Parametric estimation of spike train statistics by Gibbs distributions : an application to bio-inspired and experimental data

We review here the basics of the formalism of Gibbs distributions and its numerical implementation, (its details published elsewhere \cite{vasquez-cessac-etal:10}, in order to characterizing the statistics of multi-unit spike trains. We present this here with the aim to analyze and modeling synthetic data, especially bio-inspired simulated data e.g. from Virtual Retina \cite{wohrer-kornprobst:09}, but also experimental data Multi-Electrode-Array(MEA) recordings from retina obtained by Adrian Palacios. We remark that Gibbs distribution allow us to estimate the spike statistics, given a design choice, but also to compare different models, thus answering comparative questions about the neural code.