We introduce a new technique (i.e. \emph{sharding}) of breaking up random variables into many independent random variables that behaves together as the original single random variable. This in turn enables us to model the random variables using a Poisson distribution (i.e. \emph{Poissonization}). These two ideas, leads to an improved analysis of the Prophet Secretary problem and its variants. Beyond the (small but significant) improvement in the constants, the new analysis is significantly simpler and more intuitive than previous (quite involved) analysis. We also get several simpler proofs of existing known results. The new approach might be of independent interest to the order-selection variant of the prophet inequality.

翻译：我们引入了一种新技术（即*分片*），将随机变量拆分为多个独立的随机变量，这些变量共同作用时与原单一随机变量行为一致。这进而使我们能够使用泊松分布（即*泊松化*）对随机变量进行建模。这两个思想改进了对先知秘书问题及其变体的分析。除了（微小但重要的）常数改进外，新分析比以往（相当复杂的）分析更简单直观。我们还得到了若干已知结果的更简洁证明。这种新方法可能对先知不等式中的顺序选择变体具有独立的研究价值。