Bivariate change point detection in cell biology and neuroscience

(Moving kernel statistics for change point detection in cell biology and neuroscience)

Neuronal spike trains show a diversity of patterns, including short- and long-term changes in their intensity or regularity of spike events. To analyze their impact on information processing, point process models are needed that capture these patterns, and techniques for the localization of change points on different time scales are required. We discuss a class of point process models that exhibit changes in the intensity and variance of life times. A multi filter procedure is proposed to test the null hypothesis of constant intensity or variance. Change points are then located with a two step procedure in which changes in the intensity are located first and then incorporated to investigate changes in the regularity.

In cell biology, similar questions arise when movement patterns are quasi linear with abrupt changes in direction and speed, as in movements of plastids investigated here. We first propose a new stochastic model called linear walk that describes movement along linear structures with piecewise constant movement direction and speed. Maximum likelihood estimators are provided, and due to serial dependence 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.

This talk is based on joint work with Stefan Albert, Theresa Ernst, Philipp Gebhardt, Michael Messer, Annika Meyer, Ralph Neininger, Solveig Plomer, Jochen Roeper, Julia Schiemann and Enrico Schleiff.