Markov chain Monte Carlo can be extremely slow, particularly in high dimensions, because transitions between modes are difficult and accept-reject steps expend effort on proposals that do not advance the sampling process.

“The issue with this is that if you've ever run, like, Markov chain Monte Carlo, you will notice this is insanely slow, especially in high dimensions. Again, we have cursive dimensionality, you are basically uh it c not only do you have like these high dimensional problems where you have many modes and kind of escaping from mo one mode to the next is super difficult, but also just by the fact that you have still like an accept and reject step, you end up kind of doing a lot of work.”

“for things that don't end up going anywhere.”