Linganisha mbinu

	Mchanganuo wa Gibbs wa Angani	MCMC ya Angani
Nyanja	Mbinu za Bayes	Mbinu za Bayes
Familia	Bayesian methods	Bayesian methods
Mwaka wa asili	1984	1990s
Mwanzilishi	Stuart Geman and Donald Geman	Gelfand, Smith, and colleagues (early 1990s MCMC for spatial models)
Aina	MCMC sampling algorithm for spatial models	Bayesian computational method
Chanzo asilia	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
Majina mbadala	Gibbs sampler for spatial models, MRF Gibbs sampling, spatial MCMC via Gibbs, conditional field simulation	spatial Markov chain Monte Carlo, MCMC for spatial data, spatial Bayesian MCMC, geostatistical MCMC
Zinazohusiana	4	4
Muhtasari	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 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.