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| Bayesian Monte Carlo Simulation× | Markov Chain Monte Carlo (MCMC)× | |
|---|---|---|
| Fachgebiet | Simulation | Simulation |
| Familie | Process / pipeline | Process / pipeline |
| Entstehungsjahr≠ | 1987–1990s | 1953 (Metropolis-Hastings); 1984 (Gibbs) |
| Urheber≠ | O'Hagan, A. and colleagues | Metropolis et al. (1953); Gibbs sampler formalised by Geman & Geman (1984) |
| Typ≠ | Simulation / uncertainty quantification | Simulation-based Bayesian inference / numerical integration |
| Wegweisende Quelle≠ | O'Hagan, A., Buck, C. E., Daneshkhah, A., Eiser, J. R., Garthwaite, P. H., Jenkinson, D. J., Oakley, J. E., & Rakow, T. (2006). Uncertain Judgements: Eliciting Experts' Probabilities. Wiley. ISBN: 9780470029992 | 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 ↗ |
| Aliasnamen | Bayesian MC, BMC simulation, Bayesian stochastic simulation, Bayesian uncertainty propagation | MCMC, Metropolis-Hastings, Gibbs sampling, Markov Zinciri Monte Carlo (MCMC — Metropolis-Hastings, Gibbs) |
| Verwandt≠ | 4 | 5 |
| Zusammenfassung≠ | Bayesian Monte Carlo Simulation integrates Bayesian statistical inference with Monte Carlo sampling to propagate uncertainty through complex models. Instead of drawing samples from arbitrary distributions, it conditions sampling on observed data and expert prior knowledge via Bayes' theorem, yielding posterior-based uncertainty estimates that are both statistically coherent and interpretable in probabilistic terms. | 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. |
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