  We develop methods to deal with non-dynamical contributions to event-by-event
fluctuation measurements of net-particle numbers in relativistic nuclear
collisions. These contributions arise from impact parameter fluctuations and
from the requirement of overall net-baryon number or net-charge conservation
and may mask the dynamical fluctuations of interest, such as those due to
critical endpoints in the QCD phase diagram. Within a model of independent
particle sources we derive formulae for net-particle fluctuations and develop a
rigorous approach to take into account contributions from participant
fluctuations in realistic experimental environments and at any cumulant order.
Interestingly, contributions from participant fluctuations to the second and
third cumulants of net-baryon distributions are found to vanish at mid-rapidity
for LHC energies while higher cumulants of even order are non-zero even when
the net-baryon number at mid-rapidity is zero. At lower beam energies the
effect of participant fluctuations increases and induces spurious higher
moments. The necessary corrections become large and need to be carefully taken
into account before comparison to theory. We also provide a procedure for
selecting the optimal phase-space coverage of particles for fluctuation
analyses and discuss quantitatively the necessary correction due to global
charge conservation.
