The flow of the pore water in porous media generates an electrical current known as the streaming current. This current is due to the drag of the excess of charges contained in the electrical diffuse layer coating the surface of the grains. This current is associated with an electric field called the streaming potential field. The fluctuations of this field can be remotely measured using a set of non-polarizable electrodes located at the ground surface or in wells and a sensitive voltmeter. The self-potential method (SP) aims at passively measuring the streaming potential anomalies associated with ground water flow. We present a stochastic numerical framework for inverting self-potential data in order to localize seeps in dams and characterize their permeability and Darcy velocity. Our approach is based on the use of Markov chains Monte Carlo (McMC) method for solving the inverse problem. We performed first a validation of the method on a synthetic case study and then on large-scale field surveys on three different dams. Our approach is successful in localizing seeps and determining their permeability. A sensitivity study is performed on each of these three dams to better define the hydraulic and electrical parameters influencing the self-potential signal and the uncertainties associated with the estimation of those parameters. Our results show that the self-potential method can provide quantitative hydrogeological information for the characterization of seeps in dams and dikes.