قارن الطرق

	الاستدلال البايزي الهرمي	الاستدلال التبايني
المجال	بايزي	بايزي
العائلة	Bayesian methods	Bayesian methods
سنة النشأة	1972 (Lindley & Smith); consolidated 1995–2013	1999
صاحب الطريقة	Lindley & Smith; Gelman et al.	Jordan, Ghahramani, Jaakkola & Saul
النوع	Bayesian multilevel model	Approximate Bayesian inference
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	Jordan, M. I., Ghahramani, Z., Jaakkola, T. S., & Saul, L. K. (1999). An introduction to variational methods for graphical models. Machine Learning, 37(2), 183–233.
الأسماء البديلة	multilevel Bayesian modeling, Bayesian hierarchical model, nested Bayesian model, partial pooling model	VI, variational Bayes, VB, mean-field variational inference
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.	Variational inference (VI) is a family of techniques that turn Bayesian posterior computation into an optimisation problem. Instead of drawing samples from the exact posterior — as Markov chain Monte Carlo does — VI posits a simpler, tractable family of distributions and finds the member of that family closest to the true posterior by maximising the evidence lower bound (ELBO). Introduced in its modern graphical-model form by Jordan, Ghahramani, Jaakkola and Saul (1999) and given a comprehensive statistical treatment by Blei, Kucukelbir and McAuliffe (2017), VI is now the standard scalable inference engine in probabilistic machine learning.