Importance sampling, particularly sequential and adaptive importance sampling, have emerged as competitive simulation techniques to Markov-chain Monte-Carlo techniques. We compare importance sampling and the Metropolis algorithm as two ways of changing the output of a Markov chain to get a different stationary distribution.
"Examples comparing importance sampling and the Metropolis algorithm." Illinois J. Math. 50 (1-4) 67 - 91, 2006. https://doi.org/10.1215/ijm/1258059470