Bivariate change point detection in movement direction and speed

TL;DR

This paper introduces a new stochastic model and statistical methods for detecting abrupt change points in movement direction and speed, specifically applied to biological movement patterns like plastids in root cells.

Contribution

It presents a novel stochastic model for movement along linear structures, along with maximum likelihood estimators and a new kernel-based change point detection method accounting for serial dependencies.

Findings

Proposed a new model for movement with change points in direction and speed.

Developed a kernel-based estimator for change point detection.

Validated the consistency and convergence of the estimators.

Abstract

Biological movement patterns can sometimes be quasi linear with abrupt changes in direction and speed, as in plastids in root cells investigated here. For the analysis of such changes we propose a new stochastic model for movement along linear structures. Maximum likelihood estimators are provided, and due to serial dependencies of increments, the classical MOSUM statistic is replaced by a moving kernel estimator. Convergence of the resulting difference process and strong consistency of the variance estimator are shown. We estimate the change points and propose a graphical technique to distinguish between change points in movement direction and speed.