Linganisha mbinu

	Utafsiri wa Kibayes wa Kienyeji	MCMC ya Angani
Nyanja	Mbinu za Bayes	Mbinu za Bayes
Familia	Bayesian methods	Bayesian methods
Mwaka wa asili	1972 (Lindley & Smith); consolidated 1995–2013	1990s
Mwanzilishi	Lindley & Smith; Gelman et al.	Gelfand, Smith, and colleagues (early 1990s MCMC for spatial models)
Aina	Bayesian multilevel model	Bayesian computational method
Chanzo asilia	Gelman, A., Carlin, J. B., Stern, H. S., Dunson, D. B., Vehtari, A. & Rubin, D. B. (2013). Bayesian Data Analysis (3rd ed.). CRC Press. ISBN: 978-1439840955	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	multilevel Bayesian modeling, Bayesian hierarchical model, nested Bayesian model, partial pooling model	spatial Markov chain Monte Carlo, MCMC for spatial data, spatial Bayesian MCMC, geostatistical MCMC
Zinazohusiana	6	4
Muhtasari	Hierarchical Bayesian inference is a probabilistic modeling framework that organises parameters into levels, placing priors on the group-level parameters and hyperpriors on the parameters governing those priors. It enables partial pooling of information across groups, balancing the extremes of treating each group as independent or merging them into a single estimate.	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.