I am trying to understand the difference between these parameters, and their application. Was hoping to get some correction/clarification to my statements. I have a training set and cross-validation set. I am using bayesian statistics, I realize AIC and BIC can't be used in this context.
AIC and BIC assess how well the model fits the training set. The DIC assess how well the model will fit some future data (ie the cross-validation set).
So if using MLE methods, should one compute AIC and BIC on the cross-validation set? Conversely, when using bayesian methods, is there no need to compute the DIC for the cross-validation set because it by definition is related to future data?