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| Rumligt Kalman-filter× | Spatial MCMC× | |
|---|---|---|
| Fagområde | Bayesiansk | Bayesiansk |
| Familie | Bayesian methods | Bayesian methods |
| Oprindelsesår≠ | 1960 (base); spatial extensions 1990s–2000s | 1990s |
| Ophavsperson≠ | R. E. Kalman (base filter, 1960); extended to spatial settings by Cressie, Wikle and colleagues | Gelfand, Smith, and colleagues (early 1990s MCMC for spatial models) |
| Type≠ | Bayesian state-space model | Bayesian computational method |
| Oprindelig kilde≠ | Cressie, N. & Wikle, C. K. (2011). Statistics for Spatio-Temporal Data. Wiley. ISBN: 978-0-471-69274-4 | Banerjee, S., Carlin, B. P., & Gelfand, A. E. (2015). Hierarchical Modeling and Analysis for Spatial Data (2nd ed.). CRC Press. ISBN: 978-1439819173 |
| Aliasser | spatial state-space filter, spatio-temporal Kalman filter, SKF, spatial dynamic linear model | spatial Markov chain Monte Carlo, MCMC for spatial data, spatial Bayesian MCMC, geostatistical MCMC |
| Relaterede≠ | 6 | 4 |
| Resumé≠ | The spatial Kalman filter applies classical Kalman filtering to spatio-temporal state-space models, treating a spatially distributed latent field as the hidden state that evolves over time. At each time step, the filter recursively predicts the spatial field forward and then updates the prediction with new spatial observations, producing optimal linear estimates of the field and its uncertainty across all locations. | 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. |
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