A Bayesian Estimator of the Optimum for a Single Factor Quadratic Response Model

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.