Methoden vergleichen

	Quantifizierung von Unsicherheiten	Varianzreduktionstechniken für die Monte-Carlo-Simulation
Fachgebiet	Simulation	Simulation
Familie	Process / pipeline	Process / pipeline
Entstehungsjahr	Seminal modern form: 2002	1950s–1980s (technique family)
Urheber	Norbert Wiener (polynomial chaos, 1938); extended to Wiener–Askey scheme by Xiu & Karniadakis (2002)	Hammersley & Morton (antithetic variates, 1956); Lavenberg & Welch (control variates, 1981); importance sampling roots in Kahn & Marshall (1953)
Typ	Computational uncertainty analysis framework	Simulation variance-reduction technique family
Wegweisende Quelle	Xiu, D. & Karniadakis, G.E. (2002). The Wiener-Askey Polynomial Chaos for Stochastic Differential Equations. SIAM Journal on Scientific Computing, 24(2), 619–644.	Ross, S.M. (2012). Simulation (5th ed.). Academic Press. ISBN: 978-0124158252
Aliasnamen	UQ, polynomial chaos expansion, PCE, Kriging surrogate	antithetic variates, control variates, importance sampling, stratified sampling MC
Verwandt	9	4
Zusammenfassung	Uncertainty Quantification (UQ) is a computational framework for systematically measuring how uncertainty in the inputs of a model propagates into uncertainty in its outputs. Building on Wiener's polynomial chaos theory (1938) and formalised for general stochastic problems by Xiu and Karniadakis (2002), UQ uses two primary strategies: Polynomial Chaos Expansion (PCE), which represents the model output as a series of orthogonal polynomials matched to the input distributions, and Kriging (Gaussian process) surrogates, which replace an expensive simulation with a fast statistical approximation fitted to a small set of carefully chosen runs.	Variance reduction techniques are a family of methods that improve the efficiency of Monte Carlo simulation by achieving the same estimation accuracy with fewer random draws. Developed incrementally from the 1950s onward — with antithetic variates attributed to Hammersley and Morton, control variates formalised by Lavenberg and Welch, and importance sampling rooted in Kahn and Marshall — the family includes antithetic variates (AV), control variates (CV), importance sampling (IS), and stratification, each exploiting a different structural property of the target quantity to lower estimator variance without introducing bias.