# Different methods are needed to propagate ignorance and variability

Different methods are needed to propagate ignorance and variability There are two kinds of uncertainty. One kind arises as variability resulting from heterogeneity or stochasticity. The other arises as partial ignorance resulting from systematic measurement error or subjective (epistemic) uncertainty. As most researchers recognize, variability and ignorance should be treated separately in risk analyses. Although a second-order Monte Carlo simulation is commonly employed for this task, this approach often requires unjustified assumptions which may be inappropriate in some circumstances. We argue that the two kinds of uncertainty should be propagated through mathematical expressions with different calculation methods. Basically, interval analysis should be used to propagate ignorance, and probability theory should be used to propagate variability. We demonstrate how using an inappropriate method can yield erroneous results. We also show how ignorance and variability can be represented simultaneously and manipulated in a coherent analysis that does not confound the two forms of uncertainty and distinguishes what is known from what is assumed. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Reliability Engineering and System Safety Elsevier

# Different methods are needed to propagate ignorance and variability

Reliability Engineering and System Safety, Volume 54 (2) – Nov 1, 1996
12 pages

/lp/elsevier/different-methods-are-needed-to-propagate-ignorance-and-variability-9WTtqij0eR
Publisher
Elsevier
ISSN
0951-8320
eISSN
1879-0836
DOI
10.1016/S0951-8320(96)00071-3
Publisher site
See Article on Publisher Site

### Abstract

There are two kinds of uncertainty. One kind arises as variability resulting from heterogeneity or stochasticity. The other arises as partial ignorance resulting from systematic measurement error or subjective (epistemic) uncertainty. As most researchers recognize, variability and ignorance should be treated separately in risk analyses. Although a second-order Monte Carlo simulation is commonly employed for this task, this approach often requires unjustified assumptions which may be inappropriate in some circumstances. We argue that the two kinds of uncertainty should be propagated through mathematical expressions with different calculation methods. Basically, interval analysis should be used to propagate ignorance, and probability theory should be used to propagate variability. We demonstrate how using an inappropriate method can yield erroneous results. We also show how ignorance and variability can be represented simultaneously and manipulated in a coherent analysis that does not confound the two forms of uncertainty and distinguishes what is known from what is assumed.

### Journal

Reliability Engineering and System SafetyElsevier

Published: Nov 1, 1996

### References

• Propagation of uncertainty in risk assessments: the need to distinguish between uncertainty due to lack of knowledge and uncertainty due to variability
Hoffman, F.O.; Hammonds, J.S.
• Understanding uncertainty
Rowe, W.D.
• Linear Computations
Dwyer, P.
• Probability, frequency and reasonable expectation
Cox, R.T.
• Introduction to the Theory of Error
Beers, Y.
• Integrating uncertainty and interindividual variability in environmental risk assessments
Bogen, K.T.; Spear, R.C.
• Uncertainty and variability in human exposures to soil contaminants through home-grown food: a Monte Carlo assessment
McKone, T.E.
• Assessment of variability and uncertainty distributions for practical risk analyses
Hattis, D.; Burmaster, D.E.
• The Estimation of Probabilities
Good, I.J.
• Stepping out of your own shadow: a didactic example of how facing uncertainty can improve decision-making
Finkel, A.M.

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