Maybe not. Not all probabilistic programming relies on MCMC, you can do MAP with probabilistic programming too. But in general, it's true that it tends towards

Maybe not. Not all probabilistic programming relies on MCMC, you can do MAP with probabilistic programming too. But in general, it's true that it tends towards Bayesian integration. In a sense, MCMC tries to solve #P complete problems, while MAP "only" tries to solve NP complete problems. The former are probably intrinsically harder than the latter. However, it's quite possible that some clever implementation might yield results which are as good as MAP in the same amount of time, and progressively refine them with more time. There are two free lunches with the curse of dimensionality: - the manifold hypothesis - Monte-Carlo integration True, the dimension rears its head as an ugly multiplicative constant in the latter - still, there has to be something there.