Monte Carlo recursion

In considering fluids, a variety of approaches have been used to compute entropy and free energy a free-volume method,111-112 thermodynamic perturbation theory,113-116 thermodynamic integration,117-121 umbrella sampling,122-124 and a Monte Carlo recursion method.125-126 The entropy of association of two protein molecules in water has also been computed.127... 

Z. Li and H. A. Scheraga, /. Phys. Chem., 92,2633 (1988). Monte Carlo Recursion Evaluation of Free Energy. 

Computation of the Free Energy of Liquid Water by the Monte Carlo Recursion Method. 

Let Hk- = Hk E ) and Hk+ = Hk E ) denote the values of the histogram at its left and right boundary, and Rk = Hk+/Hk characterize their ratio. After a predetermined number of Monte Carlo steps per window, the (unnormalized) probability distribution can recursively be estimated according to ... 

Suppose that the feasible set x is convex and that at any point x G an estimate y(x) of the gradient Vg(x) can be computed, say by a Monte Carlo simulation method. The stochastic approximation method generates the iterates by the recursive equation... 

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