Vertaile menetelmiä

	Multilevel Metropolis-Hastings	Monitasoinen Gibbsin otanta
Tieteenala	Bayesilainen tilastotiede	Bayesilainen tilastotiede
Menetelmäperhe	Bayesian methods	Bayesian methods
Syntyvuosi	1953 (core); 1990s (multilevel application)	1990
Kehittäjä	Metropolis et al. (1953); hierarchical extension developed through 1980s–1990s Bayesian computation literature	Geman & Geman (1984); applied to multilevel models by Gelfand & Smith (1990)
Tyyppi	MCMC sampling algorithm	MCMC sampling algorithm
Alkuperäislähde	Gelman, A., Carlin, J. B., Stern, H. S., Dunson, D. B., Vehtari, A. & Rubin, D. B. (2013). Bayesian Data Analysis (3rd ed.). CRC Press. ISBN: 978-1439840955	Gelman, A. & Hill, J. (2007). Data Analysis Using Regression and Multilevel/Hierarchical Models. Cambridge University Press. ISBN: 978-0521686891
Rinnakkaisnimet	hierarchical Metropolis-Hastings, multilevel MH, MH for hierarchical models, blocked Metropolis-Hastings	hierarchical Gibbs sampler, blocked Gibbs sampling for multilevel models, multilevel MCMC via Gibbs, Gibbs sampler for mixed-effects models
Liittyvät	6	6
Tiivistelmä	Multilevel Metropolis-Hastings applies the Metropolis-Hastings MCMC algorithm to hierarchical (multilevel) Bayesian models, sampling jointly from group-level parameters and hyperparameters by proposing candidate values and accepting or rejecting them via a ratio that respects the full joint posterior across all levels of the model.	Multilevel Gibbs sampling applies the Gibbs MCMC algorithm to hierarchical (multilevel) Bayesian models, cycling through the conditional distributions of group-level parameters and population-level hyperparameters in turn. This exploits the conditional independence structure of the hierarchy to draw exact or near-exact samples from a posterior that would otherwise be analytically intractable.