  An important issue in cosmology is reconstructing the effective dark energy
equation of state directly from observations. With few physically motivated
models, future dark energy studies cannot only be based on constraining a dark
energy parameter space, as the errors found depend strongly on the
parameterisation considered. We present a new non-parametric approach to
reconstructing the history of the expansion rate and dark energy using Gaussian
Processes, which is a fully Bayesian approach for smoothing data. We present a
pedagogical introduction to Gaussian Processes, and discuss how it can be used
to robustly differentiate data in a suitable way. Using this method we show
that the Dark Energy Survey - Supernova Survey (DES) can accurately recover a
slowly evolving equation of state to sigma_w = +-0.04 (95% CL) at z=0 and +-0.2
at z=0.7, with a minimum error of +-0.015 at the sweet-spot at z~0.14, provided
the other parameters of the model are known. Errors on the expansion history
are an order of magnitude smaller, yet make no assumptions about dark energy
whatsoever. A code for calculating functions and their first three derivatives
using Gaussian processes has been developed and is available for download at
http://www.acgc.uct.ac.za/~seikel/GAPP/index.html .
