  Approaches to the sign problem based on the density of states have been
recently revived by the introduction of the LLR algorithm, which allows us to
compute the density of states itself with exponential error reduction. In this
work, after a review of the generalities of the method, we show recent results
for the Bose gas in four dimensions, focussing on the identification of
possible systematic errors and on methods of controlling the bias they can
introduce in the calculation.
