مقایسهٔ روش‌ها

	شبکه بیزی چندسطحی	MCMC چندسطحی (Multilevel MCMC)
حوزه	بیزی	بیزی
خانواده	Bayesian methods	Bayesian methods
سال پیدایش	1990s–2000s	1990s
پدیدآور	Extension of Pearl's Bayesian networks; multilevel formulation developed in statistical relational learning community, 1990s–2000s	Gelfand & Smith (sampling-based approach); multilevel extension developed through 1990s Bayesian hierarchical modeling literature
نوع	Probabilistic graphical model (hierarchical)	Bayesian computational inference
منبع بنیادین	Koller, D. & Friedman, N. (2009). Probabilistic Graphical Models: Principles and Techniques. MIT Press. ISBN: 978-0262013192	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
نام‌های دیگر	multi-level Bayesian network, hierarchical Bayesian network, MLBN, multilevel probabilistic graphical model	hierarchical MCMC, multilevel Bayesian sampling, MLMCMC, hierarchical Markov chain Monte Carlo
مرتبط	6	6
خلاصه	A multilevel Bayesian network extends the standard Bayesian network to data with hierarchical or grouped structure — students within schools, patients within hospitals, observations within subjects — by placing separate but linked graphical models at each level, with higher-level parameters governing the conditional probability tables of lower-level nodes. The result is a principled probabilistic framework that captures both within-group relationships and between-group variation.	Multilevel MCMC applies Markov chain Monte Carlo sampling to hierarchical (multilevel) Bayesian models. It draws samples from the joint posterior of both group-level and population-level parameters simultaneously, propagating uncertainty across levels and enabling inference in clustered or nested data structures where observations within groups share common distributional characteristics.