Downloadable - About University

Preparing for probability assessment 283
The method of relative heights is one well-known graphical technique
that is designed to elicit a probability density function. First, the decision
maker is asked to identify the most likely value of the variable
under consideration and a vertical line is drawn on a graph to represent
this likelihood. Shorter lines are then drawn for other possible
values to show how their likelihoods compare with that of the most
likely value.
To illustrate the method, let us suppose that a fire department has been
asked to specify a probability distribution for the number of emergency
calls it will receive on a public holiday. The chief administrator of the
department considers that two is the most likely number of calls. To
show this, the analyst draws on a graph a line which is 10 units long
(see Figure 10.2). Further questioning reveals that the administrator
thinks that three requests are about 80% as likely as two, so this is
represented by a line eight units long. The other lines are derived in
a similar way, so that the likelihood of seven requests, for example,
is considered to be only 10% as likely as two and it is thought to be
extremely unlikely that more than seven requests will be received. To
convert the line lengths to probabilities they need to be normalized
so that they sum to one. This can be achieved by dividing the length
of each line by the sum of the line lengths, which is 36, as shown
below (note that the probabilities do not sum to exactly one because
of rounding).
Units
10
Figure 10.2 – The method of relative heights
5
0
0 1 2 3 4 5 6 7
Number of emergency calls