قارن الطرق

	الاستدلال البايزي الهرمي	نموذج التأثيرات المختلطة
المجال	بايزي	الإحصاء
العائلة	Bayesian methods	Regression model
سنة النشأة	1972 (Lindley & Smith); consolidated 1995–2013	1982
صاحب الطريقة	Lindley & Smith; Gelman et al.	Laird & Ware
النوع	Bayesian multilevel model	Mixed effects regression
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	Laird, N. M., & Ware, J. H. (1982). Random-effects models for longitudinal data. Biometrics, 38(4), 963–974.
الأسماء البديلة	multilevel Bayesian modeling, Bayesian hierarchical model, nested Bayesian model, partial pooling model	LME, LMM, mixed model, random effects model
ذات صلة	6	4
الملخص	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.	A mixed effects model (or linear mixed model) extends ordinary regression by including both fixed effects — population-level parameters shared by all observations — and random effects that capture subject-, group-, or cluster-level variability. It is the standard tool for repeated-measures, longitudinal, and multilevel data where observations within the same unit are correlated.