Cited by 3,356Simulation Techniques and ApplicationsMarkov Chains and Monte Carlo MethodsMathematical Approximation and Integration

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Simulation and the Monte Carlo Method

Rubinstein, Reuven Y., Kroese, Dirk P.·2016·Wiley Series in Probability and Statistics

DOI 10.1002/9781118631980

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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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Beck, J. L., & Zuev, K. M. (2012) · International Journal for Uncertainty Quantification · doi:10.1615/int.j.uncertaintyquantification.2012004713 · Cited by 44
“This result is sometimes attributed to Rubinstein [7], although it was proved earlier by Kahn and Marshall [2].”
Result
Computational solution of stochastic differential equations
SAUER, T. D. (2013) · Wiley Interdisciplinary Reviews Computational Statistics · doi:10.1002/wics.1272 · Cited by 44
“Monte Carlo (MC) simulation 20,27,23 is used in many ﬁelds to compute quantities of interest in stochastic modeling scenarios.”
Background
Sequential experimental design based generalised ANOVA
Chakraborty, S., & Chowdhury, R. (2016) · Journal of Computational Physics · doi:10.1016/j.jcp.2016.04.042 · Cited by 44
On Approximately Counting Colorings of Small Degree Graphs
Bubley, R., Dyer, M., Greenhill, C., et al. (1999) · SIAM Journal on Computing · doi:10.1137/s0097539798338175 · Cited by 44
“The use of the MCMC method originated in statistical physics (see, for example, [5, 9, 17]), but rigorous analysis of the method has been a more recent development, with notable contributions from the computer science community [6, 13].”
Method
GEOSTATISTICAL ESTIMATION VARIANCE FOR THE SPATIAL MEAN IN TWO-DIMENSIONAL SYSTEMATIC SAMPLING
Aubry, P., & Debouzie, D. (2000) · Ecology · doi:10.1890/0012-9658(2000)081[0543:gevfts]2.0.co;2 · Cited by 44
Discretized Laplacian Smoothing by Fourier Methods
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“A Nonsequential Monte Carlo Simulation [7,23,24,26,31 e 33] is used to obtain a sample of all possible transmission power system states.”
Method
Implementation of machine learning techniques into the Subset Simulation method
Cui, F., & Ghosn, M. (2019) · Structural Safety · doi:10.1016/j.strusafe.2019.02.002 · Cited by 43
Economic profitability of last-mile food delivery services: Lessons from Barcelona
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Cost related reliability measures for power system equipment
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“The variance may also be reduced without increasing the sample size; procedures for this purpose are known as variance reduction techniques [ 13 ], [14].”
BackgroundMethodInfluential
Dependent-chance goal programming and its genetic algorithm based approach
Liu, B. (1996) · Mathematical and Computer Modelling · doi:10.1016/0895-7177(96)00125-2 · Cited by 43
Benchmarking the driver acceleration impact on vehicle energy consumption and CO2 emissions
Suarez, J., Makridis, M., Anesiadou, A., et al. (2022) · Transportation Research Part D Transport and Environment · doi:10.1016/j.trd.2022.103282 · Cited by 42
“We use the Monte Carlo method to solve the inverse transformation function problem of a lognormal distribution (Abramowitz and Stegun, 1972; Rubinstein and Kroese, 2017).”
Operations & supply chain management: principles and practice
Petropoulos, F., Akkermans, H. A., Akşin, O. Z., Ali, I., Babai, M. Z., Barbosa‐Póvoa, A. P., Battaïa, O., Besiou, M., Boysen, N., Brammer, S. J., et al. (2025) · International Journal of Production Research · doi:10.1080/00207543.2025.2555531 · Cited by 88
Some Basic Principles of Reliability-Based Optimization (RBO) of Structures and Mechanical Components
Gasser, M., & Schuëller, G. I. (1998) · Lecture notes in economics and mathematical systems · doi:10.1007/978-3-642-45767-8_4 · Cited by 42
A Unified Framework for Integrated Optimization Under Uncertainty
Wang, Z., Huang, H., & Liu, Y. (2010) · Journal of Mechanical Design · doi:10.1115/1.4001526 · Cited by 42
Seismic risk sensitivity of structures equipped with anti-seismic devices with uncertain properties
Scozzese, F., Dall’Asta, A., & Tubaldi, E. (2018) · Structural Safety · doi:10.1016/j.strusafe.2018.10.003 · Cited by 42
“Monte Carlo techniques [26,43,44] can be employed for solving the integral for each combination of the parameters, but this type of approach is generally computationally expensive, and it becomes unfeasible in the problem considered in the application, where the possible combinations could be numerous.”
