  Hard scattering yields in centrality-selected proton-- and deuteron--nucleus
($p$+A) collisions are generally compared to nucleon--nucleon ($NN$)
cross-sections scaled to the appropriate partonic luminosity using geometric
models derived from an analysis of minimum bias $p$+A interactions. In general,
these models assume that hard process rates and the magnitude of the soft event
activity in the underlying $NN$ collisions is uncorrelated. When included,
these correlations influence the measured yield in a nominal centrality
interval, an effect typically referred to as a "centrality bias". In this work,
the impact of a positive correlation between the hard scattering yield and the
underlying event activity in individual $NN$ collisions is investigated. This
correlation is incorporated into the centrality calculations used by ATLAS and
PHENIX, both based on a similar Monte Carlo Glauber approach but with different
models of the per-collision or per-participant event activity. It is found that
the presence of this correlation tends to increase the yield measured in more
central events and decrease it in peripheral events. Numerical factors to
correct measured yields for the centrality bias effect are calculated for $p$+A
collisions at RHIC and the LHC. Reasonable agreement with a previous
calculation of these factors by PHENIX is found, despite differences in the
implementation of the underlying bias.
