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Bell inequalities follow from a set of seemingly natural assumptions abouthow to provide a causal model of a Bell experiment. In the face of theirviolation, two types of causal models that modify some of these assumptionshave been proposed: (i) those that are parametrically conservative andstructurally radical, such as models where the parameters are conditionalprobability distributions (termed 'classical causal models') but where oneposits inter-lab causal influences or superdeterminism, and (ii) those that areparametrically radical and structurally conservative, such as models where thelabs are taken to be connected only by a common cause but where conditionalprobabilities are replaced by conditional density operators (these are termed'quantum causal models'). We here seek to adjudicate between these alternativesbased on their predictive power. The data from a Bell experiment is dividedinto a training set and a test set, and for each causal model, the parametersthat yield the best fit for the training set are estimated and then used tomake predictions about the test set. Our main result is that the structurallyradical classical causal models are disfavoured relative to the structurallyconservative quantum causal model. Their lower predictive power seems to be dueto the fact that, unlike the quantum causal model, they are prone to a certaintype of overfitting wherein statistical fluctuations away from theno-signalling condition are mistaken for real features. Our technique showsthat it is possible to witness quantumness even in a Bell experiment that doesnot close the locality loophole. It also overturns the notion that it isimpossible to experimentally test the plausibility of superdeterminist modelsof Bell inequality violations.

Experimentally adjudicating between different causal accounts of Bell inequality violations via statistical model selection