  We present a method to certify the presence of Bell correlations in
experimentally observed statistics, and to obtain new Bell inequalities. Our
approach is based on relaxing the conditions defining the set of correlations
obeying a local hidden variable model, yielding a convergent hierarchy of
semidefinite programs (SdP's). Because the size of these SdP's is independent
of the number of parties involved, this technique allows to characterize
correlations in many-body systems. As an example, we illustrate our method with
the experimental data presented in [Science 352, 441 (2016)]
