The copula approach to characterizing dependence structure in neural populations.

The question as to the role that correlated activity plays in the coding of information in the brain continues to be one of the most important in neuroscience. One approach to understanding this role is to formally model the ensemble responses as multivariate probability distributions. We have previously introduced alternatives to linear assumptions of multivariate Gaussian dependence for spike timing in neural ensembles using the probabilistic copula approach. In probability theory the copula "couples" marginal distributions to form flexible multivariate distribution functions for characterizing ensemble behavior. The parametric copula can be factored out of the joint probability density, and as such is independent and isolated from the marginal densities. This greatly simplifies the analysis, and allows a direct examination of the shape of the dependence independent of the marginals. The shape of the copula function goes beyond describing the dependence with a single summarizing statistic. In this review, we illustrate the construction of the copula, and how it contributes to the analysis of information conveyed by populations of neurons.