One of the essential tasks in the excavation of tunnels with TBM is the reliable estimation of its performance needed for the planning, cost control and other decision making on the feasibility of the tunneling project. The current study aims at predicting the rate of penetration (RoP) of TBM on the basis of the rock mass parameters including the uniaxial compressive strength (UCS), intact rock brittleness (BI), the angle between the plane of weakness and the TBM driven direction (a) and the distance between planes of weakness (DPW). To this end, datasets from the Queens Water Tunnel No. 3 project, New York City, are compiled and used to establish the models. The Bayesian inference approach is implemented to identify the most appropriate models for estimating the RoP among eight (8) candidate models that have been proposed. The selected TBM empirical models are fitted to field data. The unknown parameters of the models are considered as random variables. The WinBUGS software which uses Bayesian analysis of complex statistical models and Markov chain Monte Carlo (MCMC) techniques is employed to compute the posterior predictive distributions. The mean values of the model parameters obtained via MCMC simulations are considered for the model prediction performance evaluation. Meanwhile, the deviance information criterion (DIC) is used as the main prediction accuracy indicator and therefore, to rank the models taking into account both their fit and complexity. Overall, the results indicate that the proposed RoP model possesses satisfactory predictive performance.