  We develop an efficient, non-parametric Bayesian method for reconstructing
the time evolution of the dark energy equation of state w(z) from observational
data. Of particular importance is the choice of prior, which must be chosen
carefully to minimise variance and bias in the reconstruction. Using a
principal component analysis, we show how a correlated prior can be used to
create a smooth reconstruction and also avoid bias in the mean behaviour of
w(z). We test our method using Wiener reconstructions based on Fisher matrix
projections, and also against more realistic MCMC analyses of simulated data
sets for Planck and a future space-based dark energy mission. While the
accuracy of our reconstruction depends on the smoothness of the assumed w(z),
the relative error for typical dark energy models is <10% out to redshift
z=1.5.
