  Recently a new attempt to go beyond quantum mechanics (QM) was presented in
the form of so called prequantum classical statistical field theory (PCSFT).
Its main experimental prediction is violation of Born's rule which provides
only an approximative description of real probabilities. We expect that it will
be possible to design numerous experiments demonstrating violation of Born's
rule. Moreover, recently the first experimental evidence of violation was found
in the triple slits interference experiment, see \cite{WWW}. Although this
experimental test was motivated by another prequantum model, it can be
definitely considered as at least preliminary confirmation of the main
prediction of PCSFT. In our approach quantum particles are just symbolic
representations of "prequantum random fields," e.g., "electron-field" or
"neutron-field"; photon is associated with classical random electromagnetic
field. Such prequantum fields fluctuate on time and space scales which are
essentially finer than scales of QM, cf. `t Hooft's attempt to go beyond QM
\cite{H1}--\cite{TH2}. In this paper we elaborate a detection model in the
PCSFT-framework. In this model classical random fields (corresponding to
"quantum particles") interact with detectors inducing probabilities which match
with Born's rule only approximately. Thus QM arises from PCSFT as an
approximative theory. New tests of violation of Born's rule are proposed.
