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

## TL;DR

This paper develops tailored post-selection inference methods for changepoint detection algorithms, especially in copy number variation data, enhancing uncertainty quantification and practical usability.

## Contribution

It adapts post-selection inference techniques for specific changepoint algorithms, incorporating randomization and MCMC methods to improve test power and usability.

## Key findings

- Improved power in post-selection tests using auxiliary randomization.
- Effective application of methods to copy number variation data.
- Guidelines for practical implementation and analysis.

## Abstract

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.