I have been reading the original Goodfellow, et. al. paper on Generative Adversarial Networks and the way that they can obtain estimates of the posterior distribution of a discriminative network or autoencoder. Now usually something that generates estimates from the posterior involves either an MCMC sampling scheme, or in some cases conjugacy of the prior.
So I was wondering if someone could clarify whether GANs can act as a replacement for MCMC sampling, or are there areas which only MCMC will work?