updated the question with a small example, the example is very simplistic however. I think based on your answer however that we could restructure the data in some sort of way but lets say i have some term that modelles a carry-over effect between datapoints, it can get really really complex, there is no way we could just run the whole “mapping” once over both the train and testing data and then just draw posteriors based on the training-data and subsequently sample a posterior predictive based on the testingdata?