Linganisha mbinu

	Uiguzi wa Monte Carlo wa Angani	Uchanganuzi wa Mfumo wa Markov wa Monte Carlo (MCMC)
Nyanja	Mbinu za Bayes	Uigaji
Familia	Bayesian methods	Process / pipeline
Mwaka wa asili	1970s–1980s	1953 (Metropolis-Hastings); 1984 (Gibbs)
Mwanzilishi	B. D. Ripley and the spatial statistics tradition	Metropolis et al. (1953); Gibbs sampler formalised by Geman & Geman (1984)
Aina	computational simulation	Simulation-based Bayesian inference / numerical integration
Chanzo asilia	Ripley, B. D. (1987). Stochastic Simulation. John Wiley & Sons. ISBN: 978-0471818847	Gelman, A., Carlin, J.B., Stern, H.S., Dunson, D.B., Vehtari, A. & Rubin, D.B. (2013). Bayesian Data Analysis (3rd ed.). Chapman & Hall/CRC.
Majina mbadala	spatial MC simulation, Monte Carlo spatial analysis, stochastic spatial simulation, spatial stochastic simulation	MCMC, Metropolis-Hastings, Gibbs sampling, Markov Zinciri Monte Carlo (MCMC — Metropolis-Hastings, Gibbs)
Zinazohusiana	4	5
Muhtasari	Spatial Monte Carlo simulation applies random sampling methods to spatial problems, generating many stochastic realisations of a spatial process — such as a random field, point pattern, or network — to estimate distributional properties, propagate uncertainty, or test spatial hypotheses. It is a cornerstone technique in geostatistics, spatial epidemiology, ecology, and environmental modelling.	Markov Chain Monte Carlo (MCMC) is a family of simulation algorithms that constructs a Markov chain whose stationary distribution is the target posterior, enabling Bayesian inference and high-dimensional integral computation that would otherwise be analytically intractable. Pioneered by Metropolis and colleagues in 1953 and extended by Hastings in 1970, MCMC underpins modern Bayesian statistics. The two most widely used variants are Metropolis-Hastings, which proposes moves from a general proposal distribution, and Gibbs sampling, which draws each parameter in turn from its full conditional distribution.