方法对比
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| 分层马尔可夫链蒙特卡洛× | 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≠ | Gelfand & Smith (1990), building on Geman & Geman (1984) | Metropolis et al. (1953); generalised by Hastings (1970) |
| 类型≠ | Bayesian computational sampler | Markov chain Monte Carlo sampler |
| 开创性文献≠ | 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 | 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 MCMC, MCMC for multilevel models, Bayesian hierarchical MCMC, multilevel MCMC sampling | MH algorithm, M-H algorithm, Metropolis algorithm, Metropolis-Hastings sampler |
| 相关≠ | 6 | 5 |
| 摘要≠ | Hierarchical Markov chain Monte Carlo applies MCMC sampling to hierarchical Bayesian models, jointly drawing from the posterior over both observation-level parameters and the hyperparameters that govern them. This allows principled uncertainty propagation across all levels of a multilevel structure, from individuals to groups to population, using algorithms such as Gibbs sampling, Metropolis-Hastings, or Hamiltonian Monte Carlo. | 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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