Recent experimental advances have made it possible to record up to several hundreds of neurons simultaneously in the cortex or in the retina. Analyzing such data requires mathematical and numerical methods to describe the spatio-temporal correlations in population activity. This can be done thanks to Maximum Entropy method. Here, a crucial parameter is the product N×R where N is the number of neurons and R the memory depth of correlations (how far in the past does the spike activity affects the current state). Standard statistical mechanics methods are limited to spatial correlation structure with R = 1 (e.g. Ising model) whereas methods based on transfer matrices, allowing the analysis of spatio-temporal correlations, are limited to NR ≤ 20. In the first part of the thesis we propose a modified version of the transfer matrix method, based on the parallel version of the Montecarlo algorithm, allowing us to go to NR=100. In a second part we present EnaS, a C++ library with a Graphical User Interface developed for neuroscientists. EnaS offers highly interactive tools that allow users to manage data, perform empirical statistics, modeling and visualizing results. Finally, in a third part, we test our method on synthetic and real data sets. Real data set correspond to retina data provided by our partners neuroscientists. Our non-extensive analysis shows the advantages of considering spatio-temporal correlations for the analysis of retina spike trains, but it also outlines the limits of Maximum Entropy methods.
