Abstract Gamma-ray bursts (GRBs) are ultra-relativistic collimated outflows, which emit synchrotron radiation throughout the entire electromagnetic spectrum when they interact with their environment. This afterglow emission enables us to probe the dynamics of relativistic blast waves, the microphysics of shock acceleration, and environments of GRBs. We perform Bayesian inference on a sample of GRB afterglow data sets consisting of 22 long GRBs and 4 short GRBs, using the afterglow model scalefit, which is based on 2D relativistic hydrodynamic simulations. We make use of Gaussian processes to account for systematic deviations in the data sets, which allows us to obtain robust estimates for the model parameters. We present the inferred parameters for the sample of GRBs, and make comparisons between short GRBs and long GRBs in constant-density and stellar-wind-like environments. We find that in almost all respects such as energy and opening angle, short and long GRBs are statistically the same. Short GRBs however have a markedly lower prompt γ-ray emission efficiency than long GRBs. We also find that for long GRBs in ISM-like ambient media there is a significant anti-correlation between the fraction of thermal energy in the magnetic fields, εB, and the beaming corrected kinetic energy. Furthermore, we find no evidence that the mass-loss rates of the progenitor stars are lower than those of typical Wolf-Rayet stars.