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Post-selection inference has recently been proposed as a way of quantifyinguncertainty about detected changepoints. The idea is to run a changepointdetection algorithm, and then re-use the same data to perform a test for achange near each of the detected changes. By defining the p-value for the testappropriately, so that it is conditional on the information used to choose thetest, this approach will produce valid p-values. We show how to improve thepower of these procedures by conditioning on less information. This gives riseto an ideal selective p-value that is intractable but can be approximated byMonte Carlo. We show that for any Monte Carlo sample size, this procedureproduces valid p-values, and empirically that noticeable increase in power ispossible with only very modest Monte Carlo sample sizes. Our procedure is easyto implement given existing post-selection inference methods, as we just needto generate perturbations of the data set and re-apply the post-selectionmethod to each of these. On genomic data consisting of human GC content, ourprocedure increases the number of significant changepoints that are detectedfrom e.g. 17 to 27, when compared to existing methods.

Improving Power by Conditioning on Less in Post-selection Inference for Changepoints