Method
Real-time high-fidelity reliability updating with equality information using adaptive Kriging
Wang, Z., & Shafieezadeh, A. (2019) · Reliability Engineering & System Safety · doi:10.1016/j.ress.2019.106735 · Cited by 42
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“MCS is a technique used to perform decision-making under uncertain circumstances and to model the probability of different outcomes that are not easily predictable due to random variables [29].”
Method
Reliability analysis and initial requirements for FC systems and stacks
Åström, K., Fontell, E., & Virtanen, S. (2007) · Journal of Power Sources · doi:10.1016/j.jpowsour.2006.11.085 · Cited by 42
Simplified Monte Carlo simulation of elastic electron scattering in limited media
Baró, J., Sempau, J., Fernández‐Varea, J. M., et al. (1994) · Nuclear Instruments and Methods in Physics Research Section B Beam Interactions with Materials and Atoms · doi:10.1016/0168-583x(94)95341-4 · Cited by 42
Accelerating path tracing by re-using paths
Bekaert, P., Sbert, M., & Halton, J. H. (2002) · Max Planck Institute for Plasma Physics · doi:10.5555/581896.581914 · Cited by 42
Data-parallel load balancing strategies
Fonlupt, C., Marquet, P., & Dekeyser, J. (1998) · Parallel Computing · doi:10.1016/s0167-8191(98)00049-0 · Cited by 42
“The tracking of particles in a detector such as Mont e Carlo simulation methods is a prototype of stack algorithms [28].”
Method
Recommendations on the Testing and Use of Pseudo‐Random Number Generators Used in Monte Carlo Analysis for Risk Assessment
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Di, G. A. (2003) · doi:10.71910/supsi.7045 · Cited by 41
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A 3D contour based geometrical model generator for complex-shaped horticultural products
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US long-term energy intensity: Backcast and projection
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Multiscale modelling of the composite reinforced foam core of a 3D sandwich structure
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“Monte-Carlo numerical simulations [11] are used for assessing some statistical properties of the overall mechanical response.”
Method
A Variance Reduction Framework for Stable Feature Selection
Yue, H., & Yu, L. (2010) · Proceedings · doi:10.1109/icdm.2010.144 · Cited by 43
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Balaprakash, P., Birattari, M., Stützle, T., & Dorigo, M. (2009) · Computers & Operations Research · doi:10.1016/j.cor.2009.12.005 · Cited by 40
“The cost differences between neighboring solutions are computed using delta evaluation based on an estimation approach that includes method of common random numbers, importance sampling [33] and an adaptive sample size.”
Method
Parametric sensitivity study on regional seismic damage prediction of reinforced masonry buildings based on time-history analysis
Lu, X., Tian, Y., Guan, H., et al. (2017) · Bulletin of Earthquake Engineering · doi:10.1007/s10518-017-0168-9 · Cited by 40
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Xu, J., Zhang, Y., & Dang, C. (2020) · Mechanical Systems and Signal Processing · doi:10.1016/j.ymssp.2020.106661 · Cited by 40
Software specifications for uncertainty evaluation.
Cox, M. G., & Harris, P. M. (2004) · Cited by 40
Bayes Factors for Nonlinear Hypotheses and Likelihood Distributions
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Uncertainty evaluation from Monte-Carlo simulations by using Crystal-Ball software
González, A. G., Herrador, M. Á., & Asuero, A. G. (2005) · Accreditation and Quality Assurance · doi:10.1007/s00769-005-0934-2 · Cited by 39
“However, the use of MCS enables us to solve the problem numerically by means of the simulation of random variables [13, 14 ].”
