Obtaining mathematical models that can accurately describe nonlinear dynamics of complex processes and be further used for model-based control design is a challenging task. In this brief, a Bayesian approach is introduced for data-driven identification of linear parameter-varying regression models in an input-output dynamic representation form with an autoregressive with exogenous variable (ARX) noise structure. The applicability of the proposed approach is then investigated for the modeling of complex nonlinear process systems. In this approach, the dependence structure of the model on the scheduling variables is identified based on a Gaussian process (GP) formulation. The GP is used as a prior distribution to describe the possible realization of the scheduling-dependent coefficient functions of the estimated model. Then, a posterior distribution of these functions is obtained given the measured data and the mean value of this distribution is used to determine the estimated model. The properties and performance of the proposed method are evaluated using an illustrative example of a chemical process, namely, a distillation column, as well as an experimental case study with a three tank system.