Maximum Uncertainty Procedures for Interval-Valued Probability Distributions

Measures of uncertainty and divergence are introduced for interval-valued probability distributions and are shown to have desirable mathematical properties. A maximum uncertainty inference procedure for marginal interval distributions is presented. A technique for reconstruction of interval distributions from projections is developed based on this inference procedure. They may represent collections of confidence intervals derived from frequency data, imprecisely stated subjective probabilities, known linear equality or inequality constraints, etc. Thus, interval distributions sometimes provide a more realistic characterization of uncertainty than do real-valued probability distributions.