Quantifying uncertainty in detected changepoints is an important problem. However it is challenging as the naive approach would use the data twice, first to detect the changes, and then to test them. This will bias the test, and can lead to anti-conservative p-values. One approach to avoid this is to use ideas from post-selection inference, which conditions on the information in the data used to choose which changes to test. As a result this produces valid p-values; that is, p-values that have a uniform distribution if there is no change. Currently such methods have been developed for detecting changes in mean only. This paper presents two approaches for constructing post-selection p-values for detecting changes in variance. These vary depending on the method use to detect the changes, but are general in terms of being applicable for a range of change-detection methods and a range of hypotheses that we may wish to test.

翻译：量化检测到的变点的不确定性是一个重要问题。然而这具有挑战性，因为朴素方法会两次使用数据：首先用于检测变化，然后用于检验这些变化。这将使检验产生偏差，并可能导致反保守的p值。避免这一问题的一种方法是采用后选择推断的思想，该方法以用于选择待检验变化的数据信息为条件。因此，这种方法能产生有效的p值；即在无变化情况下服从均匀分布的p值。目前此类方法仅针对均值变化的检测而开发。本文提出了两种构建后选择p值的方法，用于检测方差变化。这些方法根据所使用的变化检测方法而有所不同，但在适用范围上具有普遍性：可应用于多种变化检测方法及多种待检验假设。