  Gaussian Process Regression (GPR) is a Bayesian method for inferring profiles
based on input data. The technique is increasing in popularity in the fusion
community due to its many advantages over traditional fitting techniques
including intrinsic uncertainty quantification and robustness to over-fitting.
This work investigates the use of a new method, the change-point method, for
handling the varying length scales found in different tokamak regimes. The use
of the Student's t-distribution for the Bayesian likelihood probability is also
investigated and shown to be advantageous in providing good fits in profiles
with many outliers. To compare different methods, synthetic data generated from
analytic profiles is used to create a database enabling a quantitative
statistical comparison of which methods perform the best. Using a full Bayesian
approach with the change-point method, Mat\'ern kernel for the prior
probability, and Student's t-distribution for the likelihood is shown to give
the best results.
