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Probabilistic Bounded Relative Error Property for Learning Rare Event Simulation Techniques

Author

Listed:
  • Ad Ridder

    (VU University Amsterdam)

  • Bruno Tuffin

    (Inria Rennes Bretagne Atlantique)

Abstract

In: Proceedings Winter Simulation Conference , 9-12 December 2012, pages 387-398. In rare event simulation, we look for estimators such that the relative accuracy of the output is ''controlled'' when the rarity is getting more and more critical. Different robustness properties have been defined in the literature, that an estimator is expected to satisfy. Though, those properties are not adapted to estimators for which the estimators come from a parametric family and the optimal parameter is learned and random. For this reason, we motivate in this paper the need to define probabilistic robustness properties, because the accuracy of the resulting estimator is therefore random. We especially focus on the so-called probabilistic bounded relative error property. We additionally provide sufficient conditions, both in general and Markov settings, to satisfy such a property, illustrate them and simple but standard examples, and hope that it will foster discussions and new works in the area.

Suggested Citation

  • Ad Ridder & Bruno Tuffin, 2012. "Probabilistic Bounded Relative Error Property for Learning Rare Event Simulation Techniques," Tinbergen Institute Discussion Papers 12-103/III, Tinbergen Institute.
    • Handle: RePEc:tin:wpaper:20120103
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    File URL: https://papers.tinbergen.nl/12103.pdf
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    References listed on IDEAS

    as
    1. Perwez Shahabuddin, 1994. "Importance Sampling for the Simulation of Highly Reliable Markovian Systems," Management Science, INFORMS, vol. 40(3), pages 333-352, March.
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    3. Reuven Rubinstein, 1999. "The Cross-Entropy Method for Combinatorial and Continuous Optimization," Methodology and Computing in Applied Probability, Springer, vol. 1(2), pages 127-190, September.
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    More about this item

    Keywords

    Rare event probability; Importance sampling; Probabilistic robustness; Markov chains;
    All these keywords.

    JEL classification:

    • C6 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling

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