  We analyze recent data on particle production yields obtained in p-p
collisions at SPS and RHIC energies within the statistical model. We apply the
model formulated in the canonical ensemble and focus on strange particle
production. We introduce different methods to account for strangeness
suppression effects and discuss their phenomenological verification. We show
that at RHIC the midrapidity data on strange and multistrange particle
multiplicity can be successfully described by the canonical statistical model
with and without an extra suppression effects. On the other hand, SPS data
integrated over the full phase-space require an additional strangeness
suppression factor that is beyond the conventional canonical model. This factor
is quantified by the strangeness saturation parameter or strangeness
correlation volume. Extrapolating all relevant thermal parameters from SPS and
RHIC to LHC energy we present predictions of the statistical model for particle
yields in p-p collisions at sqrt(s) = 14TeV. We discuss the role and the
influence of a strangeness correlation volume on particle production in p-p
collisions at LHC.
