Spike train statistics and Gibbs distributions

•We introduce Gibbs distribution in a general setting, including non stationary dynamics.•We present then three examples of such Gibbs distributions, in the context of neural networks spike train statistics.•We analyze the relations between these three approaches.

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.