In PCHB the sampling of double excitations (AB ← IJ) occurs in multiple steps. In the particle selection, a first particle I is chosen according to probability p(I), then a second particle J is chosen under the conditional probability p(J|I). Next, in the hole selection, holes A and B are chosen with probabilities p(A|IJ) and p(B|IJA), respectively. When suitably localized MOs are used, after particle I has been selected, the second particle has a high probability, p(J|I), to be selected from the vicinity of I, rather than from spatially distant orbitals. Hence, the PCHB algorithm can take advantage of locality effects.