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Minimizing Weighted Mean of Inefficiency for Robust Designs

Seo, Han-Son   (Department of Applied Statistics, Konkuk UniversityUU0000050  );
  • 초록

    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.


  • 주제어

    Bayesian design .   optimality .   robustness.  

  • 참고문헌 (11)

    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 

 저자의 다른 논문

  • Seo, Han-Son (19)

    1. 2000 "A Procedure for Fitting Nonadditive Models" 한국통계학회 논문집 = Communications of the Korean Statistical Society 7 (2): 393~401    
    2. 2002 "Dynamic Added Variable Plots" 한국통계학회 논문집 = Communications of the Korean Statistical Society 9 (3): 787~797    
    3. 2003 "사무간접부문에서의 6시그마 경영 활성화 방안" 品質經營學會誌 = Journal of the Korean Society for Quality Management 31 (2): 220~229    
    4. 2004 "Three Dimensional Dynamic Added Variable Plots" 한국통계학회 논문집 = Communications of the Korean Statistical Society 11 (2): 345~353    
    5. 2006 "Mixture Bayesian Robust Design" 品質經營學會誌 = Journal of the Korean Society for Quality Management 34 (1): 48~53    
    6. 2009 "A Dynamic Graphical Method for Transformations and Curvature Specifications in Regression" 응용통계연구 = The Korean journal of applied statistics 22 (1): 189~195    
    7. 2009 "Projected Circular and l-Axial Skew-Normal Distributions" 응용통계연구 = The Korean journal of applied statistics 22 (4): 879~891    
    8. 2011 "서포트벡터 기계를 이용한 이상치 진단" 한국통계학회 논문집 = Communications of the Korean Statistical Society 18 (2): 171~177    
    9. 2011 "동적 그림을 이용한 이상치 검색" 응용통계연구 = The Korean journal of applied statistics 24 (5): 979~986    
    10. 2012 "회귀모형에서 이상치 검색을 이용한 로버스트 변수변환방법" 응용통계연구 = The Korean journal of applied statistics 25 (1): 205~213    

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