Sequential Multiple Hypothesis Testing with Type I Error Control
Alan Malek, Sumeet Katariya, Yinlam Chow, Mohammad Ghavamzadeh
Abstract
This work studies multiple hypothesis testing in the setting when we obtain data sequentially and may choose when to stop sampling. We summarize the notion of a sequential p-value (one that can be continually updated and still maintain a type I error guarantee) and provide several examples from the literature. This tool allows us to convert step-up or step-down multiple hypothesis testing procedures in the fixed-horizon setting (which includes Benjamini-Hochberg, Holm, and Bonferroni) into sequential versions that allow the statistician to reject a hypothesis as soon as the sequential p-value reaches a threshold. We show that if the original procedure has a type I error guarantee in a certain family (including FDR and FWER), then the sequential conversion inherits an analogous guarantee. The conversion also allows for allocating samples in a data-dependent way, and we provide simulated experiments demonstrating an increased number of rejections when compared to the fixed-horizon setting.
BibTeX
@InProceedings{pmlr-v54-malek17a,
title = {{Sequential Multiple Hypothesis Testing with Type I Error Control}},
author = {Malek, Alan and Katariya, Sumeet and Chow, Yinlam and Ghavamzadeh, Mohammad},
booktitle = {Proceedings of the 20th International Conference on Artificial Intelligence and Statistics},
pages = {1468--1476},
year = {2017},
editor = {Singh, Aarti and Zhu, Jerry},
volume = {54},
series = {Proceedings of Machine Learning Research},
month = {20--22 Apr},
publisher = {PMLR},
pdf = {http://proceedings.mlr.press/v54/malek17a/malek17a.pdf},
url = {https://proceedings.mlr.press/v54/malek17a.html},
abstract = {This work studies multiple hypothesis testing in the setting when we obtain data sequentially and may choose when to stop sampling. We summarize the notion of a sequential p-value (one that can be continually updated and still maintain a type I error guarantee) and provide several examples from the literature. This tool allows us to convert step-up or step-down multiple hypothesis testing procedures in the fixed-horizon setting (which includes Benjamini-Hochberg, Holm, and Bonferroni) into sequential versions that allow the statistician to reject a hypothesis as soon as the sequential p-value reaches a threshold. We show that if the original procedure has a type I error guarantee in a certain family (including FDR and FWER), then the sequential conversion inherits an analogous guarantee. The conversion also allows for allocating samples in a data-dependent way, and we provide simulated experiments demonstrating an increased number of rejections when compared to the fixed-horizon setting.}
}