Linganisha mbinu

	Utofatishaji Tofauti wa Kiotomatiki (ADVI)	Usajili wa Bayesian	Markov Chain Monte Carlo (MCMC)
Nyanja	Mbinu za Bayes	Mbinu za Bayes	Mbinu za Bayes
Familia	Bayesian methods	Bayesian methods	Bayesian methods
Mwaka wa asili	2017	—	—
Mwanzilishi	Kucukelbir, Tran, Ranganath, Gelman, Blei	—	—
Aina	Variational inference algorithm	Bayesian linear model	Posterior sampling algorithm
Chanzo asilia	Kucukelbir, A., Tran, D., Ranganath, R., Gelman, A. & Blei, D. M. (2017). Automatic differentiation variational inference. Journal of Machine Learning Research, 18(14), 1–45.	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
Majina mbadala	ADVI, black-box variational inference, automatic variational inference, gradient-based variational inference	bayesian linear regression, probabilistic regression, bayesian regresyon	markov chain monte carlo, MCMC sampling, MCMC (Markov Zinciri Monte Carlo)
Zinazohusiana	3	2	3
Muhtasari	Automatic Differentiation Variational Inference (ADVI) is a black-box algorithm for approximate Bayesian posterior inference, introduced by Kucukelbir, Tran, Ranganath, Gelman, and Blei (2017, JMLR). Given any probabilistic model whose log-joint density is differentiable, ADVI automatically transforms constrained latent variables to unconstrained real space, fits a Gaussian variational family by maximising the evidence lower bound (ELBO) with stochastic gradient ascent, and returns an approximate posterior without model-specific derivations. It is the default variational inference engine in Stan and is available in PyMC and NumPyro.	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.	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.