Trajectory Segmentation with Statistical Reliability Guarantee

Abstract

The goal of this study is to develop a method for evaluating the statistical significance of trajectory segmentation results. The difficulty of this problem lies in the fact that the trajectory segments are identified by a segmentation algorithm, and this fact must be properly incorporated in the statistical inference. Unfortunately, if one uses traditional statistical inference, the $p$-values or confidence intervals are not valid anymore in the sense that the false positive rate cannot be controlled at the desired significance level anymore. To resolve this difficulty, we adopt Selective Inference (SI) framework. We propose a new SI method for trajectory segmentation results obtained by dynamic programming --- a common method for optimal segmentation --- which provides valid $p$-values or confidence intervals. We applied the proposed method to animal trajectory data and demonstrate the difference between the traditional invalid method and the proposed valid method.