Lower and Upper Covariance

  • Erik Quaeghebeur
Part of the Advances in Soft Computing book series (AINSC, volume 48)


We give a definition for lower and upper covariance in Walley’s theory of imprecise probabilities (or coherent lower previsions) that is direct, i.e., does not refer to credal sets. It generalizes Walley’s definition for lower and upper variance. Just like Walley’s definition of lower and upper variance, our definition for lower and upper covariance is compatible with the credal set approach; i.e., we also provide a covariance envelope theorem. Our approach mirrors the one taken by Walley: we first reformulate the calculation of a covariance as an optimization problem and then generalize this optimization problem to lower and upper previsions. We also briefly discuss the still unclear meaning of lower and upper (co)variances and mention some ideas about generalizations to other central moments.


Variance Covariance Central moment Theory of imprecise probabilities Envelope theorem 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Erik Quaeghebeur
    • 1
  1. 1.SYSTeMS Research GroupGhent UniversityZwijnaardeBelgium

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