rhalton

A randomized Halton algorithm in R. Randomized quasi-Monte Carlo (RQMC) sampling can bring orders of magnitude reduction in variance compared to plain Monte Carlo (MC) sampling. The extent of the efficiency gain varies from problem to problem and can be hard to predict. This article presents an R function rhalton that produces scrambled versions of Halton sequences. On some problems it brings efficiency gains of several thousand fold. On other problems, the efficiency gain is minor. The code is designed to make it easy to determine whether a given integrand will benefit from RQMC sampling. An RQMC sample of n points in [0,1]d can be extended later to a larger n and/or d.


References in zbMATH (referenced in 22 articles )

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  1. Pal, Shanoli Samui; Kar, Samarjit: Fuzzy time series model for unequal interval length using genetic algorithm (2019)
  2. Sobol, I. M.; Shukhman, B. V.: Quasi-Monte Carlo method for solving Fredholm equations (2019)
  3. Kailkhura, Bhavya; Thiagarajan, Jayaraman J.; Rastogi, Charvi; Varshney, Pramod K.; Bremer, Peer-Timo: A spectral approach for the design of experiments: design, analysis and algorithms (2018)
  4. Art B. Owen: A randomized Halton algorithm in R (2017) arXiv
  5. Dellnitz, Michael; Klus, Stefan; Ziessler, Adrian: A set-oriented numerical approach for dynamical systems with parameter uncertainty (2017)
  6. Hinrichs, Aicke; Markhasin, Lev; Oettershagen, Jens; Ullrich, Tino: Optimal quasi-Monte Carlo rules on order 2 digital nets for the numerical integration of multivariate periodic functions (2016)
  7. Kanjanatarakul, Orakanya; Denœux, Thierry; Sriboonchitta, Songsak: Prediction of future observations using belief functions: a likelihood-based approach (2016)
  8. Palar, Pramudita Satria; Tsuchiya, Takeshi; Parks, Geoffrey Thomas: Multi-fidelity non-intrusive polynomial chaos based on regression (2016)
  9. Peri, Daniele: Sequential quadrature methods for RDO (2016)
  10. Simmons, David; Solomon, Yaar: A Danzer set for axis parallel boxes (2016)
  11. Bouhamidi, A.; Hached, M.; Jbilou, K.: A meshless RBF method for computing a numerical solution of unsteady Burgers’-type equations (2014)
  12. Mollon, Guilhem; Zhao, Jidong: 3D generation of realistic granular samples based on random fields theory and Fourier shape descriptors (2014)
  13. Talke, Ismael S.; Borkowski, John J.: Generation of space-filling uniform designs in unit hypercubes (2012)
  14. Schlier, Christoph: On scrambled Halton sequences (2008)
  15. Sen, S. K.; Agarwal, Ravi P.; Shaykhian, Gholam Ali: Golden ratio versus pi as random sequence sources for Monte Carlo integration (2008)
  16. Schlier, Ch.: Error trends in quasi-Monte Carlo integration (2004)
  17. Rote, G.; Tichy, R. F.: Quasi-Monte-Carlo methods and the dispersion of point sequences (1996)
  18. Halton, John H.: Sequential Monto Carlo techniques for the solution of linear systems (1994)
  19. Kolář, Miroslav; O’Shea, Seamus F.: Fast, portable, and reliable algorithm for the calculation of Halton numbers (1993)
  20. Berblinger, Michael; Schlier, Christoph: Monte Carlo integration with quasi-random numbers: Some experience (1991)

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