skip to main content
10.5555/2693848.2693924acmconferencesArticle/Chapter ViewAbstractPublication PageswscConference Proceedingsconference-collections
research-article

Uniformly efficient simulation for tail probabilities of gaussian random fields

Published: 07 December 2014 Publication History

Abstract

In this paper, we consider rare-event simulation of the tail probabilities of Gaussian random fields. In particular, we design importance sampling estimators that are uniformly efficient for a family of Gaussian random fields with different mean and variance functions.

References

[1]
Adler, R., J. Blanchet, and J. Liu. 2008, December. "Efficient Simulation for Tial Probabilities of Gaussian Random Fields". In Proceedings of the 2008 Winter Simulation Conference, edited by S. J. Mason, R. R. Hill, L. Moench, O. Rose, T. Jefferson, and J. W. Fowler, 328--336. Piscataway, New Jersey: Institute of Electrical and Electronics Engineers, Inc.
[2]
Adler, R., J. Blanchet, and J. Liu. 2012. "Efficient Monte Carlo for Large Excursions of Gaussian Random Fields". Annals of Applied Probability 22 (3): 1167--1214.
[3]
Adler, R., and J. Taylor. 2007. Random fields and geometry. Springer.
[4]
Adler, R. J., P. Müller, and B. L. Rozovskii. 1996. Stochastic modelling in physical oceanography. Springer.
[5]
Adler, R. J., J. E. Taylor, and K. J. Worsley. 2010. Applications of random fields and geometry: Foundations and case studies. Available at http://webee.technion.ac.il/people/adler/hrf.pdf.
[6]
Asmussen, S., and P. Glynn. 2007. Stochastic Simulation: Algorithms and Analysis. New York, NY, USA: Springer.
[7]
Azais, J. M., and M. Wschebor. 2008. "A general expression for the distribution of the maximum of a Gaussian field and the approximation of the tail". Stochastic Processes and Their Applications 118 (7): 1190--1218.
[8]
Azaïs, J.-M., and M. Wschebor. 2009. Level sets and extrema of random processes and fields. John Wiley & Sons.
[9]
Bogachev, V. 1998. Gaussian Measures. Mathematical Surveys and Monographs Volume 62. American Mathematical Society.
[10]
Borell, C. 1975. "The Brunn-Minkowski inequality in Gauss space". Inventiones Mathematicae 30 (2): 207--216.
[11]
Ehrhard, A. 1983. "Symétrisation dans l'space de Gauss". Math. Scand. 53:281--301.
[12]
Glasserman, P., and S. Juneja. 2008. "Uniformly efficient importance sampling for the tail distribution of sums of random variables". Mathematics of Operations Research 33 (1): 36--50.
[13]
Li, X., and J. Liu. 2013. "Rare-event Simulation and Efficient Discretization for the Supremum of Gaussian Random Fields". Technical Report (arXiv:1309.7365).
[14]
Liu, J. 2012. "Tail Approximations of Integrals of Gaussian Random Fields". Annals of Probability 40 (3): 1069--1104.
[15]
Liu, J., and G. Xu. 2012a. "Rare-event simulations for exponential integrals of smooth Gaussian processes". In Proceedings of the Winter Simulation Conference. Winter Simulation Conference.
[16]
Liu, J., and G. Xu. 2012b. "Some Asymptotic Results of Gaussian Random Fields with Varying Mean Functions and the Associated Processes". Annals of Statistics 40:262--293.
[17]
Liu, J., and G. Xu. 2013. "On the Conditional Distributions and the Efficient Simulations of Exponential Integrals of Gaussian Random Fields". Annals of Applied Probability to appear. Available at http://arxiv.org/abs/1204.5546.
[18]
Liu, J., and G. Xu. 2014. "Efficient Simulations for the Exponential Integrals of Hölder Continuous Gaussian Random Fields". The ACM Transactions on Modeling and Computer Simulation 24:9:1--9:24.
[19]
Piterbarg, V. I. 1996. Asymptotic methods in the theory of Gaussian processes and fields. Providence, R. I.: American Mathematical Society.
[20]
Sun, J. Y. 1993. "Tail probabilities of the maxima of gaussian random-fields". Annals of Probability 21 (1): 34--71.
[21]
Tsirelson, B., I. Ibragimov, and V. Sudakov. 1976. "Norms of Gaussian sample functions". Proceedings of the Third Japan-USSR Symposium on Probability Theory (Tashkent, 1975) 550:20--41.
  1. Uniformly efficient simulation for tail probabilities of gaussian random fields

    Recommendations

    Comments

    Information & Contributors

    Information

    Published In

    cover image ACM Conferences
    WSC '14: Proceedings of the 2014 Winter Simulation Conference
    December 2014
    4032 pages

    Sponsors

    Publisher

    IEEE Press

    Publication History

    Published: 07 December 2014

    Check for updates

    Qualifiers

    • Research-article

    Conference

    WSC '14
    Sponsor:
    WSC '14: Winter Simulation Conference
    December 7 - 10, 2014
    Georgia, Savannah

    Acceptance Rates

    WSC '14 Paper Acceptance Rate 205 of 320 submissions, 64%;
    Overall Acceptance Rate 3,413 of 5,075 submissions, 67%

    Contributors

    Other Metrics

    Bibliometrics & Citations

    Bibliometrics

    Article Metrics

    • 0
      Total Citations
    • 34
      Total Downloads
    • Downloads (Last 12 months)0
    • Downloads (Last 6 weeks)0
    Reflects downloads up to 03 Jan 2025

    Other Metrics

    Citations

    View Options

    Login options

    View options

    PDF

    View or Download as a PDF file.

    PDF

    eReader

    View online with eReader.

    eReader

    Media

    Figures

    Other

    Tables

    Share

    Share

    Share this Publication link

    Share on social media