Krahasoni metodat

	Metropolis-Hastings me të dhëna të mungueshme	Hamiltonian Monte Carlo me te te dhenave te mungueshme
Fusha	Statistika bajesiane	Statistika bajesiane
Familja	Bayesian methods	Bayesian methods
Viti i origjinës	1953 / 1987	1996–2011
Krijuesi	Metropolis et al. (1953); missing-data extension formalised by Tanner & Wong (1987)	Radford M. Neal (HMC, 1996/2011); missing-data treatment via Bayesian data augmentation (Tanner & Wong, 1987)
Lloji	MCMC sampler with latent-variable augmentation	Bayesian computational sampler
Burimi themelues	Tanner, M. A. & Wong, W. H. (1987). The calculation of posterior distributions by data augmentation. Journal of the American Statistical Association, 82(398), 528-540.	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
Emërtime të tjera	MH with missing data, Metropolis-Hastings data augmentation, MCMC missing data imputation, MH data-augmentation sampler	HMC with missing data, HMC data augmentation, Bayesian HMC imputation, HMC with data augmentation
Të lidhura	6	6
Përmbledhja	Metropolis-Hastings with missing data treats unobserved values as latent variables and samples them jointly with model parameters inside a single MCMC chain. By augmenting the target distribution to include both parameters and missing values, the algorithm yields properly calibrated posterior inference without discarding incomplete cases or requiring a separate imputation step.	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.