Abstract
Estimating the probability that a sum of random variables (RVs) exceeds a given threshold is a well-known challenging problem. A naive Monte Carlo simulation is the standard technique for the estimation of this type of probability. However, this approach is computationally expensive, especially when dealing with rare events. An alternative approach is represented by the use of variance reduction techniques, known for their efficiency in requiring less computations for achieving the same accuracy requirement. Most of these methods have thus far been proposed to deal with specific settings under which the RVs belong to particular classes of distributions. In this paper, we propose a generalization of the well-known hazard rate twisting Importance Sampling-based approach that presents the advantage of being logarithmic efficient for arbitrary sums of RVs. The wide scope of applicability of the proposed method is mainly due to our particular way of selecting the twisting parameter. It is worth observing that this interesting feature is rarely satisfied by variance reduction algorithms whose performances were only proven under some restrictive assumptions. It comes along with a good efficiency, illustrated by some selected simulation results comparing the performance of the proposed method with some existing techniques.
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The authors are members of the KAUST Strategic Research Initiative on Uncertainty Quantification in Science and Engineering (SRI-UQ).
Part of this work has been accepted at the IEEE International Conference on Communications (ICC’2015), London, UK, Jun. 2015, (Ben Rached et al. 2015a).
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Ben Rached, N., Benkhelifa, F., Kammoun, A. et al. On the generalization of the hazard rate twisting-based simulation approach. Stat Comput 28, 61–75 (2018). https://doi.org/10.1007/s11222-016-9716-4
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DOI: https://doi.org/10.1007/s11222-016-9716-4