قارن الطرق

	متروبوليس-هاستينغز متعدد المستويات	الاستدلال البايزي متعدد المستويات
المجال	بايزي	بايزي
العائلة	Bayesian methods	Bayesian methods
سنة النشأة	1953 (core); 1990s (multilevel application)	1980s–2000s
صاحب الطريقة	Metropolis et al. (1953); hierarchical extension developed through 1980s–1990s Bayesian computation literature	Gelman, Hill, Raudenbush, Bryk
النوع	MCMC sampling algorithm	Bayesian hierarchical model
المصدر التأسيسي	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
الأسماء البديلة	hierarchical Metropolis-Hastings, multilevel MH, MH for hierarchical models, blocked Metropolis-Hastings	Bayesian multilevel model, Bayesian hierarchical model, Bayesian mixed-effects model, Bayesian random-effects model
ذات صلة	6	6
الملخص	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 Bayesian inference combines Bayesian probability with hierarchical data structures, treating group-level parameters as drawn from a common population distribution. It simultaneously estimates unit-level effects and the hyperparameters governing their variation, propagating full uncertainty through every level of the hierarchy via posterior sampling.