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首页> 外文期刊>Fuzzy sets and systems >A Monte Carlo-based Method For The Estimation Of Lower And Upper Probabilities Of Events Using Infinite Random Sets Of Indexable Type
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A Monte Carlo-based Method For The Estimation Of Lower And Upper Probabilities Of Events Using Infinite Random Sets Of Indexable Type

机译：基于可指数类型的无限随机集的基于蒙特卡洛方法的事件上下概率估计方法

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摘要

Random set theory is a useful tool to quantify lower and upper bounds on the probability of the occurrence of events given uncertain information represented for example by possibility distributions, probability boxes, or Dempster-Shafer structures, among others. In this paper it is shown that the belief and plausibility estimated by Dempster-Shafer evidence theory are basically approximations by Riemann-Stieltjes sums of the integrals of the lower and upper probability employed when using infinite random sets of indexable type. In addition, it is shown that the evaluation of the lower and upper probability is more efficient if it is done by pseudo-Monte Carlo strategies. This discourages the use of Dempster-Shafer evidence theory and suggests the use of infinite random sets of indexable type specially in high dimensions, not only because the initial discretization step of the basic variables is not required anymore, but also because the evaluation of the lower and upper probability of events is much more efficient using the different techniques for multidimensional integration like Monte Carlo simulation.
机译：随机集理论是一种有用的工具，可用于量化给定不确定信息（例如，可能性分布，概率框或Dempster-Shafer结构等）表示的事件发生概率的上下限。本文表明，由Dempster-Shafer证据理论估计的置信度和合理性基本上是Riemann-Stieltjes对使用可分度类型的无限随机集使用的上下概率积分求和的近似值。另外，还表明，如果通过伪蒙特卡洛策略进行评估，则较低和较高概率的评估将更为有效。这不鼓励使用Dempster-Shafer证据理论，并建议特别在高维中使用无限随机可索引类型集，这不仅是因为不再需要基本变量的初始离散化步骤，而且还因为对较低变量的求值使用不同的多维积分技术（例如蒙特卡洛模拟），事件的高概率要高效得多。

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