Our data show a large scatter for the critical Shields stress for initial sediment motion. The main sources of dispersion are related to the methodological procedures defining the inception of movement (i.e., visual observations or extrapolation of sediment transport rate) and to the estimation of the bed shear stress. The threshold for sediment motion varies with many factors related not only to grain size, but also with bed composition (e.g., presence of fine sediments in a coarse matrix), arrangement (e.g., bed roughness, grain orientation and characteristic lengths 1 Perret, September 2, 2022 of bed structures) and slope. New models to estimate the critical Shields number are proposed combining both grain size or/and bed slope. Model parameters and uncertainty are estimated through Bayesian inference using prior knowledge on those parameters and measured data. Apart from the uncertainty in observations, two types of uncertainty can be evaluated: one related to the parameter estimation (i.e., parametric) and one related to the choice of the model (i.e., structural). Eventually, a four-parameter model based on both the grain size and bed slope yields the best results and demonstrates a potential interaction between these two parameters. Model uncertainty remains, however, large, which indicates that other input parameters may be needed to improve the proposed model.