  Changepoint detection methods are used in many areas of science and
engineering, e.g., in the analysis of copy number variation data, to detect
abnormalities in copy numbers along the genome. Despite the broad array of
available 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 most
straightforward application of these methods results in low-powered tests and
leaves open several important questions about practical usability. In this
work, we carefully tailor post-selection inference methods towards changepoint
detection, focusing as our main scientific application on copy number variation
data. As for changepoint algorithms, we study binary segmentation, and two of
its most popular variants, wild and circular, and the fused lasso. We implement
some of the latest developments in post-selection inference theory: we use
auxiliary randomization to improve power, which requires implementations of
MCMC algorithms (importance sampling and hit-and-run sampling) to carry out our
tests. We also provide recommendations for improving practical useability,
detailed simulations, and an example analysis on array comparative genomic
hybridization (CGH) data.
