Scientists and engineers use observations, mathematical and computational models to predict the behaviour of physical realities such as turbulent ows. However, as a consequence of observational errors, errors in the mathematical models and discretisation errors in the computational models, our knowledge about what happens in reality is imperfect. The main purpose of the thesis is to investigate whether it is possible to quantify and to reduce the uncertainty of Reynolds-averaged Navier-Stokes (RANS) models - more speci_cally the Spalart-Allmaras, Smith's KL and the Launder-Sharma RANS turbulence models - using the Bayesian inference theorem. An underlying objective is to do determine the prior uncertainty by means of the analyst's knowledge of the used model, instead of merely guessing it, and the development of a methodical way to create and verify the correctness of a surrogate model for the RANS models. Inherent to using RANS models is the closure problem resulting from applying the Reynoldsaveraging technique to the Navier-Stokes equations. The model equations that are created (e.g. SA, KL and LS model) to mitigate the closure problem contain coe_cients who's values are determined from calibration with experimental values. It is for some of these so-called closure coe_cients that a prior uncertainty interval is determined.