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The device-independent approach to physics is one where conclusions aboutphysical systems (and hence of Nature) are drawn directly and solely from theobserved correlations between measurement outcomes. This operational approachto physics arose as a byproduct of Bell's seminal work to distinguish, via aBell test, quantum correlations from the set of correlations allowed bylocal-hidden-variable theories. In practice, since one can only perform afinite number of experimental trials, deciding whether an empirical observationis compatible with some class of physical theories will have to be carried outvia the task of hypothesis testing. In this paper, we show that theprediction-based-ratio method---initially developed for performing a hypothesistest of local-hidden-variable theories---can equally well be applied to testmany other classes of physical theories, such as those constrained only by thenonsignaling principle, and those that are constrained to produce any of theouter approximation to the quantum set of correlations due toNavascu\'es-Pironio-Ac\'{\i}n. We numerically simulate Bell tests usinghypothetical nonlocal sources of correlations to illustrate the applicabilityof the method in both the independent and identically distributed (i.i.d.)scenario and the non-i.i.d. scenario. As a further application, we demonstratehow this method allows us to unveil an apparent violation of the nonsignalingconditions in certain experimental data collected in a Bell test. This, inturn, highlights the importance of the randomization of measurement settings,as well as a consistency check of the nonsignaling conditions in a Bell test.

Bounding the plausibility of physical theories in a device-independent setting via hypothesis testing