On quasi-Monte Carlo integrations

By I. M. Soboĺ. 1998

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Citations in the corpus

Determinantal Point Processes for Machine Learning (2012, background): “This concern has led to the development of so-called quasirandom sets, which are in fact deterministically generated, but can be substituted for random sets in some instances to obtain improved convergence guarantees [112, 135].”
Galerkin Finite Element Approximations of Stochastic Elliptic Partial Differential Equations (2004, methodology): “Quasi Monte Carlo methods, see [14, 50, 51], offer a way to get a better convergence rate than the one of the Monte Carlo method, although this advantage seems to deteriorate in general when the number of the number of random variables present in the problem becomes large.”
A univariate dimension-reduction method for multi-dimensional integration in stochastic mechanics (2004, background): “As a result, researchers have developed or examined faster simulation methods, such as quasi-Monte Carlo simulation [22–24], importance sampling [25,26], directional simulation [27,28], and others [29–32].”
A generalized dimension‐reduction method for multidimensional integration in stochastic mechanics (2004, unknown): “Simulation and sampling methods, such as direct Monte Carlo simulation [21], quasi-Monte Carlo simulation [22–24], importance sampling [25, 26], directional simulation [27, 28], and others [29–32], are well known in the statistics and reliability literature.”
Recent Developments in Spectral Stochastic Methods for the Numerical Solution of Stochastic Partial Differential Equations (2009, methodology): “2 Quasi Monte-Carlo Quasi Monte-Carlo methods [22,119,88] consist in choosing the points {yk}k=1 from low discrepency sequences and to choose for the weights ωk = 1 K .”
CherryPick: Adaptively Unearthing the Best Cloud Configurations for Big Data Analytics (2017, methodology): “For that, we sample a few points (e.g., three) from the sample space using a quasi-random sequence [34].”
A constraint on extensible quadrature rules (2014, background): “Section 2 presents the insight from the appendix of Sobol’ (1998) and the extension by Hickernell et al. (2012).”
Eigenvector dimension reduction (EDR) method for sensitivity-free probability analysis (2008, methodology): “To relieve the computational burden, other sampling methods have been developed, such as quasi-MCS (Niederreiter and Spanier 2000; Sobol 1998), (adaptive) importance sampling (Engelund and Rackwitz 1993; Melchers 1989; Bucher 1988; Wu 1994), directional sampling (Bjerager 1988), etc.”
Reliability-based robust design optimization using the eigenvector dimension reduction (EDR) method (2009, methodology): “To relieve the computational burden, other sampling methods have been developed, such as quasi-MCS (Niederreiter and Spanier 2000; Sobol 1998), (adaptive) importance sampling (Engelund and Rackwitz 1993; Melchers 1989; Bucher 1988; Wu 1994), directional sampling (Bjerager 1988), etc.”
Globally Approximate Gaussian Processes for Big Data With Application to Data-Driven Metamaterials Design (2019, methodology): “To observe this, for each n , we generate ﬁ ve independent training samples via Sobol sequence [49,50] and plot the corresponding L .”
Analysing DSGE Models with Global Sensitivity Analysis (2008, background): “The rate of stochastic convergence for pure pseudo-random Monte Carlo methods is, in fact, N−1/2, while the actual rate of convergence of quasi-Monte Carlo methods can be N−c with c ≤ 1 (Sobol’ 1998).”
Computational microstructure characterization and reconstruction: Review of the state-of-the-art techniques (2018, methodology): “To generate the data needed to learn the constitutive law and validate the results, a design of experiments (DoE) of size 10 ; 000 was generated for the seven inputs via Sobol sequence [284,285].”