  We present a method that exploits self-consistent simulation of
coarse-grained and fine-grained models, in order to analyse properties of
physical systems. The method uses the coarse-grained model to obtain a first
estimate of the quantity of interest, before computing a correction by
analysing properties of the fine system. We illustrate the method by applying
it to the Asakura-Oosawa (AO) model of colloid-polymer mixtures. We show that
the liquid-vapour critical point in that system is affected by three-body
interactions which are neglected in the corresponding coarse-grained model. We
analyse the size of this effect and the nature of the three-body interactions.
We also analyse the accuracy of the method, as a function of the associated
computational effort.
