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| Markov Chain Monte Carlo (MCMC)× | Monte-Carlo-Simulation× | |
|---|---|---|
| Fachgebiet≠ | Simulation | Entscheidungsfindung |
| Familie≠ | Process / pipeline | MCDM |
| Entstehungsjahr≠ | 1953 (Metropolis-Hastings); 1984 (Gibbs) | 1949 |
| Urheber≠ | Metropolis et al. (1953); Gibbs sampler formalised by Geman & Geman (1984) | Metropolis, N., Ulam, S. |
| Typ≠ | Simulation-based Bayesian inference / numerical integration | Robustness wrapper — Monte Carlo uncertainty propagation |
| Wegweisende Quelle≠ | 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. DOI ↗ | Metropolis, N., Ulam, S. (1949). The Monte Carlo method. Journal of the American Statistical Association DOI ↗ |
| Aliasnamen≠ | MCMC, Metropolis-Hastings, Gibbs sampling, Markov Zinciri Monte Carlo (MCMC — Metropolis-Hastings, Gibbs) | — |
| Verwandt≠ | 5 | 0 |
| Zusammenfassung≠ | 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. | MONTE-CARLO-SIMULATION (Monte Carlo Simulation — Stochastic uncertainty propagation through MCDM model) is a ranking multi-criteria decision-making (MCDM) method introduced by Metropolis, N., Ulam, S. in 1949. It turns a decision matrix of alternatives scored on multiple criteria into a structured, reproducible result. |
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