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Sequential Sampling with Economics of Selection Procedures

Author

Listed:
  • Stephen E. Chick

    (Technology and Operations Management Area, INSEAD, 77305 Fontainebleau, France)

  • Peter Frazier

    (Department of Operations Research and Information Engineering, Cornell University, Ithaca, New York 14853)

Abstract

Sequential sampling problems arise in stochastic simulation and many other applications. Sampling is used to infer the unknown performance of several alternatives before one alternative is selected as best. This paper presents new economically motivated fully sequential sampling procedures to solve such problems, called economics of selection procedures. The optimal procedure is derived for comparing a known standard with one alternative whose unknown reward is inferred with sampling. That result motivates heuristics when multiple alternatives have unknown rewards. The resulting procedures are more effective in numerical experiments than any previously proposed procedure of which we are aware and are easily implemented. The key driver of the improvement is the use of dynamic programming to model sequential sampling as an option to learn before selecting an alternative. It accounts for the expected benefit of adaptive stopping policies for sampling, rather than of one-stage policies, as is common in the literature. This paper was accepted by Assaf Zeevi, stochastic models and simulation.

Suggested Citation

  • Stephen E. Chick & Peter Frazier, 2012. "Sequential Sampling with Economics of Selection Procedures," Management Science, INFORMS, vol. 58(3), pages 550-569, March.
  • Handle: RePEc:inm:ormnsc:v:58:y:2012:i:3:p:550-569
    DOI: 10.1287/mnsc.1110.1425
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    References listed on IDEAS

    as
    1. Peter I. Frazier & Warren B. Powell, 2010. "Paradoxes in Learning and the Marginal Value of Information," Decision Analysis, INFORMS, vol. 7(4), pages 378-403, December.
    2. Brezzi, Monica & Lai, Tze Leung, 2002. "Optimal learning and experimentation in bandit problems," Journal of Economic Dynamics and Control, Elsevier, vol. 27(1), pages 87-108, November.
    3. Stephen E. Chick & Noah Gans, 2009. "Economic Analysis of Simulation Selection Problems," Management Science, INFORMS, vol. 55(3), pages 421-437, March.
    4. Stephen E. Chick & Jürgen Branke & Christian Schmidt, 2010. "Sequential Sampling to Myopically Maximize the Expected Value of Information," INFORMS Journal on Computing, INFORMS, vol. 22(1), pages 71-80, February.
    5. Stephen E. Chick & Koichiro Inoue, 2001. "New Two-Stage and Sequential Procedures for Selecting the Best Simulated System," Operations Research, INFORMS, vol. 49(5), pages 732-743, October.
    Full references (including those not matched with items on IDEAS)

    Citations

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    Cited by:

    1. Tom Dvir & Renana Peres & Ze'ev Rudnick, 2020. "Modelling the expected probability of correct assignment under uncertainty," Papers 2008.05878, arXiv.org.
    2. Jing Xie & Peter I. Frazier, 2013. "Sequential Bayes-Optimal Policies for Multiple Comparisons with a Known Standard," Operations Research, INFORMS, vol. 61(5), pages 1174-1189, October.
    3. Nikhil Bhat & Vivek F. Farias & Ciamac C. Moallemi & Deeksha Sinha, 2020. "Near-Optimal A-B Testing," Management Science, INFORMS, vol. 66(10), pages 4477-4495, October.
    4. Eric M. Schwartz & Eric T. Bradlow & Peter S. Fader, 2017. "Customer Acquisition via Display Advertising Using Multi-Armed Bandit Experiments," Marketing Science, INFORMS, vol. 36(4), pages 500-522, July.
    5. Raluca M. Ursu & Daria Dzyabura, 2020. "Retailers’ product location problem with consumer search," Quantitative Marketing and Economics (QME), Springer, vol. 18(2), pages 125-154, June.
    6. Chao Qin & Daniel Russo, 2024. "Optimizing Adaptive Experiments: A Unified Approach to Regret Minimization and Best-Arm Identification," Papers 2402.10592, arXiv.org, revised Jul 2024.
    7. Weiwei Fan & L. Jeff Hong & Barry L. Nelson, 2016. "Indifference-Zone-Free Selection of the Best," Operations Research, INFORMS, vol. 64(6), pages 1499-1514, December.
    8. Jun Luo & L. Jeff Hong & Barry L. Nelson & Yang Wu, 2015. "Fully Sequential Procedures for Large-Scale Ranking-and-Selection Problems in Parallel Computing Environments," Operations Research, INFORMS, vol. 63(5), pages 1177-1194, October.
    9. Stephen Chick & Martin Forster & Paolo Pertile, 2017. "A Bayesian decision theoretic model of sequential experimentation with delayed response," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 79(5), pages 1439-1462, November.
    10. Banerjee, Subrato, 2020. "Sample sizes in experimental games," Research in Economics, Elsevier, vol. 74(3), pages 221-227.
    11. Daria Dzyabura & John R. Hauser, 2019. "Recommending Products When Consumers Learn Their Preference Weights," Marketing Science, INFORMS, vol. 38(3), pages 417-441, May.
    12. Subrato Banerjee, 2015. "Power analysis and sample sizes: A Binding frontier approach," Discussion Papers 15-04, Indian Statistical Institute, Delhi.
    13. Raluca M. Ursu & Qingliang Wang & Pradeep K. Chintagunta, 2020. "Search Duration," Marketing Science, INFORMS, vol. 39(5), pages 849-871, September.
    14. Victor F. Araman & René A. Caldentey, 2022. "Diffusion Approximations for a Class of Sequential Experimentation Problems," Management Science, INFORMS, vol. 68(8), pages 5958-5979, August.
    15. Annie Liang & Xiaosheng Mu & Vasilis Syrgkanis, 2019. "Optimal and Myopic Information Acquisition," Working Papers 2019-25, Princeton University. Economics Department..
    16. Weiwei Fan & L. Jeff Hong & Xiaowei Zhang, 2020. "Distributionally Robust Selection of the Best," Management Science, INFORMS, vol. 66(1), pages 190-208, January.
    17. Francisco Alvarez, 2018. "Decomposing risk in an exploitation–exploration problem with endogenous termination time," Annals of Operations Research, Springer, vol. 261(1), pages 45-77, February.
    18. Daniel Russo, 2020. "Simple Bayesian Algorithms for Best-Arm Identification," Operations Research, INFORMS, vol. 68(6), pages 1625-1647, November.
    19. Jing Xie & Peter I. Frazier & Stephen E. Chick, 2016. "Bayesian Optimization via Simulation with Pairwise Sampling and Correlated Prior Beliefs," Operations Research, INFORMS, vol. 64(2), pages 542-559, April.
    20. Annie Liang & Xiaosheng Mu & Vasilis Syrgkanis, 2021. "Dynamically Aggregating Diverse Information," Working Papers 2021-43, Princeton University. Economics Department..
    21. Haihui Shen & L. Jeff Hong & Xiaowei Zhang, 2021. "Ranking and Selection with Covariates for Personalized Decision Making," INFORMS Journal on Computing, INFORMS, vol. 33(4), pages 1500-1519, October.
    22. Elea McDonnell Feit & Ron Berman, 2019. "Test & Roll: Profit-Maximizing A/B Tests," Marketing Science, INFORMS, vol. 38(6), pages 1038-1058, November.
    23. Stephen E. Chick & Noah Gans & Özge Yapar, 2022. "Bayesian Sequential Learning for Clinical Trials of Multiple Correlated Medical Interventions," Management Science, INFORMS, vol. 68(7), pages 4919-4938, July.

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