A sampling method for estimating hard probability patterns with many random steps.
MCMC is like judging a giant school bake sale without seeing the map. You wander table to table, and your crumbs slowly reveal the crowd favorites.
You meet it in Bayesian inference. It keeps sampling until a messy probability shape becomes clearer.
VI
MCMC is often compared with VI: one samples, and one uses an approximation.
HMM
MCMC can sample and estimate hidden states in an HMM.
MCTS
MCMC and MCTS both use random sampling, but MCMC maps distributions and MCTS guides choices.