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Optimal Sequential Exploration: A Binary Learning Model

Author

Listed:
  • J. Eric Bickel

    (Department of Industrial and Systems Engineering, Texas A&M University, 236B Zachry Engineering Center, 3131 TAMU, College Station, Texas 77843-3131)

  • James E. Smith

    (Fuqua School of Business, Duke University, Box 90120, Durham, North Carolina 27708-0120)

Abstract
In this paper, we develop a practical and flexible framework for evaluating sequential exploration strategies in the case where the exploration prospects are dependent. Our interest in this problem was motivated by an oil exploration problem, and our approach begins with marginal assessments for each prospect (e.g., what is the probability that the well is wet?) and pairwise assessments of the dependence between prospects (e.g., what is the probability that both wells i and j are wet?). We then use information-theoretic methods to construct a full joint distribution for all outcomes from these marginal and pairwise assessments. This joint distribution is straightforward to calculate, has many nice properties, and appears to provide an accurate approximation for distributions likely to be encountered in practice. Given this joint probability distribution, we determine an optimal drilling strategy using an efficient dynamic programming model. We illustrate these techniques with an oil exploration example and study how dependence and risk aversion affect the optimal drilling strategies. The information-theory-based techniques for constructing joint distributions and dynamic programming model for determining optimal exploration strategies could be used together or separately in many other applications.

Suggested Citation

  • J. Eric Bickel & James E. Smith, 2006. "Optimal Sequential Exploration: A Binary Learning Model," Decision Analysis, INFORMS, vol. 3(1), pages 16-32, March.
  • Handle: RePEc:inm:ordeca:v:3:y:2006:i:1:p:16-32
    DOI: 10.1287/deca.1050.0052
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    References listed on IDEAS

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    Cited by:

