Abstract:
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There is a recent body of literature on methods for valid post-selection inference on model quantities after having applied adaptive algorithms to recover that model. In this paper, we present the application of post-selection inference tools developed in Lee et al (2016), Tibshirani et al (2016), and Fithian et al (2014) for segmentation-type algorithms for detecting changepoints from data. 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 tests types -- targeted tests of user-defined model quantities and model goodness of fit tests -- and numerical experimentation on real and synthetic data to compare against comparable fused lasso inference tools developed in Hyun et al (2016). In particular, a careful application of the tools to DNA copy number variation (CNV) data is presented to demonstrate the usefulness in a scientific application.
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