Vertaile menetelmiä

	Spatial MCMC	Hierarkkinen Bayesiläinen päättely
Tieteenala	Bayesilainen tilastotiede	Bayesilainen tilastotiede
Menetelmäperhe	Bayesian methods	Bayesian methods
Syntyvuosi	1990s	1972 (Lindley & Smith); consolidated 1995–2013
Kehittäjä	Gelfand, Smith, and colleagues (early 1990s MCMC for spatial models)	Lindley & Smith; Gelman et al.
Tyyppi	Bayesian computational method	Bayesian multilevel model
Alkuperäislähde	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
Rinnakkaisnimet	spatial Markov chain Monte Carlo, MCMC for spatial data, spatial Bayesian MCMC, geostatistical MCMC	multilevel Bayesian modeling, Bayesian hierarchical model, nested Bayesian model, partial pooling model
Liittyvät	4	6
Tiivistelmä	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.	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.