  An energy-biased method to evaluate ensemble averages requiring test-particle
insertion is presented. The method is based on biasing the sampling within the
subdomains of the test-particle configurational space with energies smaller
than a given value freely assigned. These energy-wells are located via unbiased
random insertion over the whole configurational space and are sampled using the
so called Hit&Run algorithm, which uniformly samples compact regions of any
shape immersed in a space of arbitrary dimensions. Because the bias is defined
in terms of the energy landscape it can be exactly corrected to obtain the
unbiased distribution. The test-particle energy distribution is then combined
with the Bennett relation for the evaluation of the chemical potential. We
apply this protocol to a system with relatively small probability of low-energy
test-particle insertion, liquid argon at high density and low temperature, and
show that the energy-biased Bennett method is around five times more efficient
than the standard Bennett method. A similar performance gain is observed in the
reconstruction of the energy distribution.
