Understanding Bayesian Experimental Design with Its Applications

베이지안 실험계획법의 이해와 응용

  • Lee, Gunhee (Graduate School of Business, Sogang University)
  • 이군희 (서강대학교 경영전문대학원)
  • Received : 2014.09.16
  • Accepted : 2014.10.27
  • Published : 2014.12.31


Bayesian experimental design is a useful concept in applied statistics for the design of efficient experiments especially if prior knowledge in the experiment is available. However, a theoretical or numerical approach is not simple to implement. We review the concept of a Bayesian experiment approach for linear and nonlinear statistical models. We investigate relationships between prior knowledge and optimal design to identify Bayesian experimental design process characteristics. A balanced design is important if we do not have prior knowledge; however, prior knowledge is important in design and expert opinions should reflect an efficient analysis. Care should be taken if we set a small sample size with a vague improper prior since both Bayesian design and non-Bayesian design provide incorrect solutions.

본 연구에서는 베이지안 실험계획법에 대하여 논의하고 간단한 모의실험을 통하여 최적화된 베이지안 실험계획법이 어떠한 특징을 가지고 있는지 설명하였다. 실험을 설계하는 경우 연구자는 관심있는 주제가 모수추정인지 아니면 예측인지를 결정하고 사전확률과 우도함수를 기반으로 이에 맞는 사후확률을 찾아 효용함수와 결합하여 최적의 실험설계를 찾는 것이 베이지안 실험계획법의 기본 원리이다. 만일 사전적 정보가 존재하지 않는다면 무정보적 부적합 사전확률을 이용하여 실험을 설계할 수 있으며, 이는 비 베이지안적 접근방법과 일치하게 된다. 만일 모수나 예측값에 대한 사전적 정보가 존재하는 경우에는 베이지안 실험계획법이 유일한 해결 방법이다. 하지만 모형의 복잡도가 증가하게 되면, 최적해를 찾는 과정이 매우 복잡해져서 극복해야 하는 많은 문제점들이 존재하므로 향후 많은 연구가 필요한 분야이다.



  1. Berger, J. O. (1985). Statistical Decision Theory and Bayesian Analysis, Springer, New York.
  2. Box, G. E. P. and Tiao, G. C.(1973). Bayesian Inference in Statistical Analysis, Addison-Wesley, Reading, MA.
  3. Chaloner, K. and Larntz, K.(1989). Optimal Bayesian design applied to logistic regression experiments, Journal of Statistical Planning and Inference, 21, 191-208.
  4. Chaloner, K. and Verdinellli, I.(1995). Bayesian experimental design: A review, Statistical Science, 10, 273-304.
  5. Huan, X. and Marzouk, Y. M.(2013). Simulation-based optimal Bayesian experimental design for nonlinear systems, Journal of Computational Physics, 232, 288-317.
  6. Lindley, D. V. (1972). Bayesian Statistics-A Review, SIAM, Philadelphia.
  7. Nelder, J. A. and Mead, R. (1965). A Simplex method for function minimization, Computer Journal, 7, 308-313.
  8. Raiffa, H. and Schlaifer, R. (1961). Applied Statistical Decision Theory, Harvard Business School, Boston.
  9. Shannon, C. E. (1948). A mathematical theory and communication, Bell System Technology Journal, 27, 379-423, 623-656.
  10. Sun, D., Tsutakawa, R. K. and Lu, W. S. (1996). Bayesian design of experiment for quantal response: What is promised versus what is delivered, Journal of Statistical Planning and Inference, 52, 289-306.
  11. Tanner, M. A. (1998). Tools for Statistical Inference: Methods for the Exploration of Posterior Distributions and Likelihood Functions, Springer, New York.
  12. Tsutakawa, R. K. (1972). Design of experiment for bioassay, Journal of the American Statistical Association, 67, 584-590.