Method
Risk assessment of cascading outages: Part I — Overview of methodologies
Vaiman, M. M., Bell, K. R. W., Chen, Y., et al. (2011) · IEEE Power and Energy Society General Meeting (PESGM) · doi:10.1109/pes.2011.6039405 · Cited by 39
Definition of a condition-based model for natural stone claddings
Ferreira, C., Silva, A. R., de Brito, J., et al. (2020) · Journal of Building Engineering · doi:10.1016/j.jobe.2020.101643 · Cited by 39
Multiphysics modeling and uncertainty quantification of tribocorrosion in aluminum alloys
Wang, K., Wang, Y., Yue, X., et al. (2020) · Corrosion Science · doi:10.1016/j.corsci.2020.109095 · Cited by 40
Environmental and Economic Assessments and Uncertainties of Multiple Lignocellulosic Biomass Utilization for Bioenergy Products: Case Studies
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“Monte Carlo simulation is a mathematical technique that performs risk analysis by building models with random variables for decision [78].”
Method
Multi-objective robust optimization of foam-filled tapered multi-cell thin-walled structures
Yin, H., Fang, H., Xiao, Y., et al. (2015) · Structural and Multidisciplinary Optimization · doi:10.1007/s00158-015-1299-8 · Cited by 39
Comparison and combination of factorial and Monte-Carlo design in sensitivity analysis
Fürbringer, J.-M., & Roulet, C.-A. (1995) · Building and Environment · doi:10.1016/0360-1323(95)00013-v · Cited by 39
Two-dimensional Conditional Simulations Based on the Wavelet Decomposition of Training Images
Gloaguen, E., & Dimitrakopoulos, R. G. (2009) · Mathematical Geosciences · doi:10.1007/s11004-009-9235-3 · Cited by 42
“x0|nd is given by Rubinstein (1981) Z a1,H1,V1,D1”
Method
Multinormal integrals by importance sampling for series system reliability
Mori, Y., & Kato, T. (2003) · Structural Safety · doi:10.1016/s0167-4730(03)00015-8 · Cited by 39
A Monte Carlo algorithm for probabilistic propagation in belief networks based on importance sampling and stratified simulation techniques
Hernández, L. D., Moral, S., & Salmerón, A. (1998) · International Journal of Approximate Reasoning · doi:10.1016/s0888-613x(97)10004-4 · Cited by 39
Modifying Electroglottograph-Identified Intervals of Phonation
Gow, M. L., & Ingham, R. J. (1992) · Journal of Speech Language and Hearing Research · doi:10.1044/jshr.3503.495 · Cited by 39
Augmenting approximate solutions for consistent reliability analysis
Au, S. (2006) · Probabilistic Engineering Mechanics · doi:10.1016/j.probengmech.2006.08.004 · Cited by 39
Modified Latin Hypercube Sampling Monte Carlo (MLHSMC) Estimation for Average Quality Index
Keramat, M., & Kielbasa, R. (1999) · Analog Integrated Circuits and Signal Processing · doi:10.1023/a:1008386501079 · Cited by 39
“The range of each variable is partitioned into N non overlapping intervals of equal probability 1 N .”
Background
A Bayesian analysis of the logarithmic-Poisson execution time model based on expert opinion and failure data
Campodonico, S., & Singpurwalla, N. D. (1994) · IEEE Transactions on Software Engineering · doi:10.1109/32.317426 · Cited by 39
EcliPse: A system for high performance concurrent simulation
Sunderam, V. S., & Rego, V. J. (1991) · Software Practice and Experience · doi:10.1002/spe.4380211104 · Cited by 39
Policy Improvement for POMDPs Using Normalized Importance SamplingPreprint
Shelton, C. R. (2013) · arXiv (Cornell University) · doi:10.48550/arxiv.1301.2310 · Cited by 39
“Importance sampling is typically presented as a method for reducing the variance of the estimate of an expectation by carefully choosing a sampling distribution [Rubinstein, 1981].”
