方法对比
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| 空间马尔可夫链蒙特卡洛 (Spatial MCMC)× | Hamiltonian Monte Carlo× | |
|---|---|---|
| 领域 | 贝叶斯 | 贝叶斯 |
| 方法族 | Bayesian methods | Bayesian methods |
| 起源年份≠ | 1990s | 1987 |
| 提出者≠ | Gelfand, Smith, and colleagues (early 1990s MCMC for spatial models) | — |
| 类型≠ | Bayesian computational method | Gradient-based Markov chain Monte Carlo sampler |
| 开创性文献≠ | Banerjee, S., Carlin, B. P., & Gelfand, A. E. (2015). Hierarchical Modeling and Analysis for Spatial Data (2nd ed.). CRC Press. ISBN: 978-1439819173 | Duane, S., Kennedy, A. D., Pendleton, B. J., & Roweth, D. (1987). Hybrid Monte Carlo. Physics Letters B, 195(2), 216–222. DOI ↗ |
| 别名≠ | spatial Markov chain Monte Carlo, MCMC for spatial data, spatial Bayesian MCMC, geostatistical MCMC | HMC, Hybrid Monte Carlo, NUTS, No-U-Turn Sampler |
| 相关≠ | 4 | 3 |
| 摘要≠ | Spatial MCMC applies Markov chain Monte Carlo sampling to Bayesian models that explicitly account for spatial dependence among observations. It draws posterior samples from models such as conditional autoregressive (CAR), simultaneous autoregressive (SAR), or geostatistical (Gaussian process) models, yielding full uncertainty distributions for spatially structured parameters like random effects, regression coefficients, and spatial range. | Hamiltonian Monte Carlo (HMC) is a gradient-based Markov chain Monte Carlo algorithm that uses the geometry of the log-posterior surface to make large, informed jumps through parameter space instead of the small random steps of classical MCMC. Originally introduced for lattice field theory by Duane, Kennedy, Pendleton, and Roweth (1987) under the name Hybrid Monte Carlo, and brought into mainstream statistics by Radford Neal's authoritative 2011 chapter, HMC is today the default sampler in Stan and PyMC and is widely regarded as the state-of-the-art engine for Bayesian posterior inference in high-dimensional models. |
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