Metropolis algorithm
Topic of Markov chains, Gibbs sampling, and Metropolis–Hastings, part of Bayesian statistics
Metropolis algorithm
| Type | Topic |
| Taught in | Markov chains, Gibbs sampling, and Metropolis–Hastings |
| Part | Bayesian statistics |
The Metropolis–Hastings sampler with a symmetric proposal, q(\theta'\mid\theta)=q(\theta\mid\theta'), for which the acceptance probability reduces to \min\{1,\pi(\theta')/\pi(\theta)\}. A random-walk proposal is the usual example.
In Markov chains, Gibbs sampling, and Metropolis–Hastings
This cancellation is why Metropolis methods became central in statistical physics. An Ising model on m binary sites has 2^m configurations, making its partition function impractical to sum, but ratios of unnormalised target weights are immediate. The original Metropolis algorithm used symmetric proposals; Hastings’ generalisation supplied the proposal-density correction in Equation (5) in Markov chains, Gibbs sampling, and Metropolis–Hastings.
Used in
See also
Metropolis–Hastings algorithm · Metropolis–Hastings update · Metropolis–Hastings invariance · Hastings correction · Random-walk and independent proposals · Markov chain · Stationarity and detailed balance · Detailed balance implies stationarity