In the present research, the data-driven methods (DDMs), are used to estimate the threshold velocity of sediment motion. Results of the DDMs used in this research, including artificial neural networks (FFNN & RBNN), adaptive neuro-fuzzy inference system models (ANFIS, ANFIS-GA & ANFIS-IWO), and wavelet neural network (WaveNet), are compared with those of the mathematical models and experimental observations. The obtained results indicate that the WaveNet model with the Nash-Sutcliffe coefficient of 0.997 has better performance than the other methods. Moreover, in order to specify the relative importance of the input parameters for the uncertainty of the threshold velocity, sensitivity analysis is performed, the results of which indicate that the median diameter of the particles and relative density are the most important parameters affecting the threshold velocity, respectively. In addition, the Monte Carlo simulation is used to quantify the uncertainty of the threshold velocity of motion. The uncertainty is expressed using the coefficient of variation (CV). The highest amount of CV is related to the median diameter of grain size, therefore, this parameter has the maximum effect on variations of the incipient motion. (C) 2018 Published by Elsevier B.V.