Quasi-Random Sequences and Their Discrepancies

By W. Morokoff, Russel E. Caflisch. 1994

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Citations in the corpus

On the Equivalence between Herding and Conditional Gradient Algorithms (2012, methodology): “The links between the ﬁrst two were clearly outlined by Chen et al. (2010), while the present paper provides the novel interpretation of herding as a well-established convex optimization algorithm.”
On the Equivalence between Kernel Quadrature Rules and Random Feature Expansions (2015, methodology): “Quasi Monte-carlo methods employ a sequence of points with low discrepancy with uniform weights (Morokoff and Caﬂisch, 1994), leading to approximation errors of O (1 /n ) for univariate functions with bounded variation, but typically with no adaptation to smoother functions.”
Hybrid Deterministic-Stochastic Methods for Data Fitting (2011, neutral): “Although we have analyzed an arbitrary strategy for selecting the elements of the sample, and shown that uniform sampling achieves a better bound in expectation, it is possible that a quasi-random selection of the individual gradients might further reﬁne the bound [22].”
Tractability of Multivariate Problems (2008, background): “This type of L2 discrepancy was introduced by Morokoff and Caflisch [192].”
Monte Carlo and quasi-Monte Carlo methods (1998, background): “We have observed patterns of this sort in a variety of quasi-random sequences (Morokoff and Caflisch 1994), but they are not expected to occur in the randomized quasi-random points of Owen (1995, 1997).”
Applications of randomized low discrepancy sequences to the valuation of complex securities (2000, background): “sequences and Moroko! and Ca#isch (1994) examined this phenomenon in various types of low discrepancy sequences.”
Monte Carlo and Quasi-Monte Carlo Sampling (2009, methodology): “, [306], but the unanchored version is more recent and was proposed by Morokoff and Caflisch in [300].”
MONTE CARLO METHODS IN GEOPHYSICAL INVERSE PROBLEMS (2002, methodology): “5) and are finding increasing numbers of applications in multidimensional numerical integration [Morokoff and Caflisch, 1994].”
Quasi-Random Sampling for Condensation (2000, background): “Several of these have been compared as to their discrepancy and their suitability for high-dimensional Monte Carlo calculations [14, 15 ].”
On the use of a Modified Latin Hypercube Sampling (MLHS) method in the estimation of a Mixed Logit Model for vehicle choice (2006, unknown): “The Shuffled Halton sequence was introduced by Morokoff and Caflisch (1994).”
Constructing Sobol Sequences with Better Two-Dimensional Projections (2008, background): “This issue was raised by Morokoff and Caflisch [13].”
On the Equivalence between Quadrature Rules and Random Features (2015, methodology): “Quasi Monte-carlo methods employ a sequence of points with low discrepancy with uniform weights (Morokoﬀ and Caﬂisch, 1994), leading to approximation errors of O (1 /n ) for univariate functions with bounded variation, but typically with no adaptation to smoother functions.”
Low discrepancy sequences in high dimensions: How well are their projections distributed? (2008, background): “Computational investigations of the classical discrepancy confirmed the superiority of low discrepancy point sets over random point sets only in low dimensions (say s ≤ 12), but failed to demonstrate any superiority in high dimensions (see [13]).”
Valuing American Options by Simulation: A Simple Least-Squares Approach (2001, methodology): “Important recent examples of the application of quasi-Monte-Carlo techniques include Morokoff and Caflisch (1994, 1995) .”