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A Bayesian Estimator of the Optimum for a Single Factor Quadratic Response Model
Author(s) -
Fan T. H.,
Karson M. J.,
Wang H. S.
Publication year - 1996
Publication title -
biometrical journal
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.108
H-Index - 63
eISSN - 1521-4036
pISSN - 0323-3847
DOI - 10.1002/bimj.4710380204
Subject(s) - mathematics , bayesian linear regression , bayesian probability , bayes estimator , estimator , prior probability , context (archaeology) , statistics , quadratic equation , conjugate prior , marginal likelihood , bayesian inference , paleontology , geometry , biology
Estimation of the location and magnitude of the optimum has long been considered an important problem in response surface methodology. In the industrial context, prior information accumulated by the subject matter specialist bears special significance. In this paper we use the Bayesian approach to estimating the optimum in a single factor quadratic regression model. Following the Bayesian general linear model development by Broemeling the normal/gamma conjugate prior is used. Explicit formulas for the generalized maximum likehood estimates of the characteristic parameters are obtained from the joint posterior distribution.