手法を比較

	Spatial MCMC	空間ベイズ推論
分野	ベイズ	ベイズ
系統	Bayesian methods	Bayesian methods
提唱年	1990s	1991
提唱者	Gelfand, Smith, and colleagues (early 1990s MCMC for spatial models)	Besag, York & Mollie (CAR prior, 1991); Gelfand & colleagues (Bayesian geostatistics, 1990s)
種類	Bayesian computational method	Bayesian hierarchical spatial model
原典	Banerjee, S., Carlin, B. P., & Gelfand, A. E. (2015). Hierarchical Modeling and Analysis for Spatial Data (2nd ed.). CRC Press. ISBN: 978-1439819173	Banerjee, S., Carlin, B. P. & Gelfand, A. E. (2015). Hierarchical Modeling and Analysis for Spatial Data (2nd ed.). CRC Press. ISBN: 978-1439819173
別名	spatial Markov chain Monte Carlo, MCMC for spatial data, spatial Bayesian MCMC, geostatistical MCMC	Bayesian spatial analysis, Bayesian geostatistics, spatial Bayesian modeling, Bayesian areal modeling
関連	4	2
概要	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.	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.