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We demonstrate how a prior assumption of smoothness can be used to enhancethe reconstruction of free energy profiles from multiple umbrella samplingsimulations using the Bayesian Gaussian process regression approach. The methodwe derive allows the concurrent use of histograms and free energy gradients andcan easily be extended to include further data. In Part I we review thenecessary theory and test the method for one collective variable. Wedemonstrate improved performance with respect to the weighted histogramanalysis method and obtain meaningful error bars without any significantadditional computation. In Part II we consider the case of multiple collectivevariables and compare to a reconstruction using least squares fitting of radialbasis functions. We find substantial improvements in the regimes of spatiallysparse data or short sampling trajectories. A software implementation is madeavailable on www.libatoms.org.

Free energy surface reconstruction from umbrella samples using Gaussian process regression II: Multiple collective variables