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A new proof of geometric convergence for the adaptive generalized weighted analog sampling (GWAS) method

Author

Listed:
  • Kong Rong

    (Hyundai Capital America, 3161 Michelson Drive, Suite 1900, Irvine, CA 92612, United States of America)

  • Spanier Jerome

    (Beckman Laser Institute and Medical Clinic, 1002 Health Science Road E., University of California, Irvine, California 92612, United States of America)

Abstract

Generalized Weighted Analog Sampling is a variance-reducing method for solving radiative transport problems that makes use of a biased (though asymptotically unbiased) estimator. The introduction of bias provides a mechanism for combining the best features of unbiased estimators while avoiding their limitations. In this paper we present a new proof that adaptive GWAS estimation based on combining the variance-reducing power of importance sampling with the sampling simplicity of correlated sampling yields geometrically convergent estimates of radiative transport solutions. The new proof establishes a stronger and more general theory of geometric convergence for GWAS.

Suggested Citation

  • Kong Rong & Spanier Jerome, 2016. "A new proof of geometric convergence for the adaptive generalized weighted analog sampling (GWAS) method," Monte Carlo Methods and Applications, De Gruyter, vol. 22(3), pages 161-196, September.
    • Handle: RePEc:bpj:mcmeap:v:22:y:2016:i:3:p:161-196:n:2
    DOI: 10.1515/mcma-2016-0110
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