Review of Post‐Clustering Inference Methods

Abstract In a classical testing problem, statistical hypotheses are defined before observing the data. However, this principle is violated when hypotheses are based on a clustering of the observations, leading to an inflation of the type I error rate. Recently, post‐clustering inference methods have been proposed to address this particular type of data‐driven hypothesis selection. These methods are divided into two categories: information partitioning and conditional approaches. This article provides a review of these methods and a numerical comparison on simulated Gaussian data. This contribution sheds some light on the pros and cons of each approach in terms of (i) type I error control and power, (ii) potential dependence on a specific clustering method, and (iii) assumptions on data distribution.