BackgroundMethod
Variance Reduction
Botev, Z. I., & Ridder, A. (2017) · Wiley StatsRef: Statistics Reference Online · doi:10.1002/9781118445112.stat07975 · Cited by 39
Recent advances in path integral control for trajectory optimization: An overview in theoretical and algorithmic perspectives
Kazim, M. Z., Hong, J., Kim, M.-G., & Kim, K. K. (2024) · Annual Reviews in Control · doi:10.1016/j.arcontrol.2023.100931 · Cited by 47
Evolutionary Phases in Emerging Quantum Technologies: General Theoretical and Managerial Implications for Driving Technological Evolution
Coccia, M., & Roshani, S. (2024) · IEEE Transactions on Engineering Management · doi:10.1109/tem.2024.3385116 · Cited by 39
A Bayesian Sequential Look at u-Control Charts
Bayarri, M. J., & García‐Donato, G. (2005) · Technometrics · doi:10.1198/004017005000000085 · Cited by 38
“…qr(U|α̂, β̂) can easily be computed by Monte Carlo (MC) methods; it suffices to generate N observations from the distribution of U|α̂, β̂ and simply use the sample percentiles of the generated sample (see, e.g., Rubinstein 1981 and Robert and Casella 1999 for properties and convergence results).”
Delineation of shallow resistivity structure around Malvan, Konkan region, Maharashtra by neural network inversion using vertical electrical sounding measurements
Maiti, S., Gupta, G., Erram, V. C., & Tiwari, R. K. (2012) · Environmental Earth Sciences · doi:10.1007/s12665-012-1779-8 · Cited by 37
Grand canonical Monte Carlo and molecular dynamics simulations of the structural properties, diffusion and adsorption of hydrogen molecules through poly(benzimidazoles)/nanoparticle oxides composites
Khosravanian, A., Dehghani, M., Pazirofteh, M., et al. (2018) · International Journal of Hydrogen Energy · doi:10.1016/j.ijhydene.2017.12.122 · Cited by 38
Reducing waste and ecological impacts through a sustainable and efficient management of perishable food based on the Monte Carlo simulation
Scalia, G. L., Micale, R., Miglietta, P. P., & Toma, P. (2018) · Ecological Indicators · doi:10.1016/j.ecolind.2018.10.041 · Cited by 38
Efficient parallel random field generator for large 3-D geophysical problems
Räss, L., Kolyukhin, D. R., & Minakov, A. N. (2019) · Computers & Geosciences · doi:10.1016/j.cageo.2019.06.007 · Cited by 38
“The general approaches for the sampling are described for example in Rubinstein (1981) and Sabelfeld (1991).”
Method
Direct simulation of two-dimensional isotropic or anisotropic random field from sparse measurement using Bayesian compressive sampling
Hu, Y., Zhao, T., Wang, Y., et al. (2019) · Stochastic Environmental Research and Risk Assessment · doi:10.1007/s00477-019-01718-7 · Cited by 38
Metamodel-based simulation optimisation for bed allocation
Wang, X., Gong, X., Geng, N., et al. (2019) · International Journal of Production Research · doi:10.1080/00207543.2019.1677962 · Cited by 38
Approximate query service on autonomous IoT cameras
Xu, M., Zhang, X., Liu, Y., Huang, G., Liu, X., & Lin, F. X. (2020) · International Conference on Mobile Systems, Applications, and Services · doi:10.1145/3386901.3388948 · Cited by 48
“dware prototype for testing Elf. The platform consists of two interconnected SoCs for frame capturing and processing, respectively. Typically, the CI widths are derived through Monte Carlo simulation [87]: randomly picking the same number of samples from t-distribution and NN counter’s error distribution (E′,E′′) resp…”
Method
Contaminated site–induced health risk using Monte Carlo simulation: evaluation from the brownfield in Beijing, China
Guo, P., Li, H., Zhang, G., et al. (2021) · Environmental Science and Pollution Research · doi:10.1007/s11356-021-12429-4 · Cited by 38
“…Xi’an University of Architecture and Technology, Xi’an 710055, China nervous and immune systems and can impose detrimental health effects; these include lung cancer, kidney and liver dysfunction, and bone fractures (Alissa and Ferns 2011; Edwards 2014; Johri et al. 2010; Solenkova et al. 2014).”
