Impact of including cross-covariances in GPR in the separation of coherent and incoherent components demonstrated on synthetic data. The left column shows the case where the coherent and incoherent covariance kernels are distinct, while the right column shows the case of the coherent and incoherent components having similar covariances. The corner plots in the top show the posterior distribution of the hyperparameters for the block diagonal approach (in blue) and the full covariance approach (in red). The four plots at the bottom show the recovery of a single realisation of the coherent component, for the block diagonal and full covariance approaches, respectively.