  We demonstrate how the Gaussian process regression approach can be used to
efficiently reconstruct free energy surfaces from umbrella sampling
simulations. By making a prior assumption of smoothness and taking account of
the sampling noise in a consistent fashion, we achieve a significant
improvement in accuracy over the state of the art in two or more dimensions or,
equivalently, a significant cost reduction to obtain the free energy surface
within a prescribed tolerance in both regimes of spatially sparse data and
short sampling trajectories. Stemming from its Bayesian interpretation the
method provides meaningful error bars without significant additional
computation. A software implementation is made available on www.libatoms.org.
