Methoden vergleichen

	Räumliche Bayes'sche Inferenz	Hierarchische Bayes'sche Inferenz	Spatial MCMC
Fachgebiet	Bayes-Statistik	Bayes-Statistik	Bayes-Statistik
Familie	Bayesian methods	Bayesian methods	Bayesian methods
Entstehungsjahr	1991	1972 (Lindley & Smith); consolidated 1995–2013	1990s
Urheber	Besag, York & Mollie (CAR prior, 1991); Gelfand & colleagues (Bayesian geostatistics, 1990s)	Lindley & Smith; Gelman et al.	Gelfand, Smith, and colleagues (early 1990s MCMC for spatial models)
Typ	Bayesian hierarchical spatial model	Bayesian multilevel model	Bayesian computational method
Wegweisende Quelle	Banerjee, S., Carlin, B. P. & Gelfand, A. E. (2015). Hierarchical Modeling and Analysis for Spatial Data (2nd ed.). CRC Press. ISBN: 978-1439819173	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
Aliasnamen	Bayesian spatial analysis, Bayesian geostatistics, spatial Bayesian modeling, Bayesian areal modeling	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
Verwandt	2	6	4
Zusammenfassung	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.	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.