In this paper we propose a computationally efficient multiple hypothesis testing procedure for persistent homology. The computational efficiency of our procedure is based on the observation that one can empirically simulate a null distribution that is universal across many hypothesis testing applications involving persistence homology. Our observation suggests that one can simulate the null distribution efficiently based on a small number of summaries of the collected data and use this null in the same way that p-value tables were used in classical statistics. To illustrate the efficiency and utility of the null distribution we provide procedures for rejecting acyclicity with both control of the Family-Wise Error Rate (FWER) and the False Discovery Rate (FDR). We will argue that the empirical null we propose is very general conditional on a few summaries of the data based on simulations and limit theorems for persistent homology for point processes.

翻译：在本文中,我们建议对持久性同系物进行计算效率高的多重假设测试程序。我们程序的计算效率是基于以下观察,即人们可以实验性地模拟在涉及持久性同系物的许多假设测试应用中普遍存在的无效分布。我们的观察表明,我们可以根据少量收集的数据摘要来模拟无效分布,并以古典统计数据中使用的P价值表同样的方式使用这一无效分布。为了说明无效分布的效率和效用,我们为拒绝周期性提供了程序,同时控制了家庭错误率(FWER)和假发现率(FDR)。我们将争辩说,我们提议的经验无效分布非常笼统,条件是根据模拟和限制点处理的持久性同系物理学理论,对数据作一些摘要。