Background
Simulated annealing type algorithms for multivariate optimization
Gelfand, S. B., & Mitter, S. K. (1991) · Algorithmica · doi:10.1007/bf01759052 · Cited by 38
“The sequence {Zk} could also correspond to a random search [2], where the sequence {k } arises from randomly selected search directions.”
Background
Photon migration in turbid media using a cumulant approximation to radiative transfer
Xu, M., Cai, W., Lax, M. D., et al. (2002) · Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics · doi:10.1103/physreve.65.066609 · Cited by 38
Bias and Precision of Estimates from an Age-Structured Stock Assessment Program in Relation to Stock and Data Characteristics
Yin, Y., & Sampson, D. B. (2004) · North American Journal of Fisheries Management · doi:10.1577/m03-107.1 · Cited by 38
“In this study we used Monte Carlo simulation ( Rubinstein 1981 ) to determine the impacts of input data measurement errors and stock characteristics on the bias and precision of Stock Synthesis estimates.”
Method
Ordinary Least Squares and Sample-Selection Models of Health-Care Demand Monte Carlo Comparison
Hay, J. W., Leu, R. E., & Rohrer, P. (1987) · Journal of Business and Economic Statistics · doi:10.1080/07350015.1987.10509618 · Cited by 38
“In the first set of Monte Carlo runs, these variates were transformed to iid standard normal variates vi, ei (Rubinstein 1981).”
Method
Simultaneous determination of oxygen diffusivity and respiration in pear skin and tissue
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Analytical and Monte Carlo Approaches to Evaluate Probability Distributions of Interruption Duration
LeitedaSilva, A. M., Schmitt, W. F., Cassula, A. M., et al. (2005) · IEEE Transactions on Power Systems · doi:10.1109/tpwrs.2005.851944 · Cited by 38
Cryptographically Secured Pseudo-Random Number Generators: Analysis and Testing with NIST Statistical Test Suite
Luengo, E. A., & Villaizán, J. R. (2023) · Mathematics · doi:10.3390/math11234812 · Cited by 40
Exact methods for variable selection in principal component analysis: Guide functions and pre-selection
Pacheco, J., Yusta, S. C., & Porras, S. (2012) · Computational Statistics & Data Analysis · doi:10.1016/j.csda.2012.06.014 · Cited by 36
Modelling redundancy allocation for a fuzzy random parallel–series system
Wang, S., & Watada, J. (2009) · Journal of Computational and Applied Mathematics · doi:10.1016/j.cam.2009.06.034 · Cited by 37
A design–build–test cycle using modeling and experiments reveals interdependencies between upper glycolysis and xylose uptake in recombinant S. cerevisiae and improves predictive capabilities of large-scale kinetic models
Mišković, L., Alff-Tuomala, S., Soh, K. C., Barth, D., Salusjärvi, L., Pitkänen, J., Ruohonen, L., Penttilä, M. E., & Vassily Hatzimanikatis, A. (2017) · Biotechnology for Biofuels · doi:10.1186/s13068-017-0838-5 · Cited by 38
“Furthermore, the thermodynamically feasible metabolite concentration space is not in the form of a parallelotope (nor it is in the form of a simplex or a hypersphere), and consequently the transformation techniques for the generation of random samples are not applicable [82, 83].”
