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	Spatial Gibbs Sampling	Rumslig Bayesiansk slutsats
Ämnesområde	Bayesiansk statistik	Bayesiansk statistik
Familj	Bayesian methods	Bayesian methods
Ursprungsår	1984	1991
Upphovsperson	Stuart Geman and Donald Geman	Besag, York & Mollie (CAR prior, 1991); Gelfand & colleagues (Bayesian geostatistics, 1990s)
Typ	MCMC sampling algorithm for spatial models	Bayesian hierarchical spatial model
Ursprungskälla	Geman, S. & Geman, D. (1984). Stochastic relaxation, Gibbs distributions, and the Bayesian restoration of images. IEEE Transactions on Pattern Analysis and Machine Intelligence, 6(6), 721–741.	Banerjee, S., Carlin, B. P. & Gelfand, A. E. (2015). Hierarchical Modeling and Analysis for Spatial Data (2nd ed.). CRC Press. ISBN: 978-1439819173
Alias	Gibbs sampler for spatial models, MRF Gibbs sampling, spatial MCMC via Gibbs, conditional field simulation	Bayesian spatial analysis, Bayesian geostatistics, spatial Bayesian modeling, Bayesian areal modeling
Närliggande	4	2
Sammanfattning	Spatial Gibbs sampling applies the Gibbs sampler — a coordinate-wise Markov chain Monte Carlo algorithm — to models where observations are arranged in space and nearby locations are statistically dependent. By exploiting the conditional independence implied by a spatial neighbourhood structure, each site is updated one at a time given its neighbours, making posterior inference tractable for Markov random fields, Gaussian random fields, and hierarchical geostatistical models.	Spatial Bayesian inference applies Bayesian hierarchical modeling to data indexed by geographic location. By placing structured spatial priors on location-specific random effects, the model borrows information from neighboring regions or nearby points, producing smooth, uncertainty-quantified maps of any spatially varying outcome — disease rates, pollution levels, species abundance, or environmental risk.