השוואת שיטות

	מודל היררכי בייסיאני	שרשרת מרקוב מונטה קרלו (MCMC)
תחום	בייסיאני	בייסיאני
משפחה	Bayesian methods	Bayesian methods
שנת המקור	2006	—
הוגה השיטה	Gelman & Hill (2006); Bayesian multilevel tradition	—
סוג	hierarchical probabilistic model	Posterior sampling algorithm
מקור מכונן	Gelman, A. & Hill, J. (2006). Data Analysis Using Regression and Multilevel/Hierarchical Models. Cambridge University Press.	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
כינויים	multilevel Bayes, Bayesian multilevel model, Bayesian HLM, partial pooling model	markov chain monte carlo, MCMC sampling, MCMC (Markov Zinciri Monte Carlo)
קשורות	4	3
תקציר	Bayesian hierarchical modelling, popularised by Gelman and Hill (2006), is a Bayesian approach to nested data structures — such as students within schools within districts — that estimates separate parameters at each level while allowing those levels to share statistical strength through a mechanism called partial pooling. Where a classical hierarchical linear model treats group means as fixed unknown quantities, the Bayesian version places hyperprior distributions on those group means so that information flows freely across levels, producing more reliable group-level estimates whenever any individual group has few observations.	Markov Chain Monte Carlo (MCMC) is a family of computational algorithms for sampling from complex probability distributions, most commonly the posterior distributions that arise in Bayesian inference. Rather than computing posteriors analytically — which is rarely possible for realistic models — MCMC constructs a Markov chain whose stationary distribution is the target posterior and draws dependent samples from it, enabling full probabilistic inference for virtually any model.