The degree of belief is a reflection of the state of mind of the individual person in terms of
experience, expertise and preferences. In this respect the Bayesian interpretation of probability
is subjective or more precisely person-dependent. This opens up the possibility that two
different persons may assign different probabilities to a given event and thereby contradicts
the frequentistic interpretation that probabilities are a characteristic of nature.
The Bayesian statistical interpretation of probability includes the frequentistic and the
classical interpretation in the sense that the subjectively assigned probabilities may be based
on experience from previous experiments (frequentistic) as well as considerations of e.g.
symmetry (classical).
The degree of belief is also referred to as a prior belief or prior probability, i.e. the belief,
which may be assigned prior to obtaining any further knowledge. It is interesting to note that
Immanuel Kant^2 developed the purely philosophical basis for the treatment of subjectivity at
the same time as Thomas Bayes^3 developed the mathematical framework later known as the
Bayesian statistics.
Modern structural reliability and risk analysis is based on the Bayesian interpretation of
probability. However, the degree of freedom in the assignment of probabilities is in reality not
as large as indicated in the above. In a formal Bayesian framework the subjective element
should be formulated before the relevant data are observed. Arguments of objective
symmetrical reasoning and physical constraints, of course, should be taken into account.
Practical Implications of the Different Interpretations of Probability
In some cases probabilities may adequately be assessed by means of frequentistic information.
This is e.g. the case when the probability of failure of massively produced components, such
as pumps, light bulbs and valves, is considered. However, in order to utilise reported failures
for the assessment of the probability of failure for such components it is a prerequisite that the
components are in principle identical, that they have been subject to the same operational
and/or loading conditions and that the failures can be assumed to be independent.
In other cases when the considered components are e.g. bridges, high-rise buildings, ship
structures or unique configurations of pipelines and pressure vessels, these conditions are not
fulfilled. In these cases the number of identical structures may be very small (or even just one)
and the conditions in terms of operational and loading conditions are normally significantly
(^2) Immanuel Kant, philosopher, 1724-1804
(^3) Thomas Bayes, mathematician, 1702-1761