I am curious about the use of sampling weights in Stan, and perhaps more generally in Bayes. I have read that as long as we have the covariates that were used in the probability of selection into the sample, we can just incorporate those in a typical hierarchical model. But, I have noticed that if we are actually supplied the weights (which are made up of probabilities within strata defined by the covariates), we can just use them as multiplicative constants in the likelihood. So, first, is there a preference and second, how would one use weights in a Stan set up for a normal linear hierarchical model? And, if one has weights at two sampling levels, how might that be set up? Please feel free to direct me to some existing Stan code out there.