Parametric Copula-GP model for analyzing multidimensional neuronal and behavioral relationships
Fig 2
Copula-GP finds that uncoupled neurons are independent given the stimulus.
A GLM model of two identical uncoupled neurons that receive the same time-dependent input x(t); B simulated calcium transients (fluorescence across time) showing dynamic responses to the stimulus x(t) for one of the neurons; C calcium transients of two neurons (y1(t), y2(t)) projected onto a unit cube by the probability integral transform based on unconditional marginals; colored points show transformed samples (u1, u2) corresponding to times t (color-coded). The clusters of similarly colored points (e.g. green) illustrate that the copula c(u) depends on time t; the particular shape and the location of the clusters depends on the function x(t); only 10% of data-points are shown (selected randomly). D same as C, but based on conditional marginals Fi(yi|t). The resulting empirical copula describes ‘noise correlations’ between two neurons. The colored data-points (,
) are uniformly distributed on the unit square, which suggests that there is no noise correlation between these neurons, the copula c(ut) is independent of time t, and the neurons are independent given the time-dependent stimulus.