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| Räumliche Monte-Carlo-Simulation× | Gibbs-Sampling× | |
|---|---|---|
| Fachgebiet | Bayes-Statistik | Bayes-Statistik |
| Familie | Bayesian methods | Bayesian methods |
| Entstehungsjahr≠ | 1970s–1980s | 1984 |
| Urheber≠ | B. D. Ripley and the spatial statistics tradition | Stuart Geman & Donald Geman |
| Typ≠ | computational simulation | MCMC sampling algorithm |
| Wegweisende Quelle≠ | Ripley, B. D. (1987). Stochastic Simulation. John Wiley & Sons. ISBN: 978-0471818847 | 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. DOI ↗ |
| Aliasnamen | spatial MC simulation, Monte Carlo spatial analysis, stochastic spatial simulation, spatial stochastic simulation | Gibbs sampler, coordinate-wise MCMC, systematic scan Gibbs, blocked Gibbs sampling |
| Verwandt≠ | 4 | 5 |
| Zusammenfassung≠ | 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. | 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. |
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