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We propose a method for efficient simulations in extended ensembles, useful,e.g., for the study of problems with complex energy landscapes and for freeenergy calculations. The main difficulty in such simulations is the estimationof the a priori unknown weight parameters needed to produce flat histograms.The method combines several complementary techniques, namely, a Gibbs samplerfor the parameter moves, a reweighting procedure to optimize data use, and aBayesian update allowing for systematic refinement of the free energy estimate.In a certain limit the scheme reduces to the 1/t algorithm of B.E. Belardinelliand V.D. Pereyra [Phys. Rev. E 75, 046701 (2007)]. The performance of themethod is studied on the two-dimensional Ising model, where comparison with theexact free energy is possible, and on an Ising spin glass.

Improving the efficiency of extended ensemble simulations: The accelerated weight histogram method