Inferring neural activity interaction graphs

Abstract

Neurons, and more generally neural structures are characterized by the large number of its components and the non-trivial dynamic interaction between them (Braitenberg and Schüz, 1998). To describe these structures and resulting phenomena it is necessary to develop a new class of stochastic processes, with values on the space of neural activities and interactions. First steps in this direction have already been done with by NeuroMat in the articles Galves et al. (2015), Duarte et al. (2016) and Brochini et al. (2016). All these papers do statistical model selection in the new class of process introduced in Galves and Löcherbach (2013). The goal of this Ph.D. project is to continue these efforts, by developing the development of the statistical theory needed to analyze samples generated by large systems with interactions of variable range in time and space.