Titel_SS06

the concrete belongs to another class. The likelihoods for the considered test method are given
in Table 2.1.

It is assumed that one test is performed and it is found that the concrete compressive strength
is equal to 36.2 MPa, i.e. in the interval of class B 2.

Using Bayes’ rule, the probability that concrete belongs to the different classes may now be
updated. The posterior probability that the concrete belongs to class B 2 is given by:

22

0.61 0.24

( ) 0.40

0.61 0.24 0.28 0.65 0.32 0.11



 

  

PB I B

The posterior probabilities for the other classes may be calculated in a similar manner and the
results are given in Table 2.1.

Concrete Likelihood P()IBi
Grade

Prior

Probability

IB 1 IB 2 IB 3

Posterior

probabilities

B 1 0.65 0.71 0.28 0.01 0.50

B 2 0.24 0.18 0.61 0.21 0.40

B 3 0.11 0.02 0.32 0.66 0.10

Table 2.1: Summary of prior probabilities, likelihoods of experiment outcomes and posterior
probabilities given, one test result in the interval of class B2.

2.4 Introduction to Descriptive Statistics

In order to assess the characteristics and the level of uncertainty of a given quantity of interest,
one of the first steps is to investigate the data available, such as observations and test results.
For this purpose, the use of descriptive statistics is useful. Descriptive statistics do not assume
anything in terms of the degree or natures of the randomness underlying the data analysed, but
are merely a convenient tool to reduce the data to a manageable form suitable for further
analysis, as well as for communication of the data in a standardized format to other
professionals.

In the following the so-called numerical summaries will first be introduced. These can be
considered to be numerical characteristics of the observed data containing important
information about the data and the nature of uncertainty associated with them. These are also
referred to as sample characteristics in the following. Thereafter graphical representations are
introduced as means of visual characterisation and as a useful tool for data analysis.
Descriptive statistics play an important role in engineering risk analysis as this forms a
standardized basis for assessing and documenting data obtained for the purpose of
understanding and representing uncertainties in risk assessment.