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A Closed-Form EVSI Expression for a Multinomial Data-Generating Process

Author

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  • Adam Fleischhacker

    (Department of Business Administration, University of Delaware, Newark, Delaware 19716)

  • Pak-Wing Fok

    (Department of Mathematical Sciences, University of Delaware, Newark, Delaware 19716)

  • Mokshay Madiman

    (Department of Mathematical Sciences, University of Delaware, Newark, Delaware 19716)

  • Nan Wu

    (Institute for Financial Services Analytics, University of Delaware, Newark, Delaware 19716)

Abstract

This paper derives analytic expressions for the expected value of sample information (EVSI), the expected value of distribution information, and the optimal sample size when data consists of independent draws from a bounded sequence of integers. Because of the challenges of creating tractable EVSI expressions, most existing work valuing data does so in one of three ways: (1) analytically through closed-form expressions on the upper bound of the value of data, (2) calculating the expected value of data using numerical comparisons of decisions made using simulated data to optimal decisions for which the underlying data distribution is known, or (3) using variance reduction as proxy for the uncertainty reduction that accompanies more data. For the very flexible case of modeling integer-valued observations using a multinomial data-generating process with Dirichlet prior, this paper develops expressions that (1) generalize existing beta-binomial computations, (2) do not require prior knowledge of some underlying “true” distribution, and (3) can be computed prior to the collection of any sample data.

Suggested Citation

  • Adam Fleischhacker & Pak-Wing Fok & Mokshay Madiman & Nan Wu, 2023. "A Closed-Form EVSI Expression for a Multinomial Data-Generating Process," Decision Analysis, INFORMS, vol. 20(1), pages 73-84, March.
    • Handle: RePEc:inm:ordeca:v:20:y:2023:i:1:p:73-84
    DOI: 10.1287/deca.2022.0462
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    as
    1. Li Chen & Erica L. Plambeck, 2008. "Dynamic Inventory Management with Learning About the Demand Distribution and Substitution Probability," Manufacturing & Service Operations Management, INFORMS, vol. 10(2), pages 236-256, May.
    2. Mark Strong & Jeremy E. Oakley & Alan Brennan & Penny Breeze, 2015. "Estimating the Expected Value of Sample Information Using the Probabilistic Sensitivity Analysis Sample," Medical Decision Making, , vol. 35(5), pages 570-583, July.
    3. Ronald W. Hilton, 1981. "The Determinants of Information Value: Synthesizing Some General Results," Management Science, INFORMS, vol. 27(1), pages 57-64, January.
    4. Hawre Jalal & Fernando Alarid-Escudero, 2018. "A Gaussian Approximation Approach for Value of Information Analysis," Medical Decision Making, , vol. 38(2), pages 174-188, February.
    5. Marshall Fisher & Kumar Rajaram & Ananth Raman, 2001. "Optimizing Inventory Replenishment of Retail Fashion Products," Manufacturing & Service Operations Management, INFORMS, vol. 3(3), pages 230-241, November.
    6. Gary D. Eppen & Ananth. V. Iyer, 1997. "Improved Fashion Buying with Bayesian Updates," Operations Research, INFORMS, vol. 45(6), pages 805-819, December.
    7. Yigal Gerchak & David Mossman, 1992. "On the Effect of Demand Randomness on Inventories and Costs," Operations Research, INFORMS, vol. 40(4), pages 804-807, August.
    8. Satoshi Morita & Peter F. Thall & Peter Müller, 2008. "Determining the Effective Sample Size of a Parametric Prior," Biometrics, The International Biometric Society, vol. 64(2), pages 595-602, June.
    9. Woonghee Tim Huh & Retsef Levi & Paat Rusmevichientong & James B. Orlin, 2011. "Adaptive Data-Driven Inventory Control with Censored Demand Based on Kaplan-Meier Estimator," Operations Research, INFORMS, vol. 59(4), pages 929-941, August.
    10. Jinfeng Yue & Bintong Chen & Min-Chiang Wang, 2006. "Expected Value of Distribution Information for the Newsvendor Problem," Operations Research, INFORMS, vol. 54(6), pages 1128-1136, December.
    11. Yelland, Phillip M., 2009. "Bayesian forecasting for low-count time series using state-space models: An empirical evaluation for inventory management," International Journal of Production Economics, Elsevier, vol. 118(1), pages 95-103, March.
    12. Zhiyuan Wang & Zhiqiang (Eric) Zheng & Wei Jiang & Shaojie Tang, 2021. "Blockchain‐Enabled Data Sharing in Supply Chains: Model, Operationalization, and Tutorial," Production and Operations Management, Production and Operations Management Society, vol. 30(7), pages 1965-1985, July.
    13. Retsef Levi & Georgia Perakis & Joline Uichanco, 2015. "The Data-Driven Newsvendor Problem: New Bounds and Insights," Operations Research, INFORMS, vol. 63(6), pages 1294-1306, December.
    14. Christopher Jackson & Anne Presanis & Stefano Conti & Daniela De Angelis, 2019. "Value of Information: Sensitivity Analysis and Research Design in Bayesian Evidence Synthesis," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 114(528), pages 1436-1449, October.
    15. Gregory A. Godfrey & Warren B. Powell, 2001. "An Adaptive, Distribution-Free Algorithm for the Newsvendor Problem with Censored Demands, with Applications to Inventory and Distribution," Management Science, INFORMS, vol. 47(8), pages 1101-1112, August.
    16. Joseph M. Milner & Panos Kouvelis, 2005. "Order Quantity and Timing Flexibility in Supply Chains: The Role of Demand Characteristics," Management Science, INFORMS, vol. 51(6), pages 970-985, June.
    17. A. E. Ades & G. Lu & K. Claxton, 2004. "Expected Value of Sample Information Calculations in Medical Decision Modeling," Medical Decision Making, , vol. 24(2), pages 207-227, March.
    18. Soroush Saghafian & Brian Tomlin, 2016. "The Newsvendor under Demand Ambiguity: Combining Data with Moment and Tail Information," Operations Research, INFORMS, vol. 64(1), pages 167-185, February.
    19. 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.
    20. Retsef Levi & Robin O. Roundy & David B. Shmoys, 2007. "Provably Near-Optimal Sampling-Based Policies for Stochastic Inventory Control Models," Mathematics of Operations Research, INFORMS, vol. 32(4), pages 821-839, November.
    21. Abraham Mehrez, 1985. "Technical Note—The Effect of Risk Aversion on the Expected Value of Perfect Information," Operations Research, INFORMS, vol. 33(2), pages 455-458, April.
    22. Kwak, Jin Kyung & Gavirneni, Srinagesh, 2011. "Retailer policy, uncertainty reduction, and supply chain performance," International Journal of Production Economics, Elsevier, vol. 132(2), pages 271-278, August.
    23. J. Eric Bickel, 2008. "The Relationship Between Perfect and Imperfect Information in a Two-Action Risk-Sensitive Problem," Decision Analysis, INFORMS, vol. 5(3), pages 116-128, September.
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