方法对比
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| 多层吉布斯采样× | Metropolis-Hastings算法× | |
|---|---|---|
| 领域 | 贝叶斯 | 贝叶斯 |
| 方法族 | Bayesian methods | Bayesian methods |
| 起源年份≠ | 1990 | 1953 |
| 提出者≠ | Geman & Geman (1984); applied to multilevel models by Gelfand & Smith (1990) | Metropolis et al. (1953); generalised by Hastings (1970) |
| 类型≠ | MCMC sampling algorithm | Markov chain Monte Carlo sampler |
| 开创性文献≠ | Gelman, A. & Hill, J. (2007). Data Analysis Using Regression and Multilevel/Hierarchical Models. Cambridge University Press. ISBN: 978-0521686891 | Metropolis, N., Rosenbluth, A. W., Rosenbluth, M. N., Teller, A. H., & Teller, E. (1953). Equation of state calculations by fast computing machines. The Journal of Chemical Physics, 21(6), 1087–1092. DOI ↗ |
| 别名≠ | hierarchical Gibbs sampler, blocked Gibbs sampling for multilevel models, multilevel MCMC via Gibbs, Gibbs sampler for mixed-effects models | MH algorithm, M-H algorithm, Metropolis algorithm, Metropolis-Hastings sampler |
| 相关≠ | 6 | 5 |
| 摘要≠ | 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. | The Metropolis-Hastings (MH) algorithm is a general-purpose Markov chain Monte Carlo (MCMC) method for drawing samples from any probability distribution whose density can be evaluated up to a normalising constant. Introduced by Metropolis, Rosenbluth, Rosenbluth, Teller, and Teller (1953) in computational physics and generalised by Hastings (1970) to asymmetric proposal distributions, it is the foundational algorithm from which nearly all subsequent MCMC samplers — Gibbs sampling, Hamiltonian Monte Carlo, slice sampling — are derived or can be viewed as special cases. |
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