เปรียบเทียบวิธี

	การอนุมานแบบเบย์ตามลำดับชั้น	การอนุมานแบบแปรผัน
สาขาวิชา	เบย์	เบย์
ตระกูล	Bayesian methods	Bayesian methods
ปีกำเนิด	1972 (Lindley & Smith); consolidated 1995–2013	1999
ผู้ริเริ่ม	Lindley & Smith; Gelman et al.	Jordan, Ghahramani, Jaakkola & Saul
ประเภท	Bayesian multilevel model	Approximate Bayesian inference
แหล่งต้นตำรับ	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.
ชื่อเรียกอื่น	multilevel Bayesian modeling, Bayesian hierarchical model, nested Bayesian model, partial pooling model	VI, variational Bayes, VB, mean-field variational inference
ที่เกี่ยวข้อง	6	4
สรุป	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.