  Understanding the origin of the accelerated expansion of the Universe poses
one of the greatest challenges in physics today. Lacking a compelling
fundamental theory to test, observational efforts are targeted at a better
characterization of the underlying cause. If a new form of mass-energy, dark
energy, is driving the acceleration, the redshift evolution of the equation of
state parameter w(z) will hold essential clues as to its origin. To best
exploit data from observations it is necessary to develop a robust and accurate
reconstruction approach, with controlled errors, for w(z). We introduce a new,
nonparametric method for solving the associated statistical inverse problem
based on Gaussian Process modeling and Markov chain Monte Carlo sampling.
Applying this method to recent supernova measurements, we reconstruct the
continuous history of w out to redshift z=1.5.
