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

Luis V. Montiel () and J. Eric Bickel ()
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Luis V. Montiel: The University of Texas at Austin
J. Eric Bickel: The University of Texas at Austin

Methodology and Computing in Applied Probability, 2013, vol. 15, issue 4, 951-967

Abstract: 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.

Keywords: Joint probability distributions; Simulation; Hit and run; Polytopes; 90C99; 65C05; 60H99 (search for similar items in EconPapers)
Date: 2013
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Citations: View citations in EconPapers (1)

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DOI: 10.1007/s11009-012-9292-9

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