![]() In Section V, we show that EMUS performs comparably to WHAM and MBAR, and discuss its connection with the latter. ![]() After giving some background on US in Section II, we formulate EMUS in Section III. Recent extensions seek to improve performance when the sampling is limited and to extend the algorithm to more general ensembles. vardi1985empirical gill1988 kumar1992weighted shirts2008statistically Both WHAM and MBAR can be derived from maximum-likelihood or minimum asymptotic variance principles assuming independent, identically distributed sampling in each window, and have corresponding statistical optimality properties under those conditions. The multistate Bennett acceptance ratio (MBAR) method, as it is referred to in the the molecular-simulation literature and will be referred to here, is closely related but does not rely on binning the data. By far, the most widely used of these in chemical physics applications is the weighted histogram analysis method (WHAM). The desire to use all the simulation data motivated the introduction of estimators that allow for systematically combining the data from different simulations. Initially, researchers manually adjusted the zero of free energy in each window to make the full free energy profile continuous and, often, smooth conflicting results arising from limited sampling at the window peripheries were removed. 0 0 footnotetext: Second footnote I IntroductionĬonsiderable effort has been devoted to determining how best to combine the results from different simulations. We discuss the possibility of using the estimator and, more generally, the eigenvector method for umbrella sampling to guide adaptation of the simulation parameters to accelerate convergence. We demonstrate this estimator for simulations of the alanine dipeptide and show that it emphasizes low free energy pathways between stable states in comparison to existing approaches for assessing error contributions. The central limit theorem suggests an estimator of the error contributions from individual windows, and we develop a simple and computationally inexpensive procedure for implementing it. Then, we derive a central limit theorem for averages that are obtained from umbrella sampling. We discuss how the error scales with the number of windows. ![]() The advantage to this approach is that it facilitates error analysis. Here, we introduce a mathematical framework that casts the step of combining the data as an eigenproblem. Umbrella sampling efficiently yields equilibrium averages that depend on exploring rare states of a model by biasing simulations to windows of coordinate values and then combining the resulting data with physical weighting. ![]()
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