方法对比
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| 鲁棒哈密顿蒙特卡洛× | Hamiltonian Monte Carlo× | |
|---|---|---|
| 领域 | 贝叶斯 | 贝叶斯 |
| 方法族 | Bayesian methods | Bayesian methods |
| 起源年份≠ | 2010s–2020s | 1987 |
| 提出者≠ | Livingstone, Zanella and related researchers building on Duane et al. (1987) | — |
| 类型≠ | Robust MCMC sampler | Gradient-based Markov chain Monte Carlo sampler |
| 开创性文献≠ | Livingstone, S. & Zanella, G. (2022). The Barker proposal: combining robustness and efficiency in gradient-based MCMC. Journal of the Royal Statistical Society: Series B, 84(2), 496–523. DOI ↗ | Duane, S., Kennedy, A. D., Pendleton, B. J., & Roweth, D. (1987). Hybrid Monte Carlo. Physics Letters B, 195(2), 216–222. DOI ↗ |
| 别名≠ | Robust HMC, heavy-tailed HMC, geometric-ergodic HMC, outlier-robust HMC | HMC, Hybrid Monte Carlo, NUTS, No-U-Turn Sampler |
| 相关≠ | 4 | 3 |
| 摘要≠ | Robust Hamiltonian Monte Carlo (Robust HMC) is a family of extensions to standard HMC designed to maintain geometric ergodicity and sampling efficiency when the posterior has heavy tails, strong curvature variation, or near-degenerate geometry. By modifying the kinetic energy, mass matrix, or proposal mechanism, these methods ensure reliable exploration of difficult posteriors that defeat the standard NUTS/HMC sampler. | 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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