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Multivariate point processes and their application on neurophysiological data
Bakošová, Katarína ; Pawlas, Zbyněk (advisor) ; Prokešová, Michaela (referee)
This thesis examines a multivariate point process in time with focus on a mu- tual relations of its marginal point processes. The first chapter acquaints the re- ader with the theoretical background of multivariate point processes and their properties, especially the higher-order cumulant-correlation measures. Later on, several models of multivariate point processes with different dependence structu- res are characterized, such as the random superposition model, a Poisson depen- dent superposition point process, a jitter Poisson dependent superposition point process orrenewal processes models. Simulations of each of them are provided. Furthermore, two statistical methods for higher-order correlations are presented; the cumulant based inference of higher-order correlations, and the extended til- ling coefficient. Finally, the introduced methods are applied not only on the data from simulations, but also on the real, simultaneously recorded nerve cells spike train data. The results are discussed. 1
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Two-dimensional point processes
Bakošová, Katarína ; Pawlas, Zbyněk (advisor) ; Beneš, Viktor (referee)
A point process as the special type of a random stochastic process is a theoretical model for occurrence of random events in time and space. In this thesis, we examine pairs of point processes in time and their mutual relations. The thesis acquaints the reader with the theoretical background of point processes, two- dimensional point processes and their properties based on measure theory. The purpose of this paper is to present and demonstrate methods of analyzing realizations of two point processes. Our attention is beaing focused mainly on problem of dependency of two point processes. We describe data analyses based on cross-correlation histogram, synchronization indices, and on spectral analysis using coherence. In the last chapter, we conducted these methods on nerve cell spike train data. Powered by TCPDF (www.tcpdf.org)
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