Methoden vergleichen

	Kredibilitätstheorie	Bayessches hierarchisches Modell
Fachgebiet	Versicherungsmathematik	Bayes-Statistik
Familie	Regression model	Bayesian methods
Entstehungsjahr	1967	2006
Urheber	Hans Bühlmann	Gelman & Hill (2006); Bayesian multilevel tradition
Typ	Weighted linear blend of individual and collective experience	hierarchical probabilistic model
Wegweisende Quelle	Bühlmann, H. (1967). Experience rating and credibility. ASTIN Bulletin, 4(3), 199–207.	Gelman, A. & Hill, J. (2006). Data Analysis Using Regression and Multilevel/Hierarchical Models. Cambridge University Press.
Aliasnamen	Bühlmann Credibility, Experience Rating, Linear Credibility Estimator, Güvenilirlik Teorisi	multilevel Bayes, Bayesian multilevel model, Bayesian HLM, partial pooling model
Verwandt	3	4
Zusammenfassung	Credibility Theory is an actuarial framework for estimating the pure premium of an individual risk by blending its own observed loss experience with the collective (portfolio) mean. Introduced by Hans Bühlmann in 1967, the method derives the optimal linear combination—the credibility-weighted premium—that minimises mean squared error. It extends classical experience rating to a rigorous statistical footing rooted in Bayesian and linear estimation principles.	Bayesian hierarchical modelling, popularised by Gelman and Hill (2006), is a Bayesian approach to nested data structures — such as students within schools within districts — that estimates separate parameters at each level while allowing those levels to share statistical strength through a mechanism called partial pooling. Where a classical hierarchical linear model treats group means as fixed unknown quantities, the Bayesian version places hyperprior distributions on those group means so that information flows freely across levels, producing more reliable group-level estimates whenever any individual group has few observations.