  Falsification is the basis for testing existing hypotheses, and a great
danger is posed when results incorrectly reject our prior notions (false
positives). Though nonparametric and nonlinear exploratory methods of
uncovering coupling provide a flexible framework to study network
configurations and discover causal graphs, multiple comparisons analyses make
false positives more likely, exacerbating the need for their control. We aim to
robustify the Gaussian Processes Convergent Cross-Mapping (GP-CCM) method
through Variational Bayesian Gaussian Process modeling (VGP-CCM). We alleviate
computational costs of integrating with conditional hyperparameter
distributions through mean field approximations. This approximation model, in
conjunction with permutation sampling of the null distribution, permits
significance statistics that are more robust than permutation sampling with
point hyperparameters. Simulated unidirectional Lorenz-Rossler systems as well
as 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
