Linganisha mbinu

	Mchanganuo wa Gibbs wa Angani	Mifumo Iliyopangwa ya Kibayesiyani
Nyanja	Mbinu za Bayes	Mbinu za Bayes
Familia	Bayesian methods	Bayesian methods
Mwaka wa asili	1984	2006
Mwanzilishi	Stuart Geman and Donald Geman	Gelman & Hill (2006); Bayesian multilevel tradition
Aina	MCMC sampling algorithm for spatial models	hierarchical probabilistic model
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.	Gelman, A. & Hill, J. (2006). Data Analysis Using Regression and Multilevel/Hierarchical Models. Cambridge University Press.
Majina mbadala	Gibbs sampler for spatial models, MRF Gibbs sampling, spatial MCMC via Gibbs, conditional field simulation	multilevel Bayes, Bayesian multilevel model, Bayesian HLM, partial pooling model
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.	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.