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	Hamiltonian Monte Carlo con Dati Mancanti	Hamiltonian Monte Carlo
Campo	Bayesiano	Bayesiano
Famiglia	Bayesian methods	Bayesian methods
Anno di origine	1996–2011	1987
Ideatore	Radford M. Neal (HMC, 1996/2011); missing-data treatment via Bayesian data augmentation (Tanner & Wong, 1987)	—
Tipo	Bayesian computational sampler	Gradient-based Markov chain Monte Carlo sampler
Fonte seminale	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.
Alias	HMC with missing data, HMC data augmentation, Bayesian HMC imputation, HMC with data augmentation	HMC, Hybrid Monte Carlo, NUTS, No-U-Turn Sampler
Correlati	6	3
Sintesi	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.