Pilot adaptation and a fixed proposal
Section of Markov chains, Gibbs sampling, and Metropolis–Hastings, part of Bayesian statistics
Pilot adaptation and a fixed proposal
| Type | Section |
| Taught in | Markov chains, Gibbs sampling, and Metropolis–Hastings |
| Part | Bayesian statistics |
Adaptive proposals are a practical response to this tuning problem. A conservative version has two stages:
run a pilot calculation to learn a plausible centre, scale, or covariance for the proposal;
discard the pilot output, fix the learned proposal, restart the chain, and use only the second-stage draws for inference.
Conditional on the now-fixed proposal, the ordinary Metropolis–Hastings invariance argument applies to the retained chain.
Some adaptive schemes retain the history and continue changing the proposal during the run. Then the transition rule depends on time and on more than the current state, so the fixed-kernel proof given above no longer establishes the result. Such methods can be valid, but they require additional conditions and theory. Validity does not follow merely from the fact that the proposal seems to improve.
Used in
See also
Markov chain · Stationarity and detailed balance · Detailed balance implies stationarity · Systematic-scan Gibbs sampler · Warm-up is not a convergence proof · Metropolis–Hastings update · Metropolis–Hastings invariance · Markov chains and equilibrium