Spike train statistics and Gibbs distributions

TL;DR

This paper introduces Gibbs distributions in a general setting and applies them to neural spike train models, including maximum entropy, GLMs, and conductance-based models, highlighting their statistical properties.

Contribution

It extends Gibbs distribution theory to non-stationary neural spike train models and provides three concrete examples in neural network contexts.

Findings

Gibbs distributions can model non-stationary spike train dynamics.

Maximum entropy models with spatio-temporal constraints are formulated.

Generalized Linear Models are integrated within the Gibbs framework.

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