Non-Gaussian interaction information: estimation, optimization and diagnostic application of triadic wave resonance

Pires C., Perdigão R.
Nonlin. Processes Geophys. Discuss., 1, 1539–1602, 2014, doi:10.5194/npgd-1-1539-2014.

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Non-Gaussian multivariate probability distributions, derived from climate and geofluid statistics, allow for nonlinear correlations between linearly uncorrelated components, due to joint Shannon negentropies. Triadic statistical dependence under pair-wise (total 5 or partial) independence is thus possible. Synergy or interaction information among triads is estimated. We formulate an optimization method of triads in the space of orthogonal rotations of normalized principal components, relying on the maximization of third-order cross cumulants. Its application to a minimal one-dimensional, periodic, advective model, leads to enhanced triads that occur between oscillating components 10 of circular or locally confined wave-trains satisfying the triadic wave resonance condition.