Article ID: | iaor20119377 |
Volume: | 189 |
Issue: | 1 |
Start Page Number: | 43 |
End Page Number: | 61 |
Publication Date: | Sep 2011 |
Journal: | Annals of Operations Research |
Authors: | Chan C, Kroese P |
Estimation of rare‐event probabilities in high‐dimensional settings via importance sampling is a difficult problem due to the degeneracy of the likelihood ratio. In fact, it is generally recommended that Monte Carlo estimators involving likelihood ratios should not be used in such settings. In view of this, we develop efficient algorithms based on conditional Monte Carlo to estimate rare‐event probabilities in situations where the degeneracy problem is expected to be severe. By utilizing an asymptotic description of how the rare event occurs, we derive algorithms that involve generating random variables only from the nominal distributions, thus avoiding any likelihood ratio. We consider two settings that occur frequently in applied probability: systems involving bottleneck elements and models involving heavy‐tailed random variables. We first consider the problem of estimating ℙ(