Dynamic Sampling Allocation and Design Selection

Yijie Peng (), Chun-Hung Chen (), Michael C. Fu () and Jian-Qiang Hu ()
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Yijie Peng: Department of Management Science, Fudan University, Shanghai 200433, China
Chun-Hung Chen: Department of Systems Engineering and Operations Research, George Mason University, Fairfax, Virginia 22030
Michael C. Fu: Institute for Systems Research, The Robert H. Smith School of Business, University of Maryland, College Park, Maryland 20742
Jian-Qiang Hu: Department of Management Science, Fudan University, Shanghai 200433, China

INFORMS Journal on Computing, 2016, vol. 28, issue 2, pages 195-208

Abstract: We formulate the statistical selection problem in a general dynamic framework comprising fully sequential sampling allocation and optimal design selection. Because the traditional probability of correct selection measure is not sufficient to capture both aspects in this more general framework, we introduce the integrated probability of correct selection to better characterize the objective. As a result, the usual selection policy of choosing the design with the largest sample mean as the estimate of the best is no longer necessarily optimal. Rather, the optimal selection policy is to choose the design that maximizes the posterior integrated probability of correct selection, which is a function of the posterior mean and the correlation structure induced by the posterior variance. Because determining the optimal selection policy is generally intractable, we also devise an approximation scheme to efficiently approximate the optimal selection policy. For the allocation policy, we study an asymptotic policy called general Bayesian budget allocation, which is comprised of a sampling statistic and a sequential rule. The optimal computing budget allocation algorithm can be interpreted as a special case of the asymptotical sampling statistics. Numerical examples are provided to illustrate the potential performance improvements, especially in small sample behavior.

Keywords: statistical selection; Bayesian framework; dynamic sampling allocation; optimal design selection (search for similar items in EconPapers)
Date: 2016
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Persistent link: http://EconPapers.repec.org/RePEc:inm:orijoc:v:28:y:2016:i:2:p:195-208

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