Bayesian (structural) VAR model problems

Hello, I will use a bayesian structural vector autoregressive model for a macroeconomic paper. It is very hard to find answers to many questions in academic papers which rarely presents all the steps in their thinking and model specification. I will use a minnesota prior where 3 hyper parameters need to be decided by me. In a normal non bayesian VAR model you can choose lag length by using an information criterion, you can also do autocorrelation, stability and normality tests etc. For example, autocorrelation behaves differently in a bayesian var model due to prior limitations on variables, thus limiting autocorrelation etc.

My question is, does anyone know where to find the criterion to set the "correct" lag length for bayesian var models? If this was a forecasting paper, I would naturally choose lag lengths and hyperparameter values to minimize some criterion (Root mean squared forecast error etc) but there is no clarity regarding the choice of lags for a structural bayesian var model. Also If anyone has a good idea regarding how to deal with eventual autocorrelation and how to comment it I would be thankful.

Thanks in advance.