## Abstract

Comparison of aleatory and epistemic uncertainty modelling, using @RISK

Dr Hans Schjær-Jacobsen

Copenhagen University College of Engineering

Aleatory uncertainty of a system arises from the random behavior of system input parameters typically represented by probability distributions giving rise to random output parameters also represented by probability functions. Epistemic uncertainty of a system corresponds to ignorance about the input parameters usually represented by possibility distributions like intervals and fuzzy numbers resulting in output variables represented by interval or fuzzy numbers. The alternative ways of modeling uncertainty requires quite different approaches to calculation. The first one calls for statistical methods like Monte Carlo simulation whereas the second one relies on methods for calculating interval functions. While Monte Carlo simulation is generally applicable to both monotonic and non-monotonic functions, interval calculations with non-monotonic functions calls for application of global optimisation methods because minima and maxima are not attained at the interval endpoints. For example, calculation of the non-monotonic interval function f(x) = x (1-x) on the interval x = [0; 1] gives the result [0; 1] when the interval endpoints are used, but [0; 0.25] when the global minima and maxima are found. In the presentation it will be demonstrated that uncertain numerically identical input parameters results in numerically very different output parameters depending on the input parameters being interpreted as uncertain in the aleatory or epistemic sense.

Dr Hans Schjær-Jacobsen

Copenhagen University College of Engineering

Aleatory uncertainty of a system arises from the random behavior of system input parameters typically represented by probability distributions giving rise to random output parameters also represented by probability functions. Epistemic uncertainty of a system corresponds to ignorance about the input parameters usually represented by possibility distributions like intervals and fuzzy numbers resulting in output variables represented by interval or fuzzy numbers. The alternative ways of modeling uncertainty requires quite different approaches to calculation. The first one calls for statistical methods like Monte Carlo simulation whereas the second one relies on methods for calculating interval functions. While Monte Carlo simulation is generally applicable to both monotonic and non-monotonic functions, interval calculations with non-monotonic functions calls for application of global optimisation methods because minima and maxima are not attained at the interval endpoints. For example, calculation of the non-monotonic interval function f(x) = x (1-x) on the interval x = [0; 1] gives the result [0; 1] when the interval endpoints are used, but [0; 0.25] when the global minima and maxima are found. In the presentation it will be demonstrated that uncertain numerically identical input parameters results in numerically very different output parameters depending on the input parameters being interpreted as uncertain in the aleatory or epistemic sense.

Original language | English |
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Publication date | 2012 |

Publication status | Published - 2012 |

Event | Palisade EMEA 2012 Risk Conference - London, United Kingdom Duration: 18 Apr 2012 → 19 Apr 2012 |

### Conference

Conference | Palisade EMEA 2012 Risk Conference |
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Country/Territory | United Kingdom |

City | London |

Period | 18/04/2012 → 19/04/2012 |