  Building upon recent developments of force-based estimators with a reduced
variance for the computation of densities, radial distribution functions or
local transport properties from molecular simulations, we show that the
variance can be further reduced by considering optimal linear combinations of
such estimators. This control variates approach, well known in Statistics and
already used in other branches of computational Physics, has been comparatively
much less exploited in molecular simulations. We illustrate this idea on the
radial distribution function and the one-dimensional density of a bulk and
confined Lennard-Jones fluid, where the optimal combination of estimators is
determined for each distance or position, respectively. In addition to reducing
the variance everywhere at virtually no additional cost, this approach cures an
artefact of the initial force-based estimators, namely small but non-zero
values of the quantities in regions where they should vanish. Beyond the
examples considered here, the present work highlights more generally the
underexplored potential of control variates to estimate observables from
molecular simulations.
