When the wave function approaches the ground state, the above estimator converges to the ground state energy. To minimize the relative statistical noise of the denominator, one chooses a reference determinant that has a high CI coefficient. This is typically the Hartree-Fock (HF) determinant which usually has the highest CI coefficient. However, if another determinant is found during the simulation to have a higher coefficient, a change of reference may occur, that helps in stabilizing the projected energy estimate. Note that FCIQMC samples of the numerator and the denominator of the projected energy should be averaged separately before taking their ratio.