Vertaile menetelmiä

	Spatial MCMC	Gibbs-otanta
Tieteenala	Bayesilainen tilastotiede	Bayesilainen tilastotiede
Menetelmäperhe	Bayesian methods	Bayesian methods
Syntyvuosi	1990s	1984
Kehittäjä	Gelfand, Smith, and colleagues (early 1990s MCMC for spatial models)	Stuart Geman & Donald Geman
Tyyppi	Bayesian computational method	MCMC sampling algorithm
Alkuperäislähde	Banerjee, S., Carlin, B. P., & Gelfand, A. E. (2015). Hierarchical Modeling and Analysis for Spatial Data (2nd ed.). CRC Press. ISBN: 978-1439819173	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.
Rinnakkaisnimet	spatial Markov chain Monte Carlo, MCMC for spatial data, spatial Bayesian MCMC, geostatistical MCMC	Gibbs sampler, coordinate-wise MCMC, systematic scan Gibbs, blocked Gibbs sampling
Liittyvät	4	5
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.	Gibbs sampling is a Markov chain Monte Carlo algorithm that approximates a high-dimensional posterior distribution by repeatedly drawing each parameter from its full conditional distribution given all other parameters and the data. Because each draw is exact from a conditional — not a proposal that may be rejected — the sampler is efficient when those conditionals are available in closed form.