O'Reilly logo

Uncertainty in Risk Assessment: The Representation and Treatment of Uncertainties by Probabilistic and Non-Probabilistic Methods by Piero Baraldi, Roger Flage, Terje Aven, Enrico Zio

Stay ahead with the world's most comprehensive technology and business learning platform.

With Safari, you learn the way you learn best. Get unlimited access to videos, live online training, learning paths, books, tutorials, and more.

Start Free Trial

No credit card required

2

Probabilistic Approaches for Treating Uncertainty

Probability has been, and continues to be, a fundamental concept in the context of risk assessment. Unlike the other measures of uncertainty considered in this book, probability is a single-valued measure.

The common axiomatic basis of probability is found in Kolmogorov's (1933) probability axioms. Let img denote events in a sample space img. The following probability axioms are assumed to hold:

(2.1) equation

These axioms specify that probability is a non-negative, normalized, and additive measure.

Different types of operational or conceptual interpretations of probability can be distinguished. Among the most common are:

  • Classical
  • Relative frequency
  • Subjective
  • Logical.

Modern probability theory is not based on a particular interpretation of probability, although its standard language is best suited to the classical and relative frequency interpretations (Aven, 2012). In the context of risk assessment, the relative frequency and subjective interpretations are most common. Relative frequency probability is broadly recognized as the proper representation of variation in large populations (aleatory uncertainty), also among proponents of alternative ...

With Safari, you learn the way you learn best. Get unlimited access to videos, live online training, learning paths, books, interactive tutorials, and more.

Start Free Trial

No credit card required