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| Spatiaalinen variaatioinferenssi× | Bayesiläinen hierarkkinen malli× | |
|---|---|---|
| Tieteenala | Bayesilainen tilastotiede | Bayesilainen tilastotiede |
| Menetelmäperhe | Bayesian methods | Bayesian methods |
| Syntyvuosi≠ | 2009 | 2006 |
| Kehittäjä≠ | Titsias (2009) for sparse GP; Rue, Martino & Chopin (2009) for latent Gaussian spatial models | Gelman & Hill (2006); Bayesian multilevel tradition |
| Tyyppi≠ | Approximate Bayesian inference algorithm | hierarchical probabilistic model |
| Alkuperäislähde≠ | 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. link ↗ | Gelman, A. & Hill, J. (2006). Data Analysis Using Regression and Multilevel/Hierarchical Models. Cambridge University Press. DOI ↗ |
| Rinnakkaisnimet≠ | SVI spatial, variational Bayes for spatial data, approximate Bayesian inference for spatial models, variational GP inference | multilevel Bayes, Bayesian multilevel model, Bayesian HLM, partial pooling model |
| Liittyvät≠ | 5 | 4 |
| Tiivistelmä≠ | 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. | Bayesian hierarchical modelling, popularised by Gelman and Hill (2006), is a Bayesian approach to nested data structures — such as students within schools within districts — that estimates separate parameters at each level while allowing those levels to share statistical strength through a mechanism called partial pooling. Where a classical hierarchical linear model treats group means as fixed unknown quantities, the Bayesian version places hyperprior distributions on those group means so that information flows freely across levels, producing more reliable group-level estimates whenever any individual group has few observations. |
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