Võrdle meetodeid

	Metropolis-Hastings koos puuduvate andmetega	Hamiltonian Monte Carlo koos puuduvate andmetega
Valdkond	Bayesi meetodid	Bayesi meetodid
Perekond	Bayesian methods	Bayesian methods
Tekkeaasta	1953 / 1987	1996–2011
Looja	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)
Tüüp	MCMC sampler with latent-variable augmentation	Bayesian computational sampler
Algallikas	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
Rööpnimetused	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
Seotud	6	6
Kokkuvõte	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.