  We describe fermions in terms of a classical statistical ensemble. The states
$\tau$ of this ensemble are characterized by a sequence of values one or zero
or a corresponding set of two-level observables. Every classical probability
distribution can be associated to a quantum state for fermions. If the time
evolution of the classical probabilities $p_\tau$ amounts to a rotation of the
wave function $q_\tau(t)=\pm \sqrt{p_\tau(t)}$, we infer the unitary time
evolution of a quantum system of fermions according to a Schr\"odinger
equation. We establish how such classical statistical ensembles can be mapped
to Grassmann functional integrals. Quantum field theories for fermions arise
for a suitable time evolution of classical probabilities for generalized Ising
models.
