مقایسهٔ روش‌ها

	زنجیره مارکوف مونت کارلو (MCMC)	استنتاج تغییری
حوزه	بیزی	بیزی
خانواده	Bayesian methods	Bayesian methods
سال پیدایش	—	1999
پدیدآور	—	Jordan, Ghahramani, Jaakkola & Saul
نوع	Posterior sampling algorithm	Approximate Bayesian inference
منبع بنیادین	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.
نام‌های دیگر	markov chain monte carlo, MCMC sampling, MCMC (Markov Zinciri Monte Carlo)	VI, variational Bayes, VB, mean-field variational inference
مرتبط	3	4
خلاصه	Markov Chain Monte Carlo (MCMC) is a family of computational algorithms for sampling from complex probability distributions, most commonly the posterior distributions that arise in Bayesian inference. Rather than computing posteriors analytically — which is rarely possible for realistic models — MCMC constructs a Markov chain whose stationary distribution is the target posterior and draws dependent samples from it, enabling full probabilistic inference for virtually any model.	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.