Comparing the posterior with the prior distribution

I have run a Bayesian model in Rstan, where the main parameter follows a uniform Dirichlet distribution. In case I would like to compare the prior and the posterior, my intuition is that since the prior is uniform any non-uniformity in the posterior just reflects the data. However, would it be possible to have some way to compare prior and posterior? Could be the Kullback-Leibler’s distance a good way to quantify the discrepancy between prior and posterior? How can it be calculated in Rstan? Thank you!

@cecilia I’m not familiar with Rstan exactly but in brms - another interface for Stan - you can run an ‘analysis’ on the prior alone and therefore see summary stats and make plots of the priors without having input any data. I imagine you can do something very similar, which might be helpful. I don’t know if I would trust the idea that as the prior is uniform, any non-uniformity in the posterior is caused by the data, only because if there is more than a single parameter in the model, sometimes different uniform priors add together and make something that looks very non-uniform! I’m afraid I don’t know about the KL distance so I would probably wait for someone else to respond as well!