A reference prior for the analysis of a response surface

Standard response surface methodology employs a second order polynomial model to locate the stationary point ξξ of the true response function. To make Bayesian analysis more direct and simpler, we refer to an alternative and equivalent parametrization, which contains ξξ as parameter of interest. The marginal reference prior of ξξ is derived in its general form and particular cases are also given in detail, showing the Bayesian role of rotatability.