Monte Carlo and Quasi-Monte Carlo Sampling

By Christiane Lemieux. 2009

615 citations recorded by the source corpus.

Subfields: Finance, Numerical Analysis, Statistics and Probability

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Citations in the corpus

Control functionals for Monte Carlo integration (2014, methodology): “t al., 2012), (ii) stratied sampling and related techniques such as systematic sampling, (iii) antithetic variables (Green and Han, 1992) and more generally (randomised) quasi-Monte Carlo (QMC/RQMC; Lemieux, 2009), (iv) Rao-Blackwellisation (Robert and Casella, 2004; Olsson and Ryden, 2011), (v) Rie”
Algorithms for Reinforcement Learning (2010, methodology): “Possibilities include using strip-like tilings combined with hash functions, interpolators that use low-discrepancy grids (Lemieux, 2009, Chapter 5 and 6), or random projections (Dasgupta and Freund, 2008).”
Digital Nets and Sequences: Discrepancy Theory and Quasi-Monte Carlo Integration (2010, methodology): “The books of Fox [79], Tezuka [254], Glasserman [83], and Lemieux [152] and the surveys of Keller [118] and L’Ecuyer [149] deal more directly with questions arising from applications.”
Design of computer experiments: A review (2017, methodology): “A modification of star discrepancy is L2 discrepancy where L2 norm of the departure is used instead of the absolute departure (L∞ norm) [53, 103] as shown below.”
Improving variable-fidelity surrogate modeling via gradient-enhanced kriging and a generalized hybrid bridge function (2013, methodology): “We used a quasi-Monte Carlo approach [39] to sample the parameter space with 200 points for Euler computations and 2 to 35 points for the RANS computations (as well as viscous adjoint computations).”
Hierarchical Kriging Model for Variable-Fidelity Surrogate Modeling (2012, methodology): “The sample points are chosen using the quasi–Monte Carlo method [40].”
A randomized orthogonal array-based procedure for the estimation of first- and second-order Sobol' indices (2015, positive): “We now recall the deﬁnition of a randomized OA [see 14, 15] and introduce the general notion of replicated randomized OA.”
Tractability of Multivariate Problems (2008, methodology): “The reader is also referred to a recent book [27] Analytic Number Theory: Essays in Honor of Klaus Roth edited by Chen, Gowers, Halberstam, Schmidt and Vaughan [27], which has many surveys of discrepancy as well as to a recent book of Lemieux [171] Monte Carlo and Quasi-Monte Carlo Sampling.”
Acta Numerica: High dimensional integration - the Quasi-Monte Carlo way (2014, neutral): “More information on transformations from R s to the unit cube [0, 1] s , variance reduction techniques, as well as other information for the practical use of MC and QMC can be found in Lemieux (2009).”
Monte Carlo sampling-based methods for stochastic optimization (2014, methodology): “We refer to Niederreiter [173], Lemieux [150] and Dick and Pillichshammer [63] for comprehensive treatments of QMC concepts.”