Hastings correction
Topic of Markov chains, Gibbs sampling, and Metropolis–Hastings, part of Bayesian statistics
Hastings correction
| Type | Topic |
| Taught in | Markov chains, Gibbs sampling, and Metropolis–Hastings |
| Part | Bayesian statistics |
| Questions using it | 3 |
The factor q(\theta\mid\theta')/q(\theta'\mid\theta) in the Metropolis–Hastings acceptance probability. It corrects for a proposal that is more likely in one direction than the other, and equals 1 for a symmetric proposal.
In Markov chains, Gibbs sampling, and Metropolis–Hastings
Proposal design is an art because local and global exploration pull in different directions. Tiny random-walk steps are accepted but travel slowly; huge steps travel far but are mostly rejected. An independent proposal can jump between modes, yet it wastes effort if it puts mass where the target has almost none. The Hastings correction guarantees the right equilibrium under the required conditions; it does not guarantee an efficient journey there.
Used in
- Taught in Markov chains, Gibbs sampling, and Metropolis–Hastings
- Questions that use it (3) — Metropolis–Hastings for the logit-normal posterior (answer) · Random-walk Metropolis for a correlated normal (answer) · An independent Gamma proposal
- All 31 questions on Markov chains, Gibbs sampling, and Metropolis–Hastings
See also
Metropolis–Hastings algorithm · Metropolis–Hastings update · Metropolis–Hastings invariance · Metropolis algorithm · Random-walk and independent proposals · Markov chain · Stationarity and detailed balance · Detailed balance implies stationarity