My goal is to quantify the uncertainty of the parameters used in the (molecular dynamic) simulation itself. So, check whether the data by outputs of the simulation are in the possible compared to observed data (experimental data). If we can obtain probability distributions of the parameters, we can effectively define the robustness of the parameters in the model output from the simulation. Small perturbations in the parameters can result in large changes in the outputs. The main theory has been published in a couple papers, so I am less worried on the theory and more on the implementation. I have used other methods to check if the GP represents the simulation data.
Right now my main concern is incorporating both the observed (experimental) data and the parameters into MvNormal where x is observed data in 
I think that the parameters would be pi in the equation, but I am not totally certain.
Let me know if this clears things up or not.