Journal of Korean Society for Quality Management (품질경영학회지)

Korean Society for Quality Management (한국품질경영학회)
권호 표지

Mixture Bayesian Robust Design

  • Seo, Han-Son (Konkuk University, Department of Applied Statistics)
  • Published : 2006.03.31
Download PDF
⟨ Previous Next ⟩

Abstract

Applying Bayesian optimal design principles is not easy when a prior distribution is not certain. We present a optimal design criterion which possibly yield a reasonably good design and also robust with respect to misspecification of the prior distributions. The criterion is applied to the problem of estimating the turning point of a quadratic regression. Exact mathematical results are presented under certain conditions on prior distributions. Computational results are given for some cases not satisfying our conditions.

Keywords

References

  1. Berger, J. O.(1985), Statistical Decision Theory and Bayesian Analysis, Springer-Verlag, New York
  2. Chaloner, K.(1989), 'Bayesian Design for Estimating the Turning Point of a Quadratic Regression', Communication in Statistics-Simulation and Computation, Vol. 13, pp. 723-731 https://doi.org/10.1080/03610918408812411
  3. Chaloner, K. and Larntz, K.(1989), 'Optimal Bayesian Design Applied to Logistic Regression Experiments', Journal of Statistical Planning and Inference, Vol. 21, pp. 191-208 https://doi.org/10.1016/0378-3758(89)90004-9
  4. DasGupta, A. and Studden, W. J. (1991), 'Robust Bayesian Experimental Designs in Normal Linear Models', The Analysis of Statistics, Vol. 19, pp. 1244-1256 https://doi.org/10.1214/aos/1176348247
  5. Dette, H.(1990), 'A Generalization of D-and $D_1$-optimal designs in polynomial regression', The Analysis of Statistics, Vol. 18, pp. 1784-1804 https://doi.org/10.1214/aos/1176347878
  6. Mandai, N. K.(1978), 'On Estimation of the Maximal Point of a Single Factor Quadratic Response Function', Calcutta Statistical Association Bulletin, Vol. 27, pp. 119-125 https://doi.org/10.1177/0008068319780109
  7. Nelder, J. A. and Mead, R.(1965), 'A Simplex Method for Function Minimization', Computer Journal, Vol. 7, pp. 308-313 https://doi.org/10.1093/comjnl/7.4.308
  8. Seo, H. S.(2001), 'Restricted Bayesian Optimal Designs in Turning Point Problem', JKSS, Vol. 30, pp. 163-178
  9. Whittle, P.(1973), 'Some General Points in the Theory of Optimal Experimental design', Journal of Royal Statistical Society, Series B, Vol. 35, pp. 123-130