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| マルチレベル・メトロポリス・ヘイスティングス× | 階層ベイズ推論× | |
|---|---|---|
| 分野 | ベイズ | ベイズ |
| 系統 | Bayesian methods | Bayesian methods |
| 提唱年≠ | 1953 (core); 1990s (multilevel application) | 1980s–2000s |
| 提唱者≠ | Metropolis et al. (1953); hierarchical extension developed through 1980s–1990s Bayesian computation literature | Gelman, Hill, Raudenbush, Bryk |
| 種類≠ | MCMC sampling algorithm | Bayesian hierarchical model |
| 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 | Gelman, A., & Hill, J. (2007). Data Analysis Using Regression and Multilevel/Hierarchical Models. Cambridge University Press. ISBN: 978-0521686891 |
| 別名 | hierarchical Metropolis-Hastings, multilevel MH, MH for hierarchical models, blocked Metropolis-Hastings | Bayesian multilevel model, Bayesian hierarchical model, Bayesian mixed-effects model, Bayesian random-effects model |
| 関連 | 6 | 6 |
| 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. | Multilevel Bayesian inference combines Bayesian probability with hierarchical data structures, treating group-level parameters as drawn from a common population distribution. It simultaneously estimates unit-level effects and the hyperparameters governing their variation, propagating full uncertainty through every level of the hierarchy via posterior sampling. |
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