Linganisha mbinu

	Utoaji wa Kibadala wa Kianthari	Utoaji wa Kigezo
Nyanja	Mbinu za Bayes	Mbinu za Bayes
Familia	Bayesian methods	Bayesian methods
Mwaka wa asili	2009	1999
Mwanzilishi	Titsias (2009) for sparse GP; Rue, Martino & Chopin (2009) for latent Gaussian spatial models	Jordan, Ghahramani, Jaakkola & Saul
Aina	Approximate Bayesian inference algorithm	Approximate Bayesian inference
Chanzo asilia	Titsias, M. K. (2009). Variational learning of inducing variables in sparse Gaussian processes. In Proceedings of the 12th International Conference on Artificial Intelligence and Statistics (AISTATS), PMLR 5, pp. 567-574.	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.
Majina mbadala	SVI spatial, variational Bayes for spatial data, approximate Bayesian inference for spatial models, variational GP inference	VI, variational Bayes, VB, mean-field variational inference
Zinazohusiana	5	4
Muhtasari	Spatial variational inference is a scalable approximate Bayesian method that fits latent Gaussian or Gaussian-process models to georeferenced data by optimising a lower bound on the marginal likelihood. It replaces expensive MCMC sampling with a deterministic optimisation step, making full-posterior uncertainty quantification tractable for large spatial datasets.	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.