Background
User Traffic Prediction for Proactive Resource Management: Learning-Powered Approaches
Azari, A., Papapetrou, P., Denic, S. Z., & Peters, G. (2019) · Globecom · doi:10.1109/globecom38437.2019.9014115 · Cited by 39
“In the first two categories, we carry out a comprehensive set of Monte Carlo MATLAB simulations [20], over the dataset, for different lengths of the training sets, length of future prediction, feature sets used in learning and prediction, and etc.”
Method
Error Quantification and Control for Adaptive Kriging-Based Reliability Updating with Equality Information
Zhang, C., Wang, Z., & Shafieezadeh, A. (2020) · Reliability Engineering & System Safety · doi:10.1016/j.ress.2020.107323 · Cited by 37
Reliability analysis with corrosion defects in submarine pipeline case study: Oil pipeline in Ab-khark island
Pourahmadi, M., & Saybani, M. (2022) · Ocean Engineering · doi:10.1016/j.oceaneng.2022.110885 · Cited by 37
Predictable mobility
Ishigami, G., Kewlani, G., & Iagnemma, K. D. (2009) · IEEE Robotics & Automation Magazine · doi:10.1109/mra.2009.934823 · Cited by 37
“IEEE Robotics & Automation MagazineDECEMBER 2009 1070-9932/09/$26.00ª2009 IEEE 61”
Background
Probabilistic evaluation for the implicit limit-state function of stability of a highway tunnel in China
Su, Y., Li, X., & Xie, Z. (2010) · Tunnelling and Underground Space Technology · doi:10.1016/j.tust.2010.11.009 · Cited by 37
Assessment of offshore platforms under extreme waves by probabilistic incremental wave analysis
Golafshani, A. A., Ebrahimian, H., Bagheri, V., et al. (2011) · Journal of Constructional Steel Research · doi:10.1016/j.jcsr.2011.01.005 · Cited by 37
Droplet size estimation of two-phase flashing jets
Razzaghi, M. (1989) · Nuclear Engineering and Design · doi:10.1016/0029-5493(89)90130-1 · Cited by 37
An efficient simulation method for reliability analysis of linear dynamical systems using simple additive rules of probability
Yuen, K., & Katafygiotis, L. S. (2004) · Probabilistic Engineering Mechanics · doi:10.1016/j.probengmech.2004.07.003 · Cited by 37
New Approximations for Reliability Integrals
Breitung, K., Polidori, D., Beck, J. L., et al. (2001) · Journal of Engineering Mechanics · doi:10.1061/(asce)0733-9399(2001)127:2(207 · Cited by 37
Sampling variance in the correlation coefficient under indirect range restriction: Implications for validity generalization.
Aguinis, H., & Whitehead, R. (1997) · Journal of Applied Psychology · doi:10.1037/0021-9010.82.4.528 · Cited by 35
“Accordingly, the purpose of our study was to use an MC strategy (Hartley & Harris, 1963; Noreen, 1989; Rubinstein, 1981) to examine (a) whether IRR increases the sampling error variance in the correlation coefficient above its analytically expected value and (b) the extent to which the sampling error variance estimato…”
Method
Probabilistic fracture analysis of cracked pipes with circumferential flaws
Rahman, S. (1997) · International Journal of Pressure Vessels and Piping · doi:10.1016/s0308-0161(96)00034-8 · Cited by 37
Stochastic approximation algorithms: Overview and recent trends
Bharath, B. N., & Borkar, V. S. (1999) · Sadhana · doi:10.1007/bf02823149 · Cited by 33
“Traditional techniques for simulation-based algorithms, such as use of common randomness, control variates, importance sampling etc. have been extensively dealt with in standard textbook treatments such as Ripley (1987) and Rubinstein (1981).”
Method
Statistical inference and Monte Carlo algorithms
Casella, G., Ferrándiz, J., Peña, D., Insua, D. R., Bernardo, J. M., García-López, P., González, A. G., Berger, J. O., Dawid, A. P., DiCiccio, T. J., et al. (1996) · Test · doi:10.1007/bf02562621 · Cited by 36

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)
DOI: 10.1002/9781118631980
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
Licence: doi.wiley.com/10.1002/tdm_license_1.1 (tdm)
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

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