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A Simple Entropy-oriented Measure of

By Bryan Cole,2014-08-08 20:57
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A Simple Entropy-oriented Measure of

    Epistemic Sensitivity Analysis Based on

    the Concept of Entropy

    B. Krzykacz-Hausmann

    Gesellschaft für Anlagen- und Reaktorsicherheit, Germany

     Contents :

    - What is epistemic sensitivity analysis ?

    - Motivation for introducing the concept of entropy

    - Derivation of entropy-based epistemic sensitivity

     measure and its interpretations

- A simple analytical example

    (=linear normal case)

- A simple estimator from samples

    - numerical/graphical examples and comparison with

     standard sensitivity measures

     Y = M(U,U,...,U) 2n1

    M : computational Model

    Y : a scalar model output

    U,U,...,U: uncertain parameters subject to 2n 1

     "epistemic" uncertainty

    (="lack-of-knowledge", "subjective", "reducible" u.) probability distributions over parameters U=(U,...,U) 1n

    quantify the degree of state of knowledge

     subjectivistic concept of probability interpretation

     (=degree-of-belief)

to be distinguished from

     "aleatory" uncertainty

    (="stochastic", "random", "population heterogeneity" "irreducible", "ontological"),

    probability distributions over variables V=(V,...,V) 1n

    describe random laws

     frequentistic concept of probability interpretation

     (=relative frequency)

    Principal goal of Epistemic Sensitivity Analysis:

     To identify the most important contributors among the parameters U,U,...,U to the epistemic uncertainty in 12n

    output Y.

    ( indicates where the important uncertainty sources are and how to reduce output uncertainty in the most

    effective way i.e. where to make more investigations, or more experiments, or to consult more experts etc. )

     Epistemic sensitivity measure (SM),

     (uncertainty importance indicator):

    indicates the "degree of impact" of the epistemic uncertainty in a parameter U on the epistemic i

    uncertainty in output Y

    ( global SM)

    doesn't indicate how sensitive is the value of outcome Y to small variations of parameter U around a nominal value. i

standard correlation/regression-related SM:

     CC , SRC, PCC, RCC, SRRC, PRCC

    (may not be appropriate for highly non-linear, non-monotonic models)