RECONSTRUCTABILITY ANALYSIS USING PROBABILITY INTERVALS

It is proposed that probability intervals be used in reconstructability analysis. A probability interval is a subinterval of the real interval 0,1]. Regarded as “interval-valued probabilities”, these intervals generalize real-valued probabilities and arise naturally in many situations. They may represent confidence intervals resulting from sampling; imprecisely stated subjective probabilities; known linear equality or inequality constraints; etc. Thus, probability intervals are sometimes a more realistic characterization of uncertainty than are real-valued probabilities. Furthermore, the problem of inconsistency can often be avoided by their use

Although the utility of interval-valued probability distributions for the identification problem is emphasized, a reconstruction technique is also developed. This reconstruction method employs a metric distance for interval distributions that is monotonic with respect to model refinement.