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Changepoint detection methods are used in many areas of science andengineering, e.g., in the analysis of copy number variation data, to detectabnormalities in copy numbers along the genome. Despite the broad array ofavailable tools, methodology for quantifying our uncertainty in the strength(or presence) of given changepoints, post-detection, are lacking.Post-selection inference offers a framework to fill this gap, but the moststraightforward application of these methods results in low-powered tests andleaves open several important questions about practical usability. In thiswork, we carefully tailor post-selection inference methods towards changepointdetection, focusing as our main scientific application on copy number variationdata. As for changepoint algorithms, we study binary segmentation, and two ofits most popular variants, wild and circular, and the fused lasso. We implementsome of the latest developments in post-selection inference theory: we useauxiliary randomization to improve power, which requires implementations ofMCMC algorithms (importance sampling and hit-and-run sampling) to carry out ourtests. We also provide recommendations for improving practical useability,detailed simulations, and an example analysis on array comparative genomichybridization (CGH) data.

Post-Selection Inference for Changepoint Detection Algorithms with Application to Copy Number Variation Data