Metropolis-Hastings
The Metropolis-Hastings algorithm builds a Markov chain whose stationary distribution is the target distribution, sampling complex distributions via accept-reject.
Purpose
To sample from complex, unnormalized probability distributions; the core of Bayesian inference.
Mechanism
Propose x' from a proposal distribution q and accept with probability α=min(1, p(x')q(x|x')/p(x)q(x'|x)); on rejection, stay at the current state. Detailed balance guarantees that the stationary distribution is the target p.
Use cases
- Bayesian inference
- MCMC sampling
- Statistical physics