Detailed balance implies stationarity
Theorem taught in Markov chains, Gibbs sampling, and Metropolis–Hastings, part of Bayesian statistics
Detailed balance implies stationarity
| Type | Theorem |
| Taught in | Markov chains, Gibbs sampling, and Metropolis–Hastings |
| Part | Bayesian statistics |
If a transition kernel q satisfies Equation (3) in Markov chains, Gibbs sampling, and Metropolis–Hastings for a probability distribution \pi, then \pi satisfies global balance and is a stationary distribution of the chain.
Used in
- Taught in Markov chains, Gibbs sampling, and Metropolis–Hastings, where the derivation and examples are.
- All 31 questions on Markov chains, Gibbs sampling, and Metropolis–Hastings
See also
Stationarity and detailed balance · Markov chain · Systematic-scan Gibbs sampler · Warm-up is not a convergence proof · Metropolis–Hastings update · Metropolis–Hastings invariance