A0828
Title: Improving power by conditioning on less in post-selection inference for changepoints
Authors: Rachel Carrington - University of Bath (United Kingdom) [presenting]
Paul Fearnhead - Lancaster University (United Kingdom)
Abstract: Post-selection inference has recently been proposed as a way of quantifying uncertainty about detected changepoints. The idea is to run a changepoint detection algorithm and then re-use the same data to perform a test for a change near each of the detected changes. By defining the p-value for the test appropriately so that it is conditional on the information used to choose the test, this approach will produce valid p-values. It is shown how to improve the power of these procedures by conditioning on less information. This gives rise to an ideal post-selection p-value that is intractable but can be approximated by Monte Carlo. It is shown that for any Monte Carlo sample size, this procedure produces valid p-values, and empirically, that noticeable increase in power is possible with only very modest Monte Carlo sample sizes. The procedure is easy to implement given existing post-selection inference methods, as there is a need to generate perturbations of the data set and re-apply the post-selection method to each of these. On genomic data consisting of human GC content, the procedure increases the number of significant changepoints that are detected when compared to existing methods.
