Journal Article

AdaPT

Lei, Lihua, Fithian, William

2018

Overview

We consider the problem of multiple-hypothesis testing with generic side information: for each hypothesis Hi we observe both a p-value pi and some predictor xi encoding contextual information about the hypothesis. For large-scale problems, adaptively focusing power on the more promising hypotheses (those more likely to yield discoveries) can lead to much more powerful multiple-testing procedures. We propose a general iterative framework for this problem, the adaptive p-value thresholding procedure which we call AdaPT, which adaptively estimates a Bayes optimal p-value rejection threshold and controls the false discovery rate in finite samples. At each iteration of the procedure, the analyst proposes a rejection threshold and observes partially censored p-values, estimates the false discovery proportion below the threshold and proposes another threshold, until the estimated false discovery proportion is below α. Our procedure is adaptive in an unusually strong sense, permitting the analyst to use any statistical or machine learning method she chooses to estimate the optimal threshold, and to switch between different models at each iteration as information accrues. We demonstrate the favourable performance of AdaPT by comparing it with state of the art methods in five real applications and two simulation studies.

• Publisher: Wiley,Oxford University Press
• Subject: Adaptive inference / artificial intelligence / Bayesian analysis / Computer simulation / Contextual information / Discovery / Encoding / equations / False discovery rate / Grammatical aspect / Hypotheses / Hypothesis testing / Information / Iterative methods / Machine learning / Martingales / Multiple testing / Power / p‐value weighting / Regression analysis / Rejection / Selective inference / Simulation / Statistical analysis / Statistical methods / Statistics / Test procedures / Thresholds