قارن الطرق

	النموذج الهرمي البيزي	الانحدار البايزي
المجال	بايزي	بايزي
العائلة	Bayesian methods	Bayesian methods
سنة النشأة	2006	—
صاحب الطريقة	Gelman & Hill (2006); Bayesian multilevel tradition	—
النوع	hierarchical probabilistic model	Bayesian linear model
المصدر التأسيسي	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
الأسماء البديلة	multilevel Bayes, Bayesian multilevel model, Bayesian HLM, partial pooling model	bayesian linear regression, probabilistic regression, bayesian regresyon
ذات صلة	4	2
الملخص	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.	Bayesian regression is a probabilistic version of linear regression that treats the model parameters as uncertain quantities. Instead of returning a single best-fit estimate, it combines prior knowledge with the observed data to produce a full posterior probability distribution for each parameter, from which credible intervals and predictions are read off.