Minimizing Weighted Mean of Inefficiency for Robust Designs

Seo, Han-Son

  • 발행 : 2008.01.31


This paper addresses issues of robustness in Bayesian optimal design. We may have difficulty applying Bayesian optimal design principles because of the uncertainty of prior distribution. When there are several plausible prior distributions and the efficiency of a design depends on the unknown prior distribution, robustness with respect to misspecification of prior distribution is required. We suggest a new optimal design criterion which has relatively high efficiencies across the class of plausible prior distributions. The criterion is applied to the problem of estimating the turning point of a quadratic regression, and both analytic and numerical results are shown to demonstrate its robustness.


Bayesian design;optimality;robustness


  1. Chaloner, K. and Larntz, K. (1989). Optimal Bayesian design applied to logistic regression experiments. Journal of Statistical Planning and Inference, 21, 191-208
  2. DasGupta, A and Studden, W. J. (1991). Robust Bayesian experimental designs in normal linear models. The Annals of Statistics, 19, 1244-1256
  3. El-Krunz, M. Sadi and Studden, W. J. (1991). Bayesian optimal designs for linear regression models. The Annals of Statistics, 19, 2183-2208
  4. Mandal, N. K. (1978). On estimation of the maximal point of a single factor quadratic response function. Calcutta Statistical Association Bulletin, 27, 119-125
  5. Seo, H. S. (2006). Mixture Bayesian Robust Design. Journal of the Korean Society for Quality Management, 34, 48-53
  6. Silvey, S. D. (1980). Optimal Design. Chapman & Hall/CRC, London
  7. Nelder, J. A. and Mead, R. (1965). A simplex method for function minimization. Computer Journal, 7, 308-313
  8. Seo, H. S. (2002). Restricted Bayesian optimal designs in turning point problem. Journal of the Korean Statistical Society, 30, 163-178
  9. Whittle, P. (1973). Some general points in the theory of optimalexperimental design. Journal of the Royal Statistical Society, Ser. B, 35, 123-130
  10. Chaloner, K. (1989). Bayesian design for estimating the turning point of a quadratic regression. Communication in Statistics and Methods, 18, 1385-1400
  11. Dette, H (1990). A generalization of D- and Dl-optimal designs in polynomial regression. The Annals of Statistics, 18, 1784-1804