title: Spike train statistics and Gibbs distributions.
abstract: This paper is based on a lecture given in the LACONEU summer school, Valparaiso, January 2012. We introduce Gibbs distribution in a general setting, including non stationary dynamics, and present then three examples of such Gibbs distributions, in the context of neural networks spike train statistics: (i) maximum entropy model with spatio-temporal constraints; (ii) generalized linear models; and (iii) conductance based integrate and fire model with chemical synapses and gap junctions.
authors.affiliation: NeuroMathComp team (INRIA, UNSA LJAD) 2004 Route des Lucioles, 06902 Sophia-Antipolis, France. Electronic address: bruno.cessac@inria.fr.
authors.forename: B
authors.initials: B
authors.lastname: Cessac
authors.forename: R
authors.initials: R
authors.lastname: Cofré
mesh_terms: D000200:Action Potentials / Q000502:physiology; D000818:Animals; D017629:Gap Junctions / Q000502:physiology; D006801:Humans; D016014:Linear Models; D016571:Neural Networks, Computer; D013569:Synapses / Q000502:physiology
keywords: Generalized linear models; Gibbs distributions; Higher order correlations; Neural networks dynamics; Spike train statistics