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Generating A Random Collection Of Discrete Joint Probability Distributions Subject To Partial Information, Luis V. Montiel, J. Eric Bickel

Eric Bickel

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 aMonte Carlo procedure, the Hit-and- Run algorithm, to sample points uniformly from the truth set. Each sampled …