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| Dynamischer Metropolis-Hastings-Algorithmus× | Gibbs-Sampling× | |
|---|---|---|
| Fachgebiet | Bayes-Statistik | Bayes-Statistik |
| Familie | Bayesian methods | Bayesian methods |
| Entstehungsjahr≠ | 1970 (algorithm); 1992 (dynamic application) | 1984 |
| Urheber≠ | W. K. Hastings (algorithm); applied to dynamic models by Carlin, Polson & Stoffer | Stuart Geman & Donald Geman |
| Typ≠ | Bayesian MCMC sampler for dynamic models | MCMC sampling algorithm |
| Wegweisende Quelle≠ | Hastings, W. K. (1970). Monte Carlo sampling methods using Markov chains and their applications. Biometrika, 57(1), 97–109. DOI ↗ | Geman, S. & Geman, D. (1984). Stochastic relaxation, Gibbs distributions, and the Bayesian restoration of images. IEEE Transactions on Pattern Analysis and Machine Intelligence, 6(6), 721-741. DOI ↗ |
| Aliasnamen | Dynamic MH, MH for state-space models, Metropolis-Hastings in dynamic models, time-varying parameter MH | Gibbs sampler, coordinate-wise MCMC, systematic scan Gibbs, blocked Gibbs sampling |
| Verwandt | 5 | 5 |
| Zusammenfassung≠ | The Dynamic Metropolis-Hastings (Dynamic MH) algorithm applies the Metropolis-Hastings MCMC sampler to Bayesian state-space and time-varying parameter models. At each time step, latent states or evolving parameters are updated via proposal-and-accept moves, yielding full posterior distributions over trajectories rather than single filtered estimates. | Gibbs sampling is a Markov chain Monte Carlo algorithm that approximates a high-dimensional posterior distribution by repeatedly drawing each parameter from its full conditional distribution given all other parameters and the data. Because each draw is exact from a conditional — not a proposal that may be rejected — the sampler is efficient when those conditionals are available in closed form. |
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