A characterization of the time-rescaled gamma process as a model for spike trains.

The occurrence of neuronal spikes may be characterized by not only the rate but also the irregularity of firing. We have recently developed a Bayes method for characterizing a sequence of spikes in terms of instantaneous rate and irregularity, assuming that interspike intervals (ISIs) are drawn from a distribution whose shape may vary in time. Though any parameterized family of ISI distribution can be installed in the Bayes method, the ability to detect firing characteristics may depend on the choice of a family of distribution. Here, we select a set of ISI metrics that may effectively characterize spike patterns and determine the distribution that may extract these characteristics. The set of the mean ISI and the mean log ISI are uniquely selected based on the statistical orthogonality, and accordingly the corresponding distribution is the gamma distribution. By applying the Bayes method equipped with the gamma distribution to spike sequences derived from different ISI distributions such as the log-normal and inverse-Gaussian distribution, we confirm that the gamma distribution effectively extracts the rate and the shape factor

Detecting rate changes in spike trains

Neurone sind elementare Bausteine des Gehirns, welche Informationen über Aktionspotentiale (spikes) austauschen bzw. kodieren. In der statistischen Analyse von spike trains werden diese als Realisierung von stochastischen Punktprozessen betrachtet, oftmals unter der Annahme von stationären Feuerraten. Allerdings können diese Modellannahmen zu Fehlinterpretationen führen. Das Ziel dieser Arbeit war es, die Stationaritätsannahme zu prüfen und einen statistischen Test zu entwickeln, um Ratenveränderungen zu lokalisieren. Unter der Annahme, dass der spike train ein nichtstationärer Poisson Prozess mit stückweise konstanter Feuerrate ist, wurde ein Stufen-Filter-Test entwickelt, welcher die Zeitpunkte der Ratenänderung schätzt. Der Test operiert auf unterschiedlichen Zeitskalen und wird somit der großen Variation an Feuerraten in experimentellen spike trains gerecht. Zusätzlich wurde eine grafische Darstellung zur Veränderung der Feuerrate vorgeschlagen. Die Anwendung auf realen Daten ergab, dass die Methode plausible Ratenwechsel findet und somit das Schätzen der Ratenfunktion gemäß einer Stufenfunktion ermöglicht.Neuronal activity in the brain is often investigated in the presence of stimuli, termed externally driven activity. This stimulus-response-perspective has long been focussed on in order to find out how the nervous system responds to different stimuli. The neuronal response consists of baseline activity, so called spontaneous activity1, and activity which is caused by the stimulus. The baseline activity is often considered as constant over time which allows the identification of the stimulus-evoked part of the neuronal response by averaging over a set of trials. However, during the last years it has been recognized that own dynamics of the nervous system plays an important role in information processing. As a consequence, spontaneous activity is no longer regarded only as background ’noise’ and its role in cortical processing is reconsidered. Therefore, the study of spontaneous firing pattern gains more importance as these patterns may shape neuronal responses to a larger extent as previously thought. For example, recent findings suggest that prestimulus activity can predict a person’s visual perception performance on a single trial basis (Hanslmayr et al., 2007). In this context, Ringach (2009) remarks that one can learn much about even the quiescent state of the brain which “underlies the importance of understanding cortical responses as the fusion of ongoing activity and sensory input”. Taking into account that spontaneous activity reflects anything else but noise, new challenges arise when analysing neuronal data. In this thesis one of these problems related to the analysis of neuronal activity will be adressed, namely the nonstationarity of firing rates. The present work consists of four chapters. First of all the introduction gives neurophysiological background information to get an idea of neuronal information processing. Afterwords the theory of point processes is provided which forms the basis for modeling neuronal spiking data. In the last section of the introduction a statement of the problem is given. Chapter 2 proposes an easily applicable statistical method for the detection of nonstationarity. It is applied to simulations and to real data in order to show its capabilities. Thereafter, four other approaches are presented which provide useful illustrations concerning the nonstationarity of the firing rate but share the problem that one cannot make objective statements on the basis of their results. They were developed in the course of establishing a suitable method. In chapter 4 the results are discussed and suggestions for further study are given