When the same response, in this case lattice energy, is measured at different levels of computational complexity and accuracy, a hierarchical Autoregressive Gaussian Process (ARGP) model 66 can be constructed, which links a higher-level complexity response, y t (e.g. PBE0 lattice energies), to a lower-complexity response, y t-1 (PBE lattice energies), through a scaling parameter ρ, with the difference δ modelled as a GPR, independently of the GPR assumed for y t-1 . For our problem: