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	Inferenza Variazionale con Differenziazione Automatica (ADVI)	Catena di Markov Monte Carlo (MCMC)
Campo	Bayesiano	Bayesiano
Famiglia	Bayesian methods	Bayesian methods
Anno di origine	2017	—
Ideatore	Kucukelbir, Tran, Ranganath, Gelman, Blei	—
Tipo	Variational inference algorithm	Posterior sampling algorithm
Fonte seminale	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
Alias	ADVI, black-box variational inference, automatic variational inference, gradient-based variational inference	markov chain monte carlo, MCMC sampling, MCMC (Markov Zinciri Monte Carlo)
Correlati	3	3
Sintesi	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.	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.