How to tune the hyperparameters in graphical models such as a Markov random field?

What’s a good way to tune the hyperparemter of a Markov random field (MRF) with a Gaussian prior that’s not uncommon in image segmentation tasks? The structure of the graphical model is not a big issue, but we can assume a 4-connected graph. Say there’s no ground truth for training, but we only use the MRF for inference task in segmentation.

It seems like for graphical models, people tend to set the values of hyperparameters without tuning it (at least approximately).