Noninformative Bayesian estimation for the optimum in a single factor quadratic response model

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Abstract

The estimation of the location and magnitude of the optimum has long been considered as an important problem in the realm of response surface methodology. In this paper, we consider the Bayes estimates in a single factor quadratic response function, after a reparametrization from the linear model, using noninformative priors. The usual constant noninformative prior for the reparametrized model does not yield a proper posterior, thus it is desirable to consider other noninformative priors such as the Jeffreys prior and reference priors. Comparisons will be made based on the resulting posterior means, variances and credible intervals by examples and simulations.

Original languageEnglish
Pages (from-to)225-240
Number of pages16
JournalTest
Volume10
Issue number2
DOIs
StatePublished - Dec 2001

Keywords

  • Credible interval
  • Jeffreys prior
  • Noninformative prior
  • Posterior mean
  • Posterior variance
  • Reference prior
  • Response surface

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