قارن الطرق

	الاستدلال البايزي متعدد المستويات	الاستدلال البايزي الهرمي
المجال	بايزي	بايزي
العائلة	Bayesian methods	Bayesian methods
سنة النشأة	1980s–2000s	1972 (Lindley & Smith); consolidated 1995–2013
صاحب الطريقة	Gelman, Hill, Raudenbush, Bryk	Lindley & Smith; Gelman et al.
النوع	Bayesian hierarchical model	Bayesian multilevel model
المصدر التأسيسي	Gelman, A., & Hill, J. (2007). Data Analysis Using Regression and Multilevel/Hierarchical Models. Cambridge University Press. ISBN: 978-0521686891	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
الأسماء البديلة	Bayesian multilevel model, Bayesian hierarchical model, Bayesian mixed-effects model, Bayesian random-effects model	multilevel Bayesian modeling, Bayesian hierarchical model, nested Bayesian model, partial pooling model
ذات صلة	6	6
الملخص	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.	Hierarchical Bayesian inference is a probabilistic modeling framework that organises parameters into levels, placing priors on the group-level parameters and hyperpriors on the parameters governing those priors. It enables partial pooling of information across groups, balancing the extremes of treating each group as independent or merging them into a single estimate.