השוואת שיטות

	הסקה וריאציונית מרחבית	MCMC מרחבי
תחום	בייסיאני	בייסיאני
משפחה	Bayesian methods	Bayesian methods
שנת המקור	2009	1990s
הוגה השיטה	Titsias (2009) for sparse GP; Rue, Martino & Chopin (2009) for latent Gaussian spatial models	Gelfand, Smith, and colleagues (early 1990s MCMC for spatial models)
סוג	Approximate Bayesian inference algorithm	Bayesian computational method
מקור מכונן	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.	Banerjee, S., Carlin, B. P., & Gelfand, A. E. (2015). Hierarchical Modeling and Analysis for Spatial Data (2nd ed.). CRC Press. ISBN: 978-1439819173
כינויים	SVI spatial, variational Bayes for spatial data, approximate Bayesian inference for spatial models, variational GP inference	spatial Markov chain Monte Carlo, MCMC for spatial data, spatial Bayesian MCMC, geostatistical MCMC
קשורות	5	4
תקציר	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.	Spatial MCMC applies Markov chain Monte Carlo sampling to Bayesian models that explicitly account for spatial dependence among observations. It draws posterior samples from models such as conditional autoregressive (CAR), simultaneous autoregressive (SAR), or geostatistical (Gaussian process) models, yielding full uncertainty distributions for spatially structured parameters like random effects, regression coefficients, and spatial range.