Random number generation and Quasi-Monte Carlo methods

By H. Niederreiter. 1992

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Citations in the corpus

An evaluation of adaptive surrogate modeling based optimization with two benchmark problems (2014, methodology): “A QMC method can be viewed as a deterministic version of Monte Carlo method (Niederreiter, 1992).”
Strong orthogonal arrays of strength two plus (2018, methodology): “Inspired by (t,m, s)-nets from quasi-Monte Carlo [Niederreiter (1992)], He and Tang Received August 2016; revised February 2017.”
Improved Multilevel Monte Carlo Convergence using the Milstein Scheme (2008, methodology): “For these low dimensional levels it is reasonable to expect that quasi-Monte Carlo methods [KS05, Ecu04, Nie92 ] will be very much more eectiv e than the standard Monte Carlo methods used in this paper.”
Pricing and Hedging Spread Options (2003, methodology): “These methods have gained great popularity in the last few years, and the standard reference is Niederreiter [54].”
Sampling strategies and stopping criteria for stochastic dual dynamic programming: a case study in long-term hydrothermal scheduling (2011, unknown): “Two of the most popular families of methods are lattice rules and digital nets; we refer to [ 25 ] and [19] for comprehensive reviews.”
The Design and Analysis of Computer Experiments (2003, methodology): “The next method of estimating the S i and Ti sensitivity indices is Bayesian or empirical/plug-in Bayesian depending on whether unknown parameters are modeled hierarchically or estimated (see Oakley (2009), Moon (2010), Svenson (2011)).”
HESS Opinions "A random walk on water" (2009, unknown): “Specifically, it is easily shown (e.g., Metropolis and Ulam, 1949; Niederreiter, 1992) that for a number of dimensions d>4,15 a stochastic (Monte Carlo) integration method (in which the function evaluation points are taken at random) is more accurate (for the same total number of evaluation points)…”
Lattice Particle Filters (2001, methodology): “QMC over MC has been demonstrated in numerous applications [2, 12, 17]. As a special case of QMC methods we consider lattice rules here [13, 21]. By comparison to the Sobol and Niederreiter sequences [16] used in [18], lattice rules are easy to implement (only one parameter, the gen erator, is requi”
Expected Residual Minimization Method for Stochastic Variational Inequality Problems (2008, methodology): “Since an expectation function is generally difficult to evaluate exactly, we employ a quasi-Monte Carlo method for numerical integration [ 15 ]t o solve (5) in this section.”
Fast Numerical Methods for Stochastic Computations: A Review (2009, unknown): “[18, 54, 55]), to name a few.”
The inverse of the star-discrepancy depends linearly on the dimension (2001, background): “The classical Lp-star discrepancy is intimately related to the worst case error of multivariate integration for the Sobolev class of functions that are once differentiable in each variable with finite Lq-norm, 1/p+ 1/q = 1 (see Drmota and Tichy (1997), and Niederreiter (1992)).”