Krahasoni metodat

	Markov Chain Monte Carlo (MCMC)	Regresioni Bajesian	Inferencë Variacionale
Fusha	Statistika bajesiane	Statistika bajesiane	Statistika bajesiane
Familja	Bayesian methods	Bayesian methods	Bayesian methods
Viti i origjinës	—	—	1999
Krijuesi	—	—	Jordan, Ghahramani, Jaakkola & Saul
Lloji	Posterior sampling algorithm	Bayesian linear model	Approximate Bayesian inference
Burimi themelues	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	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.
Emërtime të tjera	markov chain monte carlo, MCMC sampling, MCMC (Markov Zinciri Monte Carlo)	bayesian linear regression, probabilistic regression, bayesian regresyon	VI, variational Bayes, VB, mean-field variational inference
Të lidhura	3	2	4
Përmbledhja	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.	Bayesian regression is a probabilistic version of linear regression that treats the model parameters as uncertain quantities. Instead of returning a single best-fit estimate, it combines prior knowledge with the observed data to produce a full posterior probability distribution for each parameter, from which credible intervals and predictions are read off.	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.