M., Kamali, N., & Rajabi, M. M. (2013) · Environmental Science and Pollution Research · doi:10.1007/s11356-012-1451-6 · Cited by 132
“The term “Monte Carlo” was first used by Metropolis and Ulam (1949) for a statistical sampling technique in obtaining a probabilistic approximation to the solution of a mathematical equation or model (Rubinstein 1981).”
MethodChen, Y., & Jin, J. (2005) · IEEE Transactions on Reliability · doi:10.1109/tr.2005.853441 · Cited by 131
“It is known that the efficiency of the Monte Carlo method for integral evaluation can be improved by sampling from a distribution with a pdf of a similar shape to the absolute value of the integrand [30], [31].”
BackgroundMethodProbabilistic Theorem ProvingPreprint
Gogate, V., & Domingos, P. (2012) · arXiv (Cornell University) · doi:10.48550/arxiv.1202.3724 · Cited by 131
“We first apply this importance sampling approach [33] to WMC, yielding the MC-WMC algorithm.”
BackgroundMethodInfluentialThe fast simulation of electromagnetic and hadronic showers
Grindhammer, G., Rudowicz, M., & Peters, S. (1990) · Nuclear Instruments and Methods in Physics Research Section A Accelerators Spectrometers Detectors and Associated Equipment · doi:10.1016/0168-9002(90)90566-o · Cited by 130
HONG, H. P. (1999) · Structural Safety · doi:10.1016/s0167-4730(99)00016-8 · Cited by 130
New stochastic models for capacitated location-allocation problem
Zhou, J., & Liu, B. (2003) · Computers & Industrial Engineering · doi:10.1016/s0360-8352(03)00021-4 · Cited by 129
“…U1ðVkÞ=10; 000: Note that Step 2 is for generating random numbers with the distribution function Nð5; 1Þ: In fact, for the main known distributions, direct generating processes have been proposed (Bratley, Fox, & Schrage, 1987; Fishman, 1996; Law & Kelton, 1991; Liu, 1999a,b; Rubinstein, 1981).”
BackgroundProbabilistic models for condition assessment of oil and gas pipelines
Pandey, M. D. (1998) · NDT & E International · doi:10.1016/s0963-8695(98)00003-6 · Cited by 128
Grid-free simulation of diffusion using random walk methods
Ghoniem, A. F., & Sherman, F. S. (1985) · Journal of Computational Physics · doi:10.1016/0021-9991(85)90058-0 · Cited by 127
Simulation and Estimation of Reliability in a Wind Farm Considering the Wake Effect
Kim, H., Singh, C., & Sprintson, A. (2012) · IEEE Transactions on Sustainable Energy · doi:10.1109/tste.2011.2174260 · Cited by 127
19 Simulation estimation methods for limited dependent variable models
Hajivassiliou, V. A. (1993) · Handbook of statistics · doi:10.1016/s0169-7161(05)80054-9 · Cited by 127
Time-dependent system reliability analysis by adaptive importance sampling
Mori, Y., & Ellingwood, B. R. (1993) · Structural Safety · doi:10.1016/0167-4730(93)90018-v · Cited by 126
Constructions of particular random processes
Johnson, G. E. (1994) · Proceedings of the IEEE · doi:10.1109/5.265353 · Cited by 126
A Stochastic Branch-and-Bound Approach to Activity Crashing in Project Management
Gutjahr, W. J., Strauß, C., & Wagner, E. (2000) · INFORMS journal on computing · doi:10.1287/ijoc.12.2.125.11894 · Cited by 125
“Combinatorial Optimization: Algorithms andComplexity, Prentice-Hall, Englewood Cli s, NJ.[10] R.Y. Rubinstein, 1981.”
Gu, X., Sun, G., Li, G., et al. (2013) · Structural and Multidisciplinary Optimization · doi:10.1007/s00158-013-0921-x · Cited by 123
“The MCS technique is employed to generate the random data that have the same scatter as what could likely occur in reality (Rubinstein 1981).”
MethodImportance-Weighted Marginal Bayesian Posterior Density Estimation
Chen, M. (1994) · Journal of the American Statistical Association · doi:10.1080/01621459.1994.10476815 · Cited by 122
Model-based multidimensional clustering of categorical data
Chen, T., Zhang, N., Liu, T., Poon, K., & Wang, Y. (2012) · Artificial Intelligence · doi:10.1016/j.artint.2011.09.003 · Cited by 125
“In such cases, we resort to the Monte Carlo method [38] and compute the MI values based on”
MethodDependent-chance programming: A class of stochastic optimization
Liu, B. (1997) · Computers & Mathematics with Applications · doi:10.1016/s0898-1221(97)00237-x · Cited by 121
Herrador, M. Á., Asuero, A. G., & González, A. G. (2005) · Chemometrics and Intelligent Laboratory Systems · doi:10.1016/j.chemolab.2005.04.010 · Cited by 121
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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