Сравнение методов

	Пространственный вариационный вывод	Пространственный MCMC
Область	Байесовские методы	Байесовские методы
Семейство	Bayesian methods	Bayesian methods
Год появления	2009	1990s
Автор метода	Titsias (2009) for sparse GP; Rue, Martino & Chopin (2009) for latent Gaussian spatial models	Gelfand, Smith, and colleagues (early 1990s MCMC for spatial models)
Тип	Approximate Bayesian inference algorithm	Bayesian computational method
Основополагающий источник	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
Другие названия	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
Связанные	5	4
Сводка	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.