Free energy simulations error analysis

Understanding and Improving Free Energy Calculations in Molecular Simulations Error Analysis and Reduction Methods... 

Certainly, as the number of windows used increases, the amount of sampling at each window may be decreased. Simple statistical analysis can be used to show that if the variance and correlation in the data collected at each window is constant over the entire free energy simulation, then the error associated with the total calculated free energy in a TI simulation is given as ... 

What level of inaccuracy can be expected for a simulation with a certain sample size N1 This question can be transformed to another one what is the effective limit-perturbation Xf or xg in the inaccuracy model [(6.22) or (6.23)] To assess the error in a free energy calculation using the model, one may histogram / and g using the perturbations collected in the simulations, and plot x in the tail of the distribution. However, if Xf is taken too small the accuracy is overestimated, and the assessed reliability of the free energy is therefore not ideal. In the following, we discuss the most-likely analysis, which provides a more systematic way to estimate the accuracy of free energy calculations. 

The difficult analysis of the sources of error in free energy difference evaluations by computer simulation and the effect of particular implementations of free energy difference techniques has been the subject of a number of recent studies. The error inherent in any computer simulation can formally be categorized by statistical and systematic errors. In practice, these errors are often difficult to separate. 

The sensitivity analysis approach has also been shown to be useful for studying error propagations due to the use of nonoptimal parameters in biomolecular simulations and for examining how error cancellations may occur in free energy difference calculations. The sensitivity analysis approach can also suggest how potential functions could be simplified and how the parameters of these functions can be effectively refined. 

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