  We show that the method of partial covariance is a very efficient way to
introduce constraints (such as the centrality selection) in data analysis in
ultra-relativistic nuclear collisions. The technique eliminates spurious
event-by-event fluctuations of physical quantities due to fluctuations of
control variables. Moreover, in the commonly used superposition approach to
particle production the method can be used to impose constraints on the initial
sources rather than on the finally produced particles, thus separating out the
trivial fluctuations from statistical hadronization or emission from sources
and focusing strictly on the initial-state physics. As illustration, we use
simulated data from hydrodynamics started on the wounded-quark event-by-event
initial conditions, followed with statistical hadronization, to show the
practicality of the approach in analyzing the forward-backward multiplicity
fluctuations. We mention generalizations to the case with several constraints
and other observables, such as the transverse momentum or eccentricity
correlations.
