Computational investigations of low-discrepancy sequences

By L. Kocis, William J. Whiten. 1997

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Design of computer experiments: A review (2017, methodology): “To address these issues with Halton sequence, researchers like Braaten and Weller [17], Hellekalek [77], Faure [55], Krommer and Ueberhuber [98], and Kocis and Whiten [95] proposed several variations and modifications of them.”
On the use of a Modified Latin Hypercube Sampling (MLHS) method in the estimation of a Mixed Logit Model for vehicle choice (2006, methodology): “Different methods for producing the permutations have been proposed; the most commonly used method was proposed by Braaten and Weller (1979), other approaches are given by Hellekalek (1984), Kocis and Whiten (1997) and Tuffin (1998).”
Good permutations for deterministic scrambled Halton sequences in terms of L2-discrepancy (2006, result): “Similar investigations for different sequences and using test-integrals instead of L2-discrepancy were done in [7].”
Control Functionals for Quasi-Monte Carlo Integration (2015, methodology): “In the first experiment, the random QMC point set vM+1:N was generated by truncating the Halton sequence, scrambling the digits of the resulting points using the reverse-radix algorithm [16] and applying a uniform random shift.”
Building Efficient Response Surfaces of Aerodynamic Functions with Kriging and Cokriging (2008, methodology): “Quasi-random sequences enable methods such as generalized Halton or Sobol [23] to give ordered space filling sampling.”
Quasi-random maximum simulated likelihood estimation of the mixed multinomial logit model (2001, methodology): “The generation and application of QMC sequences for multi-dimensional integration has been the subject of intensive research in recent years in mathematics and physics (see, for example, Sloan and Wozniakowski, 1998; Owen, 1998; Mullen et al., 1995; Kocis and Whiten, 1997).”
Advances of the probability density evolution method for nonlinear stochastic systems (2012, background): “The properties of several low discrepancy sequences such as the irrational number sequence [41], Halton sequence [42], Hammersley sequence [43] and Sobol sequence [44] in high dimension were studied.”
Using Supervised Learning to Improve Monte Carlo Integral Estimation (2011, methodology): “Two such methods are the scrambled Halton sequence [11] and the Sobol sequence [12].”
A multi-level cross-classified model for discrete response variables (2000, methodology): “…Carlo simulation methods for multi-dimensional integration has been receiving substantial attention in recent years with increasingly sophisticated quasirandom sequences being proposed (see, for example, Sloan and Wozniakowski, 1998; Owen, 1998; Mullen et al., 1995; Kocis and Whiten, 1997).”
Monte Carlo and Quasi-Monte Carlo Sampling (2009, background): “An approach that has been studied by several researchers to try to improve its properties is to permute the digits al(i) in each dimension before applying the radical-inverse function [16, 17, 38, 56, 105, 107, 201, 283, 411, 414].”
Simulation estimation of mixed discrete choice models using randomized and scrambled Halton sequences (2003, background): “Different researchers (see Braaten and Weller, 1979; Hellekalek, 1984; Kocis and Whiten, 1997) have suggested different algorithms for arriving at the permutations of the coefficients in Equation (4).”