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On average dimensions of particle transport estimators

Author

Listed:
  • Sobol Ilya M.

    (Keldysh Institute of Applied Mathematics, 4, Miusskaya sq., Moscow, 125047, Russia)

  • Shukhman Boris V.

    (1H-580 Place de la Fontaine, Montreal, QC, Canada)

Abstract

We considered average dimensions of the weighted Monte Carlo algorithm for a particle transport problem with multi-scattering setting and estimated the probability of particles penetration through a layer. The average dimension d^{\hat{d}} of the algorithm turned out to be small so that quasi-Monte Carlo estimates of the probability converge much faster than the Monte Carlo estimates. We justified the reasons to expect that the convergence of quasi-Monte Carlo estimates continue to be faster as the thickness of the layer increases. Here we calculated d^{\hat{d}} without the use of the ANOVA expansion.

Suggested Citation

  • Sobol Ilya M. & Shukhman Boris V., 2018. "On average dimensions of particle transport estimators," Monte Carlo Methods and Applications, De Gruyter, vol. 24(2), pages 147-151, June.
    • Handle: RePEc:bpj:mcmeap:v:24:y:2018:i:2:p:147-151:n:7
    DOI: 10.1515/mcma-2018-0013
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    References listed on IDEAS

    as
    1. Liu, Ruixue & Owen, Art B., 2006. "Estimating Mean Dimensionality of Analysis of Variance Decompositions," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 712-721, June.
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