مقایسهٔ روش‌ها

	همیلتونیَن مونت کارلو با داده‌های گمشده	چندگانه سازی
حوزه	بیزی	آمار
خانواده	Bayesian methods	Process / pipeline
سال پیدایش	1996–2011	1987
پدیدآور	Radford M. Neal (HMC, 1996/2011); missing-data treatment via Bayesian data augmentation (Tanner & Wong, 1987)	Donald B. Rubin
نوع	Bayesian computational sampler	Missing-data handling procedure
منبع بنیادین	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	Rubin, D.B. (1987). Multiple Imputation for Nonresponse in Surveys. Wiley.
نام‌های دیگر	HMC with missing data, HMC data augmentation, Bayesian HMC imputation, HMC with data augmentation	MICE, Multivariate Imputation by Chained Equations, Çoklu Atama (Multiple Imputation — MICE)
مرتبط	6	1
خلاصه	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.	Multiple Imputation (MI), formally introduced by Donald B. Rubin in 1987, is a principled statistical procedure for handling missing data. Rather than replacing each missing value once, MI fills the gaps m times — each time drawing plausible values from the posterior predictive distribution of the missing data — producing m complete datasets. Each dataset is analysed independently, and the results are combined into a single set of estimates using Rubin's pooling rules. The MICE variant (Multivariate Imputation by Chained Equations), popularised by van Buuren and Groothuis-Oudshoorn (2011), extends the approach to mixed variable types by imputing each variable in turn through a sequence of conditional regression models.