Over the years the modeling and treatment of aleatory and epistemic uncertainties in probabilistic assessments has repeatedly been an issue of discussion and also some controversy. The philosophical and mathematical aspects may be said to be well appreciated, however, there are cases in practice where principles seem to be violated and frequently the effects of the epistemic uncertainty are treated inconsistently in the probabilistic modeling. The present paper first reviews the general principles for the modeling and treatment of uncertain characteristics subject to both aleatory and epistemic uncertainties. Thereafter, the general principles are applied considering three examples concerning the probabilistic modeling of extreme events; 1) the n-year maximum distribution, 2) the corresponding return period and 3) the exceedance probability in hazard analysis. Through these examples typical inconsistencies made in practical probabilistic assessments are pointed out. The results from the examples are interpreted and discussed from a structural design perspective and from a rational risk-based decision perspective. Finally, a practical solution to avoid the inconsistencies is suggested emphasizing the analogy of the analysis of extreme events with the analysis of portfolios.

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