  In the present work we study the statistics of haloes, which in the halo
model determines the distribution of galaxies. Haloes are known to be biased
tracer of dark matter, and at large scales it is usually assumed there is no
intrinsic stochasticity between the two fields. Following the work of Seljak &
Warren (2004), we explore how correct this assumption is and, moving a step
further, we try to qualify the nature of stochasticity. We use Principal
Component Analysis applied to the outputs of a cosmological N-body simulation
to: (1) explore the behaviour of stochasticity in the correlation between
haloes of different masses; (2) explore the behaviour of stochasticity in the
correlation between haloes and dark matter. We show results obtained using a
catalogue with 2.1 million haloes, from a PMFAST simulation with box size of
1000h^{-1}Mpc. In the relation between different populations of haloes we find
that stochasticity is not-negligible even at large scales. In agreement with
the conclusions of Tegmark & Bromley (1999) who studied the correlations of
different galaxy populations, we found that the shot-noise subtracted
stochasticity is qualitatively different from `enhanced' shot noise and,
specifically, it is dominated by a single stochastic eigenvalue. We call this
the `minimally stochastic' scenario, as opposed to shot noise which is
`maximally stochastic'. In the correlation between haloes and dark matter, we
find that stochasticity is minimized, as expected, near the dark matter peak (k
~ 0.02 h Mpc^{-1} for a LambdaCDM cosmology) and, even at large scales, it is
of the order of 15 per cent above the shot noise. Moreover, we find that the
reconstruction of the dark matter distribution is improved when we use
eigenvectors as tracers of the bias. [Abridged]
