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| Metropolis-Hastings Multilivello× | Campionamento di Gibbs multilivello× | |
|---|---|---|
| Campo | Bayesiano | Bayesiano |
| Famiglia | Bayesian methods | Bayesian methods |
| Anno di origine≠ | 1953 (core); 1990s (multilevel application) | 1990 |
| Ideatore≠ | Metropolis et al. (1953); hierarchical extension developed through 1980s–1990s Bayesian computation literature | Geman & Geman (1984); applied to multilevel models by Gelfand & Smith (1990) |
| Tipo | MCMC sampling algorithm | MCMC sampling algorithm |
| Fonte seminale≠ | Gelman, A., Carlin, J. B., Stern, H. S., Dunson, D. B., Vehtari, A. & Rubin, D. B. (2013). Bayesian Data Analysis (3rd ed.). CRC Press. ISBN: 978-1439840955 | Gelman, A. & Hill, J. (2007). Data Analysis Using Regression and Multilevel/Hierarchical Models. Cambridge University Press. ISBN: 978-0521686891 |
| Alias | hierarchical Metropolis-Hastings, multilevel MH, MH for hierarchical models, blocked Metropolis-Hastings | hierarchical Gibbs sampler, blocked Gibbs sampling for multilevel models, multilevel MCMC via Gibbs, Gibbs sampler for mixed-effects models |
| Correlati | 6 | 6 |
| Sintesi≠ | Multilevel Metropolis-Hastings applies the Metropolis-Hastings MCMC algorithm to hierarchical (multilevel) Bayesian models, sampling jointly from group-level parameters and hyperparameters by proposing candidate values and accepting or rejecting them via a ratio that respects the full joint posterior across all levels of the model. | 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. |
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