Consider a set of multivariate distributions, $F_1,\dots,F_M$, aiming to explain the same phenomenon. For instance, each $F_m$ may correspond to a different candidate background model for calibration data, or to one of many possible signal models we aim to validate on experimental data. In this article, we show that tests for a wide class of apparently different models $F_{m}$ can be mapped into a single test for a reference distribution $Q$. As a result, valid inference for each $F_m$ can be obtained by simulating \underline{only} the distribution of the test statistic under $Q$. Furthermore, $Q$ can be chosen conveniently simple to substantially reduce the computational time.
翻译:考虑一组多变量分布, $F_ 1,\ dots, F_ M$, 目的是解释同样的现象。 例如, 每1 $F_ m$可能对应不同的校准数据候选背景模型, 或者我们旨在验证实验数据的许多可能的信号模型之一 。 在本篇文章中, 我们显示, 对一大类明显不同的模型的测试可以绘制成一个参考分布的单一测试 Q 美元 。 因此, 每1 $F_ m$ 的有效推论可以通过模拟\ underline 来获得 $ 的测试统计数据在 $ 下的分布。 此外, $ Q 也可以简单选择, 以大幅缩短计算时间 。