Single and Multiple Change Point Detection in Spike Trains: Comparison of Different CUSUM Methods

In a natural environment, sensory systems are faced with ever-changing stimuli that can occur, disappear or change their properties at any time. For the animal to react adequately the sensory systems must be able to detect changes in external stimuli based on its neuronal responses. Since the nervous system has no prior knowledge of the stimulus timing, changes in stimulus need to be inferred from the changes in neuronal activity, in particular increase or decrease of the spike rate, its variability, and shifted response latencies. From a mathematical point of view, this problem can be rephrased as detecting changes of statistical properties in a time series. In neuroscience, the CUSUM (cumulative sum) method has been applied to recorded neuronal responses for detecting a single stimulus change. Here, we investigate the applicability of the CUSUM approach for detecting single as well as multiple stimulus changes that induce increases or decreases in neuronal activity. Like the nervous system, our algorithm relies exclusively on previous neuronal population activities, without using knowledge about the timing or number of external stimulus changes. We apply our change point detection methods to experimental data obtained by multi-electrode recordings from turtle retinal ganglion cells, which react to changes in light stimulation with a range of typical neuronal activity patterns. We systematically examine how variations of mathematical assumptions (Poisson, Gaussian, and Gamma distributions) used for the algorithms may affect the detection of an unknown number of stimulus changes in our data and compare these CUSUM methods with the standard Rate Change method. Our results suggest which versions of the CUSUM algorithm could be useful for different types of specific data sets.