variational inference versus mcmc
Variational inference versus MCMC: when to choose one over the other?
For a long answer, see Blei, Kucukelbir and McAuliffe here. This short answer draws heavily therefrom. Meaning, when we have computational time to kill and value precision of our estimates, MCMC wins. If we can tolerate sacrificing that for expediency--or we're working with data so large we have to make the tradeoff--VI is a natural choice. Thus, variational inference is suited to large data sets and scenarios where we want to quickly explore many models; MCMC is suited to smaller data sets and scenarios where we happily pay a heavier computational cost for more precise samples.