方法对比

	贝叶斯模型平均 (Bayesian Model Averaging, BMA)	变分推断
领域	贝叶斯	贝叶斯
方法族	Bayesian methods	Bayesian methods
起源年份	1999	1999
提出者	Hoeting, Madigan, Raftery & Volinsky	Jordan, Ghahramani, Jaakkola & Saul
类型	Bayesian model averaging	Approximate Bayesian inference
开创性文献	Hoeting, J. A., Madigan, D., Raftery, A. E. & Volinsky, C. T. (1999). Bayesian Model Averaging: A Tutorial. Statistical Science, 14(4), 382–401.	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.
别名	BMA, Bayesian model combination, Bayesian Model Ortalaması (BMA)	VI, variational Bayes, VB, mean-field variational inference
相关	5	4
摘要	Bayesian Model Averaging (BMA), formalised as a tutorial by Hoeting, Madigan, Raftery and Volinsky in 1999, addresses model uncertainty by averaging over all plausible model specifications rather than selecting a single best model. Each candidate model receives a posterior probability that reflects how well it fits the data given a prior, and predictions or coefficient estimates are formed as weighted averages across the entire model space. This approach reduces the bias and overconfidence that arise when a single selected model is treated as the true one.	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.