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.

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  1. Clément, François; Doerr, Carola; Paquete, Luís: Star discrepancy subset selection: problem formulation and efficient approaches for low dimensions (2022)
  2. Ben Abdellah, Amal; L’Ecuyer, Pierre; Owen, Art B.; Puchhammer, Florian: Density estimation by randomized quasi-Monte Carlo (2021)
  3. Coeurjolly, Jean-François; Mazoyer, Adrien; Amblard, Pierre-Olivier: Monte Carlo integration of non-differentiable functions on ([0,1]^\iota), (\iota=1,\ldots, d), using a single determinantal point pattern defined on ([0,1]^d) (2021)
  4. Dell’Accio, Francesco; Di Tommaso, Filomena; Siar, Najoua: On the numerical computation of bivariate Lagrange polynomials (2021)
  5. Giani, Stefano; Hakula, Harri: On effects of perforated domains on parameter-dependent free vibration (2021)
  6. Guo, Liang; Liu, Jianya; Lu, Ruodan: Subsampling bias and the best-discrepancy systematic cross validation (2021)
  7. Liu, Jianxu; Sriboonchitta, Songsak; Wiboonpongse, Aree; Denœux, Thierry: A trivariate Gaussian copula stochastic frontier model with sample selection (2021)
  8. Marcotte, Denis; Dutaut, Raphaël: Linking Gy’s formula to QA/QC duplicates statistics (2021)
  9. Hoyt, Christopher R.; Owen, Art B.: Mean dimension of ridge functions (2020)
  10. Sipin, Alexander S.: A randomized quasi-Monte Carlo algorithms for some boundary value problems (2020)
  11. Hariri-Ardebili, Mohammad A.; Pourkamali-Anaraki, F.: Matrix completion for cost reduction in finite element simulations under hybrid uncertainties (2019)
  12. Keller, Alexander; Dahm, Ken: Integral equations and machine learning (2019)
  13. Pal, Shanoli Samui; Kar, Samarjit: Fuzzy time series model for unequal interval length using genetic algorithm (2019)
  14. Poëtte, Gaël: A gPC-intrusive Monte-Carlo scheme for the resolution of the uncertain linear Boltzmann equation (2019)
  15. Sobol, I. M.; Shukhman, B. V.: Quasi-Monte Carlo method for solving Fredholm equations (2019)
  16. 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)
  17. Art B. Owen: A randomized Halton algorithm in R (2017) arXiv
  18. Dellnitz, Michael; Klus, Stefan; Ziessler, Adrian: A set-oriented numerical approach for dynamical systems with parameter uncertainty (2017)
  19. 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)
  20. Kanjanatarakul, Orakanya; Denœux, Thierry; Sriboonchitta, Songsak: Prediction of future observations using belief functions: a likelihood-based approach (2016)

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