Let X be a random vector with distribution μ on ℝ d and Φ be a mapping from ℝ d to ℝ. That mapping acts as a black box, e.g., the result from some computer experiments for which no analytical expression is available. This paper presents an efficient algorithm to estimate a tail probability given a quantile or a quantile given a tail probability. The algorithm improves upon existing multilevel splitting methods and can be analyzed using Poisson process tools that lead to exact description of the distribution of the estimated probabilities and quantiles. The performance of the algorithm is demonstrated in a problem related to digital watermarking.
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机译：令X为一个随机向量，在ℝ d 上具有μ分布，Φ为从ℝ d 到ℝ的映射。该映射充当黑匣子，例如，一些计算机实验的结果，这些分析没有可用的分析表达式。本文提出了一种有效的算法来估计给定分位数的分位数或给定分位数的分位数的分位数。该算法对现有的多级拆分方法进行了改进，可以使用泊松过程工具进行分析，从而可以精确描述估计的概率和分位数的分布。在与数字水印有关的问题中证明了该算法的性能。
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