Simulation and the Monte Carlo method

By Reuven Y. Rubinstein. 1981

Subfields: Probabilistic & Bayesian Methods, Numerical Methods & Scientific Computing

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Citations in the corpus

Survey on Automated Machine Learning (2019, methodology): “The cubic time complexity of Gaussian processes is clearly visible for RoBO and partially for BTB. Due to the usage of Markov chain Monte Carlo (Rubinstein and Kroese, 2008), RoBO has a significantly larger overhead.”
Control functionals for Monte Carlo integration (2014, background): “These include (a) importance sampling and its extensions (Cornuet et al., 2012; Li et al., 2013), (b) stratified sampling and related techniques (Rubinstein and Kroese, 2011), (c) antithetic variables (Green and Han, 1992) and more generally (randomized) quasi- Monte-Carlo (RQMC) sampling (Dick and…”
Learning from Scarce Experience (2002, methodology): “It is well known (Rubinstein, 1981) that variance of WIS estimate is O( 1 N ).”
Reinforcement Learning with Replacing Eligibility Traces (2005, methodology): “Thisis what is classically done in Monte Carlo (MC) prediction methods (Rubinstein,1981; Curtiss, 1954; Wasow, 1952; Barto & Du , 1994).”
Theoretical framework and experimental procedure for modelling mesoscopic volume fraction stochastic fluctuations in fiber reinforced composites (2008, background): “(24) can be solved by Monte-Carlo numerical simulations [13] which require the computation of the macroscopic moduli for each realization.”
S-TaLiRo: A Tool for Temporal Logic Falsification for Hybrid Systems (2011, methodology): “At its core, S-TaLiRo integrates robustness computation for traces of hybrid systems (TaLiRo) [4,6] with stochastic simulation [9].”
An Introduction to MCMC for Machine Learning (2004, background): “Importance sampling is an alternative “classical” solution that goes back to the 1940’s; see for example (Geweke, 1989; Rubinstein, 1981).”
Random uncertainties model in dynamic substructuring using a nonparametric probabilistic model (2003, methodology): “In order to carry out the Monte Carlo numerical simulation (Cochran 1977, Kalos & Whitlock 1986, Rubinstein 1981) of random dynamical responses of the coupled system , we use the adapted algebraic representation of random matrices [GM ], [GD] and [GK ] defined by Eqs.”
Design of computer experiments: A review (2017, background): “This has resulted in an abundant literature [44, 66, 67, 94, 108, 136, 137, 154].”
Lattice gauge theory simulations in the quantum information era (2016, methodology): “However, a number of approximate analytical and numerical methods have been developed to describe faithfully the usually small portion of interest of the exponentially big Hilbert space: they range from renormalisation group (RG) methods (which rely on a truncation in a particular energy sector of t”
Riemann sums for MCMC estimation and convergence monitoring (2001, background): “For instance, when the sample is (independently) generated from a density g, the importance sampling reweighting of the average (2) leads to an unbiased estimator whose variance may, at least formally, decrease down to 0 (see Rubinstein, 1981).”
Why the Monte Carlo method is so important today (2014, methodology): “When applied to physical systems, Monte Carlo techniques can reduce complex models to a set of basic events and interactions, opening the possibility to encode model behavior through a set of rules which can be efficiently implemented on a computer.”
Structural reliability analysis using a copula-function-based evidence theory model (2014, methodology): “00416 [1,2] [2,3] [5,8] 0.”