手法を比較

	クレディビリティ理論	ベイズ階層モデル	ボーナス・マルス制度
分野	保険数理学	ベイズ	保険数理学
系統	Regression model	Bayesian methods	Regression model
提唱年	1967	2006	1995
提唱者	Hans Bühlmann	Gelman & Hill (2006); Bayesian multilevel tradition	Jean Lemaire
種類	Weighted linear blend of individual and collective experience	hierarchical probabilistic model	Actuarial experience-rating model
原典	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.	Lemaire, J. (1995). Bonus-Malus Systems in Automobile Insurance. Kluwer Academic Publishers. ISBN: 978-0-7923-9545-5
別名	Bühlmann Credibility, Experience Rating, Linear Credibility Estimator, Güvenilirlik Teorisi	multilevel Bayes, Bayesian multilevel model, Bayesian HLM, partial pooling model	No-Claim Discount System, Merit Rating System, Experience Rating in Automobile Insurance, Prim-Ceza Sistemi
関連	3	4	2
概要	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.	A Bonus-Malus System (BMS) is an actuarial experience-rating mechanism used primarily in automobile insurance to adjust individual policyholders' premiums based on their personal claim history. Policyholders who remain claim-free receive premium discounts (bonus), while those who file claims are penalised with surcharges (malus). The framework was comprehensively formalised and analysed by Jean Lemaire in his landmark 1995 monograph, which remains the definitive reference for the design and evaluation of such systems worldwide.