Methoden vergleichen

	MCMC bei fehlenden Daten	Hamiltonian Monte Carlo
Fachgebiet	Bayes-Statistik	Bayes-Statistik
Familie	Bayesian methods	Bayesian methods
Entstehungsjahr	1987	1987
Urheber	Tanner & Wong (data augmentation); extended by Gelfand & Smith, Rubin	—
Typ	Bayesian computational method	Gradient-based Markov chain Monte Carlo sampler
Wegweisende Quelle	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.
Aliasnamen	MCMC missing data, data augmentation MCMC, Bayesian multiple imputation, MCMC imputation	HMC, Hybrid Monte Carlo, NUTS, No-U-Turn Sampler
Verwandt	6	3
Zusammenfassung	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.