We consider a statistical test whose p value can only be approximated using Monte Carlo simulations. We are interested in deciding whether the p value for an observed data set lies above or below a given threshold such as 5%. We want to ensure that the resampling risk, the probability of the (Monte Carlo) decision being different from the true decision, is uniformly bounded. This article introduces a simple open-ended method with this property, the confidence sequence method (CSM). We compare our approach to another algorithm, SIMCTEST, which also guarantees an (asymptotic) uniform bound on the resampling risk, as well as to other Monte Carlo procedures without a uniform bound. CSM is free of tuning parameters and conservative. It has the same theoretical guarantee as SIMCTEST and, in many settings, similar stopping boundaries. As it is much simpler than other methods, CSM is a useful method for practical applications.

中文翻译：

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一种实现蒙特卡洛测试的简单方法

我们考虑一个统计检验，其p值只能使用蒙特卡洛模拟来近似。我们感兴趣的是决定是否对p观察到的数据集的值高于或低于给定阈值（例如5％）。我们要确保重采样风险（Monte Carlo决策与真实决策不同）的界限是一致的。本文介绍了一种具有此属性的简单开放式方法，即置信序列方法（CSM）。我们将我们的方法与另一种算法SIMCTEST进行了比较，SIMCTEST还确保了重采样风险的（渐近）统一边界，以及没有统一边界的其他Monte Carlo过程。CSM没有调整参数，而且很保守。它具有与SIMCTEST相同的理论保证，并且在许多情况下具有相似的停止边界。因为它比其他方法简单得多，所以CSM是实际应用中的有用方法。