On the distribution of points in a cube and the approximate evaluation of integrals
By Ilya M. Sobol. 1967
How researchers see this paper
The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.
- Andrea Saltelli
- Francesca Campolongo
- Yang Liu
- Frank Hutter
- Christiane Lemieux
- G. Em Karniadakis
- Stefano Tarantola
- Sergei S. Kucherenko
Citations in the corpus
- An evaluation of adaptive surrogate modeling based optimization with two benchmark problems (2014, methodology): “Many case studies have demonstrated that SCE-UA algorithm is an effective and efficient method for model calibration (Sorooshian et al., 1993; Gan and Biftu, 1996; Hogue et al., 2000; Boyle et al., 2000; Moreno et al., 2012).”
- Determinantal Point Processes for Machine Learning (2012, background): “The Sobol sequence [134], introduced later, offers improved uniformity properties and can be generated efficiently [18].”
- Variance-based sensitivity analysis of a forest growth model (2012, methodology): “We generated a quasi-random sequence matrix of size (N, 2k), where P and Q are the left and right half of this matrix, respectively (Saltelli et al., 2010; Sobol’, 1967; Tang et al., 2007).”
- Exploring multi-dimensional spaces: a Comparison of Latin Hypercube and Quasi Monte Carlo Sampling Techniques (2015, background): “Sobol’ LDS aim to meet three main requirements [23]: 1.”
- Financial market models with Lévy processes and time-varying volatility. (2008, unknown): “Uniformly distributed random number is obtained by the Sobol’ method (Sobol (1967)).”
- Alternative sampling methods for estimating multivariate normal probabilities (2003, methodology): “These deterministic numbers, called quasi-Monte Carlo samples, were typically constructed using number theoretic methods (e.g., Korobov, 1959; Halton, 1960; Sobol, 1967).”
- Design of computer experiments: A review (2017, background): “In 1967, Sobol proposed a QRLD sequence to approximate high dimensional integrals [152].”
- Monte Carlo and Quasi-Monte Carlo Sampling (2009, methodology): “134 4.4.1 Sobol’ sequence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 138 4.4.2 Faure sequence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .”