Accuracy of Free Energy A Model

As discussed in Sect. 6.1, the bias due to finite sampling is usually the dominant error in free energy calculations using FEP or NEW. In extreme cases, the simulation result can be precise (small variance) but inaccurate (large bias) [24, 32], In contrast to precision, assessing the systematic part (accuracy) of finite sampling error in FEP or NEW calculations is less straightforward, since these errors may be due to choices of boundary conditions or potential functions that limit the results systematically. 

Consider the forward calculation as an example. Earlier in this chapter, we concluded that the most important contribution to a forward free energy calculation comes from the low-x tail of f(x)9 and its poor sampling results in the major systematic error of the calculation. To simplify further the analysis we assume that there is a limit-perturbation x f such that x Xf is well sampled and x Xf is never sampled. This is illustrated in Fig. 6.5. 

In this model, the finite sampling systematic error is due to the missed sampling of the important region x Xf. The free energy estimate given by the model is 

The denominator on the right-hand side is the renormalization factor, which is usually close to unity for large sample sizes and thus can be safely ignored (otherwise, the analysis presented below requires minor modification). Then we have 

Meanwhile, the exact free energy difference A A is given by 

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