Linganisha mbinu

	Uchanganuzi wa Bayesi wa Ngazi Nyingi	Utoaji wa Kigezo
Nyanja	Mbinu za Bayes	Mbinu za Bayes
Familia	Bayesian methods	Bayesian methods
Mwaka wa asili	1980s–2000s	1999
Mwanzilishi	Gelman, Hill, Raudenbush, Bryk	Jordan, Ghahramani, Jaakkola & Saul
Aina	Bayesian hierarchical model	Approximate Bayesian inference
Chanzo asilia	Gelman, A., & Hill, J. (2007). Data Analysis Using Regression and Multilevel/Hierarchical Models. Cambridge University Press. ISBN: 978-0521686891	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.
Majina mbadala	Bayesian multilevel model, Bayesian hierarchical model, Bayesian mixed-effects model, Bayesian random-effects model	VI, variational Bayes, VB, mean-field variational inference
Zinazohusiana	6	4
Muhtasari	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.	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.