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.