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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“A variety of variance-reduction techniques are available, including control variates, antithetic variates, stratified sampling, correlated sampling and importance sampling;([10-12]) however, none are routinely used within economic models.”
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“On the other hands, the sampling methods mainly use random sampling in the probabilistic domain (Denny 2001; Rubinstein and Kroese 2016).”
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“The usability of MCS had efficient performance to produce knowledge extraction of the best predictors while considering the uncertainties of meteorological and hydrological variables in streamflow forecasts (Adeloye, 2012; Kroese et al. 2014; Rubinstein and Kroese 2016).”
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The PEAR Method for Sample Sizes in Multiple Linear Regression
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“[15, 17 ]). As the temperature parameter decreases to zero, the Boltzmann distribution concentrates more around the global optimum.”
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“These values help solve the problem as a deterministic problem (Rubinstein and Kroese, 2016).”
Background
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., B. N. R., & Chowdhury, R. (2008) · Engineering Computations · doi:10.1108/02644400810909580 · Cited by 29
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Method
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“Some variants of MCS (Dey and Mahadevan, 1998; Moarefzadeh and Melchers, 1999; Rubinstein, 1981), such as importance sampling and adaptive importance sampling, have been developed to address rare events with small probability.”
Background
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“In this study, a Monte Carlo simulation is adopted [ 2 ].”
Method
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“2005b) and because a Monte Carlo simulation approach (Rubinstein 1981), requiring multiple model repetitions, is often used for ABM, signiﬁcant computational power is consumed during each step of agent-based modeling (e.g., development, calibration, validation, and experimentation).”
Method
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“estimation approach additionally includes an adaptive sample size procedure based on Student’s t test and two variance reduction techniques: the method of common random numbers and importance sampling [44].”
Method
Probabilistic load flow with versatile non-Gaussian power injections
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“See for example Devroye (1986) or Rubinstein (1981).”
Background
Modelling uncertainty in incompressible flow simulation using Galerkin based generalized ANOVA
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Bi-fidelity stochastic gradient descent for structural optimization under uncertainty
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Probabilistic theorem proving
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“We first apply this importance sampling approach [33] to WMC, yielding the MC-WMC algorithm.”
BackgroundMethodInfluential
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Hemodynamic Flow Modeling Through an Abdominal Aorta Aneurysm Using Data Mining Tools
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“sequently, the resulting data are postprocessed to estimate the output statistics [10].”
Method
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The Utilization of Outpatient Medical Services in Japan
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“Repeated rounds of Monte Carlo simulation were used to find the most efficient and robust experimental design (12, 23, 24).”
Method
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“(10) cannot be solved analytically, but by using Monte Carlo method [71, 72], we can approximate the cost function as”
Method
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“Various methods, including first and second order reliability methods (FORM & SORM) [2], random simulation methods [3], [4], surrogate model-based methods [5]–[7], etc.”
Method
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“These include, among others, crude Monte Carlo simulation (MCS) (Rubinstein and Kroese 2016; Fishman 1996), importance sampling (Echard et al. 2013), sub-set simulation (SS) (Au and Beck 2001), first or second order reliability method (FORM & SORM) (Rackwitz and Flessler 1978; Der Kiureghian and De…”
Method
Recommendations on Statistical Randomness Test Batteries for Cryptographic Purposes
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“%) and usually the higher the better [51].”
Background
UHF sensors positioning on the power transformer tank to enhance the partial discharge localization accuracy
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Backwards Abstract Interpretation of Probabilistic Programs
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“Subsequently, each particle in the sample population is assigned to an appropriately selected volume, Vi , and an appropriately selected value of the internal property, xi , so that the particle array at time zero, Ns(0), closely represents the initial distribution, according to the “inverse transform method” (Rubinst…”
Method
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“The estimation of the likelihood function is performed using the Monte Carlo simulation method (see [18]) with ns = 350 simulations for which the convergence is achieved.”
Method
Adaptive sample size and importance sampling in estimation-based local search for the probabilistic traveling salesman problem
Balaprakash, P., Birattari, M., Stützle, T., & Dorigo, M. (2008) · European Journal of Operational Research · doi:10.1016/j.ejor.2008.11.027 · Cited by 27
“For this purpose, we use the variance reduction technique known as importance sampling (Rubinstein, 1981).”
Method
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Kolyukhin, D. R., Schueller, S., Espedal, M. S., et al. (2009) · Computational Geosciences · doi:10.1007/s10596-009-9148-8 · Cited by 27
“The standard estimation has the following form [ 27 ]:”
Background
Multilevel model reduction for uncertainty quantification in computational structural dynamics
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“…by The hyperparameter δ A of random matrix [ G n (δ A ) ] has to verify 0 δ δ max with δ max given by Using the Monte-Carlo simulation method [122], the C-SROM allows for computing the random displacements vector U (ω) associated with U (ω) , in which the random complex vector Q (ω) of the…”
Method
A novel approach for reliability analysis with correlated variables based on the concepts of entropy and polynomial chaos expansion
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“See e.g. Rubinstein (1981) (p. 86-87).”
Estimation of performance measures for product form cellular mobile communications networks
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A global least mean square algorithm for adaptive IIR filtering
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“with as where is the global minimum of The application of this technique to the LMS algorithm requires a gradient operation on the functional i.e., As described in [5], [ 14 ], if is a standard multinormal distribution, then the unbiased gradient estimate of the smoothed functional when only the gradient of is known c…”
BackgroundMethodInfluential

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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