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 $L_{\rm X}$ that exceeded the Eddington limit by a factor of $\sim 10$. 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 and the Alfvén radius 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.