Extensive research has been conducted regarding fitting of ARGP models and their variations. We adopt the recursive Bayesian multi-fidelity approach, suitable for nested training sets. Sequential estimation of GPRs is performed for the two levels; first, a standard GPR for y 1 (x) is fitted on the n 1 structures composing the lower-level training set D 1 = {x 1 , . . . , x n 1 }. Secondly, the higher-level response y 2 (x) is modelled with a GPR on the subset D 2 ⊆ D 1 of size n 2 , with the GPR prior for y 1 (x) in (1) being replaced by its GPR posterior obtained at the first stage.