  Gaussian processes are a fully Bayesian smoothing technique that allows for
the reconstruction of a function and its derivatives directly from
observational data, without assuming a specific model or choosing a
parameterization. This is ideal for constraining dark energy because physical
models are generally phenomenological and poorly motivated. Model-independent
constraints on dark energy are an especially important alternative to
parameterized models, as the priors involved have an entirely different source
so can be used to check constraints formulated from models or
parameterizations. A critical prior for Gaussian process reconstruction lies in
the choice of covariance function. We show how the choice of covariance
function affects the result of the reconstruction, and present a choice which
leads to reliable results for present day supernovae data. We also introduce a
method to quantify deviations of a model from the Gaussian process
reconstructions.
