Σύγκριση μεθόδων

	Μέση Τιμή Βαγιεσιανών Χωρικών Μοντέλων	Χωρική Μεταβλητή Συμπερασματολογία
Πεδίο	Μπεϋζιανή Στατιστική	Μπεϋζιανή Στατιστική
Οικογένεια	Bayesian methods	Bayesian methods
Έτος προέλευσης	2008	2009
Δημιουργός	LeSage & Fischer (building on Raftery et al. BMA framework, 1997)	Titsias (2009) for sparse GP; Rue, Martino & Chopin (2009) for latent Gaussian spatial models
Τύπος	Bayesian model combination with spatial structure	Approximate Bayesian inference algorithm
Θεμελιώδης πηγή	LeSage, J. P. & Pace, R. K. (2009). Introduction to Spatial Econometrics. CRC Press / Taylor & Francis. ISBN: 978-1420064247	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.
Εναλλακτικές ονομασίες	spatial BMA, BMA for spatial data, Bayesian model averaging with spatial effects, spatial model uncertainty averaging	SVI spatial, variational Bayes for spatial data, approximate Bayesian inference for spatial models, variational GP inference
Συναφείς	5	5
Σύνοψη	Spatial Bayesian model averaging (spatial BMA) extends classical BMA to settings where observations are georeferenced and spatial dependence must be modelled. Rather than selecting a single spatial regression model — which spatial weight matrix to use, which regressors to include, which spatial lag or error structure to adopt — it averages the predictions and parameter estimates across all candidate models, weighting each by its posterior probability given the data.	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.