The prediction of time evolution of gas turbine performance is an emerging requirement of modern prognostics and health management (PHM), aimed at improving system reliability and availability, while reducing life cycle costs. In this work, a data-driven Bayesian Hierarchical Model (BHM) is employed to perform a probabilistic prediction of gas turbine future behavior, thanks to its capability to deal with fleet data from multiple units. First, the theoretical background of the predictive methodology is outlined to highlight the inference mechanism and data processing for estimating BHM predicted outputs. Then, the BHM approach is applied to both simulated and field data representative of gas turbine degradation to assess its prediction reliability and grasp some rules of thumb for minimizing BHM prediction error. For the considered field data, the average values of the prediction errors are found to be lower than 1.0 % or 1.7 % for single- or multi- step prediction, respectively.