  There is a vast body of literature related to methods for detecting
changepoints (CP). However, less attention has been paid to assessing the
statistical reliability of the detected CPs. In this paper, we introduce a
novel method to perform statistical inference on the significance of the CPs,
estimated by a Dynamic Programming (DP)-based optimal CP detection algorithm.
Based on the selective inference (SI) framework, we propose an exact
(non-asymptotic) approach to compute valid p-values for testing the
significance of the CPs. Although it is well-known that SI has low statistical
power because of over-conditioning, we address this disadvantage by introducing
parametric programming techniques. Then, we propose an efficient method to
conduct SI with the minimum amount of conditioning, leading to high statistical
power. We conduct experiments on both synthetic and real-world datasets,
through which we offer evidence that our proposed method is more powerful than
existing methods, has decent performance in terms of computational efficiency,
and provides good results in many practical applications.
