Overlap Sampling in FEP

As concluded in Sect. 6.3.1, when the important phase spaces // and r have partial overlap, the appropriate staging strategy is to construct an intermediate M whose 

No sampling on the intermediate M in (6.58) is required. This feature offers the flexibility of optimization, as tv( Au) can be adjusted freely without imposing any changes or a redesign of the simulation processes. In practice, the sampling requirement for the OS is the same as performing two separate FEP simulations one in the forward direction (0 — 1) and the other in the reverse direction (1 — 0) and the same sets of forward and reverse perturbation data Au are used. 

The second choice does not require such additional analysis. In addition, it is helpful for considering the precision and the accuracy of free energy differences simultaneously. The idea is that one can reduce the systematic error by balancing fAZf w(AU) [f(AU)g(AU) 1/2 dAU and JZg vj(AU) [f(AU)g(AU) 1/2 dAU, to make both of them as small as possible, and then increase weight on the regions, in which f(AU) and g(AU) overlap well. 

The minimization of the statistical error can be done by examining the variance of cxp(—/ zL4) directly. Bennett [55] has studied this problem by combining the forward and reverse FEP simulations, and the same analysis can be followed for the OS case. In Bennett s analysis, the weighting function w is placed to balance the forward and reverse FEP contributions [7, 55] 

The variance of the free energy calculation is (with error propagation) 

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