In this study we present a method to estimate posterior distributions for standard accretion torque model parameters and binary orbital parameters for X-ray binaries using a nested sampling algorithm for Bayesian Parameter Estimation. We study the spin evolution of two Be X-ray binary systems in the Magellanic Clouds, RX J0520.5-6932 and RX J0209-7427, during major outbursts, in which they surpassed the Eddington-limit. Moreover, we apply our method to the recently discovered Swift J0243.6+6124; the only known Galactic pulsating ultra-luminous X-ray source. This is an excellent candidate for studying the disc evolution at super-Eddington accretion rates, for its luminosity span several orders of magnitude during its outburst, with a maximum L_X that exceeded the Eddington limit by a factor of ~10. Our method, when applied to RX J0520.5-6932 and RX J0209-7427, is able to identify the more favourable torque model for each system, while yielding meaningful ranges for the NS and orbital parameters. Our analysis for Swift J0243.6+6124 illustrates that, contrary to the standard torque model predictions, the magnetospheric radius (R_m) and the Alvfén radius (R_A) are not proportional to each other when surpassing the Eddington limit. Reported distance estimates of this source range between 5 and 7 kpc. Smaller distances require non-typical neutron star properties (i.e. mass and radius) and possibly lower radiative efficiency of the accretion column.