While learning frequentist linear regressions, one thing the professors always talked about was about the number of degrees of freedom, I never saw this expression in a bayesian book though. Perhaps because bayesian methods don't need this number to infer things like variance and such?
My question is: is the number of degrees of freedom equals the number of parameters in an hierarchical bayesian model and if it's not, is there something equivalent one can calculate? In particular, I'm interested in when a model is overidentified in a hierarchical framework.
For example, if I have 1000 observations and about 10 possible competing models with about 100 parameters each, if mix them all in an hierarchical model using, for example, trans-dimensional MCMC/Bayes factor, the will I have an overidentified model?
My intuition says that it's possible that it won't, although the total number of parameters is greater than the number of observed parameters.