Given multiple possible models b1, b2, . . . bn for a protein structure, a common sub-task in in-silico Protein Structure Prediction is ranking these models according to their quality. Extant approaches use MLE estimates of parameters ri to obtain point estimates of the Model Quality. We describe a Bayesian alternative to assessing the quality of these models that builds an MRF over the parameters of each model and performs approximate inference to integrate over them. Hyperparameters w are learnt by optimizing a listwise loss function over training data. Our results indicate that our Bayesian approach can significantly outperform MLE estimates and that optimizing the hyper-parameters can further improve results.