    1. Sushil Bikhchandani & John W. Mamer, 2013. "Decreasing Marginal Value of Information Under Symmetric Loss," Decision Analysis, INFORMS, vol. 10(3), pages 245-256, September.
    2. David B. Brown & James E. Smith, 2013. "Optimal Sequential Exploration: Bandits, Clairvoyants, and Wildcats," Operations Research, INFORMS, vol. 61(3), pages 644-665, June.
    3. Bell, Peter N, 2015. "Mineral exploration as a game of chance," MPRA Paper 62159, University Library of Munich, Germany.
    4. L. Robin Keller & Ali Abbas & Manel Baucells & Vicki M. Bier & David Budescu & John C. Butler & Philippe Delquié & Jason R. W. Merrick & Ahti Salo & George Wu, 2010. "From the Editors..," Decision Analysis, INFORMS, vol. 7(4), pages 327-330, December.
      • L. Robin Keller & Manel Baucells & Kevin F. McCardle & Gregory S. Parnell & Ahti Salo, 2007. "From the Editors..," Decision Analysis, INFORMS, vol. 4(4), pages 173-175, December.
      • L. Robin Keller & Manel Baucells & John C. Butler & Philippe Delquié & Jason R. W. Merrick & Gregory S. Parnell & Ahti Salo, 2008. "From the Editors..," Decision Analysis, INFORMS, vol. 5(4), pages 173-176, December.
      • L. Robin Keller & Manel Baucells & John C. Butler & Philippe Delquié & Jason R. W. Merrick & Gregory S. Parnell & Ahti Salo, 2009. "From the Editors ..," Decision Analysis, INFORMS, vol. 6(4), pages 199-201, December.
    5. Finn Olesen, 1999. "Monetær integration i EU," Working Papers 2/99, University of Southern Denmark, Department of Sociology, Environmental and Business Economics.
    6. Tianyang Wang & James S. Dyer, 2012. "A Copulas-Based Approach to Modeling Dependence in Decision Trees," Operations Research, INFORMS, vol. 60(1), pages 225-242, February.
    7. Smith, James L. & Thompson, Rex, 2009. "Rational plunging and the option value of sequential investment: The case of petroleum exploration," The Quarterly Review of Economics and Finance, Elsevier, vol. 49(3), pages 1009-1033, August.
    8. Maarten J. Punt & Brooks A. Kaiser, 2021. "Seismic Shifts from Regulations: Spatial Trade-offs in Marine Mammals and the Value of Information from Hydrocarbon Seismic Surveying," Environmental & Resource Economics, Springer;European Association of Environmental and Resource Economists, vol. 80(3), pages 553-585, November.
    9. Luis V. Montiel & J. Eric Bickel, 2013. "Generating a Random Collection of Discrete Joint Probability Distributions Subject to Partial Information," Methodology and Computing in Applied Probability, Springer, vol. 15(4), pages 951-967, December.
    10. Debarun Bhattacharjya & Jo Eidsvik & Tapan Mukerji, 2013. "The Value of Information in Portfolio Problems with Dependent Projects," Decision Analysis, INFORMS, vol. 10(4), pages 341-351, December.
    11. L. Robin Keller, 2009. "From the Editor..," Decision Analysis, INFORMS, vol. 6(3), pages 121-123, September.
    12. Zachary J. Smith & J. Eric Bickel, 2020. "Additive Scoring Rules for Discrete Sample Spaces," Decision Analysis, INFORMS, vol. 17(2), pages 115-133, June.
    13. Martinelli, Gabriele & Eidsvik, Jo & Hauge, Ragnar, 2013. "Dynamic decision making for graphical models applied to oil exploration," European Journal of Operational Research, Elsevier, vol. 230(3), pages 688-702.
    14. L. Robin Keller & Ali Abbas & J. Eric Bickel & Vicki M. Bier & David V. Budescu & John C. Butler & Enrico Diecidue & Robin L. Dillon-Merrill & Raimo P. Hämäläinen & Kenneth C. Lichtendahl & Jason R. W, 2012. "From the Editors ---Brainstorming, Multiplicative Utilities, Partial Information on Probabilities or Outcomes, and Regulatory Focus," Decision Analysis, INFORMS, vol. 9(4), pages 297-302, December.
    15. Tianyang Wang & James S. Dyer & John C. Butler, 2016. "Modeling Correlated Discrete Uncertainties in Event Trees with Copulas," Risk Analysis, John Wiley & Sons, vol. 36(2), pages 396-410, February.
    16. L. Robin Keller, 2008. "From the Editor..," Decision Analysis, INFORMS, vol. 5(3), pages 113-115, September.
    17. van Valkenhoef, Gert & Tervonen, Tommi, 2016. "Entropy-optimal weight constraint elicitation with additive multi-attribute utility models," Omega, Elsevier, vol. 64(C), pages 1-12.
    18. Rakesh K. Sarin & L. Robin Keller, 2013. "From the Editors: Probability Approximations, Anti-Terrorism Strategy, and Bull's-Eye Display for Performance Feedback," Decision Analysis, INFORMS, vol. 10(1), pages 1-5, March.
    19. Tao Huang & J. Eric Bickel, 2019. "Sparse Probability Assessment Heuristic Based on Orthogonal Matching Pursuit," Decision Analysis, INFORMS, vol. 16(4), pages 281-300, December.
    20. Fan, Lin & Hobbs, Benjamin F. & Norman, Catherine S., 2010. "Risk aversion and CO2 regulatory uncertainty in power generation investment: Policy and modeling implications," Journal of Environmental Economics and Management, Elsevier, vol. 60(3), pages 193-208, November.
    21. Christoph Werner & Tim Bedford & John Quigley, 2018. "Sequential Refined Partitioning for Probabilistic Dependence Assessment," Risk Analysis, John Wiley & Sons, vol. 38(12), pages 2683-2702, December.
    22. 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.
    23. Luis V. Montiel & J. Eric Bickel, 2013. "Approximating Joint Probability Distributions Given Partial Information," Decision Analysis, INFORMS, vol. 10(1), pages 26-41, March.
    24. Luis V. Montiel & J. Eric Bickel, 2012. "A Simulation-Based Approach to Decision Making with Partial Information," Decision Analysis, INFORMS, vol. 9(4), pages 329-347, December.

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