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. Hoyt, Christopher R.; Owen, Art B.: Mean dimension of ridge functions (2020)
  2. Hariri-Ardebili, Mohammad A.; Pourkamali-Anaraki, F.: Matrix completion for cost reduction in finite element simulations under hybrid uncertainties (2019)
  3. Pal, Shanoli Samui; Kar, Samarjit: Fuzzy time series model for unequal interval length using genetic algorithm (2019)
  4. Sobol, I. M.; Shukhman, B. V.: Quasi-Monte Carlo method for solving Fredholm equations (2019)
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  6. Art B. Owen: A randomized Halton algorithm in R (2017) arXiv
  7. Dellnitz, Michael; Klus, Stefan; Ziessler, Adrian: A set-oriented numerical approach for dynamical systems with parameter uncertainty (2017)
  8. 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)
  9. Kanjanatarakul, Orakanya; Denœux, Thierry; Sriboonchitta, Songsak: Prediction of future observations using belief functions: a likelihood-based approach (2016)
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