Post-Selection Inference for Changepoint Problems

• Activity Number: 412 - Theory and Methods for Change-Point and Abnormality Detection
• Type: Contributed
• Date/Time: Tuesday, July 31, 2018 : 2:00 PM to 3:50 PM
• Sponsor: IMS
• Author(s): Sangwon Hyun* and Kevin Lin and Max G'Sell and Ryan Tibshirani
• Companies: Carnegie Mellon University and Carnegie Mellon University and Carnegie Mellon University and Carnegie Mellon University
• Keywords: Changepoint detection; Post-selection inference; Hypothesis testing; Copy Number Variation

Abstract

There is a recent body of literature on methods for finite-sample valid post-selection inference after having applied adaptive algorithms to the same data. In this paper, we present the post-selection inference methodology for segmentation-type algorithms for detecting changepoints. The algorithms discussed include standard/circular/wild binary segmentation and scan statistics. The main contributions of this work include characterizing polyhedral selection events of segmentation algorithms, specifying several types of null hypotheses and tests, and incorporating randomization for power boosts. We outline the MCMC sampling procedure, and show various numerical experimentation on real and synthetic data to demonstrate performance. Application of the tools to DNA copy number variation (CNV) data is presented to demonstrate the usefulness in a scientific problem.