  Quantum violation of Bell inequalities is now used in many quantum
information applications and it is important to analyze it both quantitatively
and conceptually. In the present paper, we analyze violation of multipartite
Bell inequalities via the local probability model - the LqHV (local quasi
hidden variable) model [Loubenets, J. Math. Phys. 53, 022201 (2012)],
incorporating the LHV model only as a particular case and correctly reproducing
the probabilistic description of every quantum correlation scenario, more
generally, every nonsignaling scenario. The LqHV probability framework allows
us to construct nonsignaling analogs of Bell inequalities and to specify
parameters quantifying violation of Bell inequalities - Bell's nonlocality - in
a general nonsignaling case. For quantum correlation scenarios on an N-qudit
state, we evaluate these nonlocality parameters analytically in terms of
dilation characteristics of an N-qudit state and also, numerically - in d and
N. In view of our rigorous mathematical description of Bell's nonlocality in a
general nonsignaling case via the local probability model, we argue that
violation of Bell inequalities in a quantum case is not due to violation of the
Einstein-Podolsky-Rosen (EPR) locality conjectured by Bell but due to the
improper HV modelling of "quantum realism".
