Data-based prediction under uncertainty: CDF-quantile distributions and info-gap robustness

Yakov Ben-Haim*, Michael Smithson

*Corresponding author for this work

    Research output: Contribution to journalArticlepeer-review

    2 Citations (Scopus)


    Data underlie understanding of processes and prediction of the future. However, things change; data from one population at one time may have uncertain relevance for modeling or prediction in another population or at another time. Data-based prediction in a changing world requires two complementary capabilities: versatile modeling, integrated with management of uncertainty. We develop a response to this challenge. We focus on statistical models of bounded random variables, associated with additional non-probabilistic uncertainties. We employ CDF-quantile distributions to model the probabilistic aspects of these phenomena. Non-probabilistic uncertainties in parameter values and in the shapes of probability distributions are modeled and managed with the method of robust satisficing from info-gap theory. The robustness to uncertainty is evaluated for alternative estimators. We show that putatively optimal estimators may be less robust than sub-optimal estimators, suggesting preference for a sub-optimal estimator in some circumstances. These two attributes –statistical accuracy and info-gap robustness –trade off against one another. The info-gap robustness function quantifies this trade off. Generic propositions specify the robustness functions and their trade offs, and characterize a class of situations in which preference for sub-optimal estimators can occur. Three examples are discussed.

    Original languageEnglish
    Pages (from-to)11-30
    Number of pages20
    JournalJournal of Mathematical Psychology
    Publication statusPublished - Dec 2018


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