Spike train statistics and Gibbs distributions

Bruno Cessac (1) , Rodrigo Cofre (1)

1 NEUROMATHCOMP - Mathematical and Computational Neuroscience

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; (iii) Conductance based Inte- grate and Fire model with chemical synapses and gap junctions.

Domaines: Physique mathématique [math-ph]; Physique mathématique [math-ph]

Bruno Cessac, Rodrigo Cofre. Spike train statistics and Gibbs distributions. Journal of Physiology - Paris, 2013, 107 (5), pp.360-368. ⟨hal-00850155⟩