方法对比
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| 分层哈密顿蒙特卡洛× | 分层马尔可夫链蒙特卡洛× | |
|---|---|---|
| 领域 | 贝叶斯 | 贝叶斯 |
| 方法族 | Bayesian methods | Bayesian methods |
| 起源年份≠ | 2015 | 1990 |
| 提出者≠ | Betancourt & Girolami | Gelfand & Smith (1990), building on Geman & Geman (1984) |
| 类型≠ | Bayesian sampling algorithm | Bayesian computational sampler |
| 开创性文献≠ | Betancourt, M. & Girolami, M. (2015). Hamiltonian Monte Carlo for hierarchical models. In S. K. Upadhyay, U. Singh, D. K. Dey & A. Loganathan (Eds.), Current Trends in Bayesian Methodology with Applications (pp. 79-101). CRC Press. link ↗ | 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 |
| 别名 | Hierarchical HMC, HMC for hierarchical models, HMC with reparameterization, NUTS for hierarchical Bayesian models | hierarchical MCMC, MCMC for multilevel models, Bayesian hierarchical MCMC, multilevel MCMC sampling |
| 相关≠ | 5 | 6 |
| 摘要≠ | Hierarchical Hamiltonian Monte Carlo (Hierarchical HMC) applies Hamiltonian Monte Carlo sampling to Bayesian hierarchical models, addressing the severe geometric challenges those models pose. By combining non-centered parameterizations with HMC's gradient-driven proposals, it achieves efficient posterior exploration of the multi-level funnel-shaped geometries that standard MCMC methods struggle with. | 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. |
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