The MAPK/ERK pathway is one of the major signal transduction systems which regulates the cellular growth control of all eukaryotes like the cell proliferation and the apoptosis. Because of its importance in cellular lifecycle, it has been studied intensively, resulting in a number of qualitative descriptions of this regulatory mechanism. In this study we describe the MAPK/ERK pathway as an explicit set of reactions by combining different sources. Our reaction set takes into account the localization and different binding sites of the molecules in the cell by implementing the multiple parametrization. Then we estimate the model parameters of the network in a Bayesian setting via MCMC and data augmentation schemes. In the estimation we apply the Euler approximation, which is the discretized version of the diffusion technique. Additionally in inference of such a realistic and complex system we consider all possible kinds of dependencies coming from distinct stages of updates. To test the inference method we use the simulated data generated by the Gillespie algorithm. From the analysis it is clear that the sampler mixes well and partially is able to identify the dynamics of the MAPK/ERK pathway.