The generation of heterogeneous microstructures using surrogate models plays an important role in order to quantify the resultant material properties given only limited specimen. Using Gaussian Random Fields, material microstructure realizations can be obtained through a surrogate model from which new realizations can quickly be generated. The given paper explores the opportunities of identifying the surrogate model parameters using Bayesian Inference. The use of stochastic methods enables the future application to uncertainty propagation, for example in the area of reliability analysis.