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| マルチレベル・メトロポリス・ヘイスティングス× | メトロポリス・ヘイスティングス法× | |
|---|---|---|
| 分野 | ベイズ | ベイズ |
| 系統 | Bayesian methods | Bayesian methods |
| 提唱年≠ | 1953 (core); 1990s (multilevel application) | 1953 |
| 提唱者≠ | Metropolis et al. (1953); hierarchical extension developed through 1980s–1990s Bayesian computation literature | Metropolis et al. (1953); generalised by Hastings (1970) |
| 種類≠ | MCMC sampling algorithm | Markov chain Monte Carlo sampler |
| 原典≠ | 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 ↗ |
| 別名≠ | hierarchical Metropolis-Hastings, multilevel MH, MH for hierarchical models, blocked Metropolis-Hastings | MH algorithm, M-H algorithm, Metropolis algorithm, Metropolis-Hastings sampler |
| 関連≠ | 6 | 5 |
| 概要≠ | 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. | 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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