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Generating a Random Collection of Discrete Joint Probability Distributions Subject to Partial Information

Author

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  • Luis V. Montiel

    (The University of Texas at Austin)

  • J. Eric Bickel

    (The University of Texas at Austin)

Abstract

In this paper, we develop a practical and flexible methodology for generating a random collection of discrete joint probability distributions, subject to a specified information set, which can be expressed as a set of linear constraints (e.g., marginal assessments, moments, or pairwise correlations). Our approach begins with the construction of a polytope using this set of linear constraints. This polytope defines the set of all joint distributions that match the given information; we refer to this set as the “truth set.” We then implement a Monte Carlo procedure, the Hit-and-Run algorithm, to sample points uniformly from the truth set. Each sampled point is a joint distribution that matches the specified information. We provide guidelines to determine the quality of this sampled collection. The sampled points can be used to solve optimization models and to simulate systems under different uncertainty scenarios.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:metcap:v:15:y:2013:i:4:d:10.1007_s11009-012-9292-9
    DOI: 10.1007/s11009-012-9292-9
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    References listed on IDEAS

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    1. Brian K. Schmidt & T. H. Mattheiss, 1977. "The Probability that a Random Polytope is Bounded," Mathematics of Operations Research, INFORMS, vol. 2(3), pages 292-296, August.
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    Cited by:

    1. Ying Chen & John J. Hasenbein, 2017. "Staffing large-scale service systems with distributional uncertainty," Queueing Systems: Theory and Applications, Springer, vol. 87(1), pages 55-79, October.

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