Chapter 10
Defining Probabilities of Events
This chapter, Defining probabilities of events discusses how probabilities of single
events can be evaluated, updated and delivers some examples of portfolio analyses.
Probabilities measure the chance an event will occur. In risk assessments and
project evaluations we are not dealing with absolute probabilities, but with relative
probabilities (within a portfolio) over a specific time. Generally the time is one
year and we use therefore annual probabilities. Do not confuse annual probabilities
and frequencies which measure average number of occurrence over a certain time
interval. The confusion comes from the fact that the number expressing probability
and frequency is very similar, once it goes below say 1/10. Hence a probability of
1/10 has the same number—0.1—as a frequency of 1/10, but they do not mean at all
the same conceptually.
In particular, the use of frequencies expressed as one event occurrence over n
years (e.g., 1 flood over 200 years) misleads people into thinking that that event
will actually only occur every n = 200 years. Nothing could be more wrong: there
are plenty of 1/200 years events that have occurred several times in a decade, for
example!
Using the Poisson distribution, it is possible to link the number of occurrences of
an event over a selected time t to the mean occurrence rate (frequency). For example,
if 15 catastrophic tailings dam breach events over 10 years have been observed
(this has occurred in the world portfolio in the recent past), that means a measured
frequency of 1.5 events/year.
Using Poisson’s distribution it is easy to compute and graph the probability of
seeing any number of events (1, 2, … n) during, for example, a single year. In
Fig. 10.1 the vertical axis shows the annual probability and the horizontal axis the
number of events. We can see that with that frequency one event per year has p =
0.33 to occur “next year”, and three events per year has p = 0.12, etc. As on-site
monitoring and/or space observations deliver new occurrences of events, frequency
and related probabilities can be updated in a new cycle, leading to updated risks.
© Springer Nature Switzerland AG 2020
F. Oboni and C. Oboni, Tailings Dam Management for the Twenty-First Century,
https://doi.org/10.1007/978-3-030-19447-5_10
139
Defining Probabilities of Events
This chapter, Defining probabilities of events discusses how probabilities of single
events can be evaluated, updated and delivers some examples of portfolio analyses.
Probabilities measure the chance an event will occur. In risk assessments and
project evaluations we are not dealing with absolute probabilities, but with relative
probabilities (within a portfolio) over a specific time. Generally the time is one
year and we use therefore annual probabilities. Do not confuse annual probabilities
and frequencies which measure average number of occurrence over a certain time
interval. The confusion comes from the fact that the number expressing probability
and frequency is very similar, once it goes below say 1/10. Hence a probability of
1/10 has the same number—0.1—as a frequency of 1/10, but they do not mean at all
the same conceptually.
In particular, the use of frequencies expressed as one event occurrence over n
years (e.g., 1 flood over 200 years) misleads people into thinking that that event
will actually only occur every n = 200 years. Nothing could be more wrong: there
are plenty of 1/200 years events that have occurred several times in a decade, for
example!
Using the Poisson distribution, it is possible to link the number of occurrences of
an event over a selected time t to the mean occurrence rate (frequency). For example,
if 15 catastrophic tailings dam breach events over 10 years have been observed
(this has occurred in the world portfolio in the recent past), that means a measured
frequency of 1.5 events/year.
Using Poisson’s distribution it is easy to compute and graph the probability of
seeing any number of events (1, 2, … n) during, for example, a single year. In
Fig. 10.1 the vertical axis shows the annual probability and the horizontal axis the
number of events. We can see that with that frequency one event per year has p =
0.33 to occur “next year”, and three events per year has p = 0.12, etc. As on-site
monitoring and/or space observations deliver new occurrences of events, frequency
and related probabilities can be updated in a new cycle, leading to updated risks.
© Springer Nature Switzerland AG 2020
F. Oboni and C. Oboni, Tailings Dam Management for the Twenty-First Century,
https://doi.org/10.1007/978-3-030-19447-5_10
139