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Detecting Rate Changes in Point Processes

Tuesday, October 21, 2014 - 11:00
Dr. Michael Messer, PhD in Mathematics (Goethe University, Frankfurt, Germany)
Seminar
Room 4192, Earth Sciences Building (2207 Main Mall)
Speaker Bio
Dr. Michael Messer completed his doctorate in Mathematics with specialization in Statistics at the department of Computer Science and Mathematics at Goethe University Frankfurt, Germany. His thesis was supervised by Prof. Gaby Schneider and reported by Prof. Anton Wakolbinger (both Frankfurt) and Prof. Roland Fried from Dortmund. The research was conducted in collaboration with neuroscientists in an interdisciplinary research project for the investigation of neuronal disorders (NeFF - Neuronal Coordination Research Focus Frankfurt). He developed statistical techniques for the analysis of neuronal spike trains. The main paper was recently accepted for publication at The Annals of Applied Statistics.
Abstract

Nonstationarity of the event rate is a persistent problem in modeling time series of events, such as neuronal spike trains. Motivated by a variety of patterns in neurophysiological spike train recordings, we de fine a general class of renewal processes. This class is used to test the null hypothesis of stationary rate versus a wide alternative of renewal processes with finitely many rate changes (change points). Our test extends ideas from the filtered derivative approach by using multiple moving windows simultaneously. We also develop a multiple filter algorithm, which can be used when the null hypothesis is rejected in order to estimate the number and location of change points. We analyze the benefi ts of multiple filtering and its increased detection probability as compared to a single window approach. Application to spike trains recorded from dopamine midbrain neurons of anesthetized mice illustrates the relevance of the proposed techniques as preprocessing steps for methods that assume rate stationarity.