方法对比

	缺失数据下的MCMC	Hamiltonian Monte Carlo
领域	贝叶斯	贝叶斯
方法族	Bayesian methods	Bayesian methods
起源年份	1987	1987
提出者	Tanner & Wong (data augmentation); extended by Gelfand & Smith, Rubin	—
类型	Bayesian computational method	Gradient-based Markov chain Monte Carlo sampler
开创性文献	Little, R. J. A. & Rubin, D. B. (2002). Statistical Analysis with Missing Data (2nd ed.). Wiley. ISBN: 978-0471183860	Duane, S., Kennedy, A. D., Pendleton, B. J., & Roweth, D. (1987). Hybrid Monte Carlo. Physics Letters B, 195(2), 216–222.
别名	MCMC missing data, data augmentation MCMC, Bayesian multiple imputation, MCMC imputation	HMC, Hybrid Monte Carlo, NUTS, No-U-Turn Sampler
相关	6	3
摘要	MCMC with missing data is a Bayesian computational strategy that treats unobserved values as additional unknown parameters. By alternating between sampling the missing values from their predictive distribution and sampling the model parameters from their posterior, the algorithm produces a valid joint posterior that fully accounts for uncertainty introduced by the missingness.	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.