方法对比

	Hamiltonian Monte Carlo with Missing Data	Hamiltonian Monte Carlo
领域	贝叶斯	贝叶斯
方法族	Bayesian methods	Bayesian methods
起源年份	1996–2011	1987
提出者	Radford M. Neal (HMC, 1996/2011); missing-data treatment via Bayesian data augmentation (Tanner & Wong, 1987)	—
类型	Bayesian computational sampler	Gradient-based Markov chain Monte Carlo sampler
开创性文献	Neal, R. M. (2011). MCMC using Hamiltonian dynamics. In S. Brooks, A. Gelman, G. Jones & X.-L. Meng (Eds.), Handbook of Markov Chain Monte Carlo (pp. 113-162). CRC Press. ISBN: 978-1420079418	Duane, S., Kennedy, A. D., Pendleton, B. J., & Roweth, D. (1987). Hybrid Monte Carlo. Physics Letters B, 195(2), 216–222.
别名	HMC with missing data, HMC data augmentation, Bayesian HMC imputation, HMC with data augmentation	HMC, Hybrid Monte Carlo, NUTS, No-U-Turn Sampler
相关	6	3
摘要	Hamiltonian Monte Carlo with missing data extends the gradient-based HMC sampler to handle incomplete observations by treating missing values as additional unknown parameters. The posterior over model parameters and missing values is sampled jointly in one efficient pass, exploiting gradient information to explore the high-dimensional joint space with far fewer rejected proposals than random-walk MCMC.	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.