  Gaussian process regression (GPR) is a non-parametric Bayesian technique for
interpolating or fitting data. The main barrier to further uptake of this
powerful tool rests in the computational costs associated with the matrices
which arise when dealing with large data sets. Here, we derive some simple
results which we have found useful for speeding up the learning stage in the
GPR algorithm, and especially for performing Bayesian model comparison between
different covariance functions. We apply our techniques to both synthetic and
real data and quantify the speed-up relative to using nested sampling to
numerically evaluate model evidences.
