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| Multilevel Gibbs Sampling× | Gibbs sampling× | |
|---|---|---|
| Ämnesområde | Bayesiansk statistik | Bayesiansk statistik |
| Familj | Bayesian methods | Bayesian methods |
| Ursprungsår≠ | 1990 | 1984 |
| Upphovsperson≠ | Geman & Geman (1984); applied to multilevel models by Gelfand & Smith (1990) | Stuart Geman & Donald Geman |
| Typ | MCMC sampling algorithm | MCMC sampling algorithm |
| Ursprungskälla≠ | Gelman, A. & Hill, J. (2007). Data Analysis Using Regression and Multilevel/Hierarchical Models. Cambridge University Press. ISBN: 978-0521686891 | 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 ↗ |
| Alias | hierarchical Gibbs sampler, blocked Gibbs sampling for multilevel models, multilevel MCMC via Gibbs, Gibbs sampler for mixed-effects models | Gibbs sampler, coordinate-wise MCMC, systematic scan Gibbs, blocked Gibbs sampling |
| Närliggande≠ | 6 | 5 |
| Sammanfattning≠ | Multilevel Gibbs sampling applies the Gibbs MCMC algorithm to hierarchical (multilevel) Bayesian models, cycling through the conditional distributions of group-level parameters and population-level hyperparameters in turn. This exploits the conditional independence structure of the hierarchy to draw exact or near-exact samples from a posterior that would otherwise be analytically intractable. | 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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