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Falsification is the basis for testing existing hypotheses, and a greatdanger is posed when results incorrectly reject our prior notions (falsepositives). Though nonparametric and nonlinear exploratory methods ofuncovering coupling provide a flexible framework to study networkconfigurations and discover causal graphs, multiple comparisons analyses makefalse positives more likely, exacerbating the need for their control. We aim torobustify the Gaussian Processes Convergent Cross-Mapping (GP-CCM) methodthrough Variational Bayesian Gaussian Process modeling (VGP-CCM). We alleviatecomputational costs of integrating with conditional hyperparameterdistributions through mean field approximations. This approximation model, inconjunction with permutation sampling of the null distribution, permitssignificance statistics that are more robust than permutation sampling withpoint hyperparameters. Simulated unidirectional Lorenz-Rossler systems as wellas mechanistic models of neurovascular systems are used to evaluate the method.The results demonstrate that the proposed method yields improved specificity,showing promise to combat false positives

Inferring Parsimonious Coupling Statistics in Nonlinear Dynamics with Variational Gaussian Processes