146
10 Defining Probabilities of Events
In particular, sudden and significant changes of climatic conditions should prompt a
re-evaluation of the results of any risk assessment.
To conclude this section we need to talk again about the Bayesian inference
model. The Bayesian inference model is indeed one of the cornerstones available to
analysts among the tools for estimating probabilities and consequences. Allowing
for rational updates when new data become available (from semi-static to real-time
updates, depending on the applications and resources) will become the norm due
to social and legal requirements, social and media pressure, etc. To allow Bayesian
inference to be included (possibly at a later date of development of a risk management
approach) a few conditions are required from day one:
(1) Always start by identifying hazards using threats-to and threats-from (see
Sect. 8.2.1).
(2) All probabilities and consequences need to be expressed as ranges rather than
single values, and uncertainty needs to be recorded. For example, for every
parameter range there must be a justification recorded with the different opinions
that led to its definition recorded as well.
(3) Inter-dependencies need to be transparently implemented, i.e., the methodology
has to provide results for singe failures and domino effects.
Once these conditions are met, then on the basis of specific geotechnical (or
other) data reports, weather data, etc., a Bayesian inference model can be developed
to determine posterior probabilities. In time, as data are gathered and changes occur,
probabilities will be seamlessly updated.
At each new data entry, at discrete time intervals, as required or in real time,
depending on the application, it will be necessary to perform new probabilitymagnitude estimates for the hazards and their consequences. That will allows for
Bayesian updates of the risks.
10.2 Probability of Failure in a Portfolio
10.2.1 Independent Elements
Let’s use as an example a theoretical portfolio of independent dams. Each facility/dam
has its own probability p f of incurring Maximum Foreseeable Loss (MFL).
If the failure criteria states, very simply, that the failure of one single dam means
the portfolio fails, if the MFL events are also independent, the overall system’s
probability of failure p fS can be evaluated using the series probability Formula (4.1).
This failure criteria would be interesting, for example, for an insurer that wants to
decide whether to insure or deny insurance on a specific dam portfolio.
Independent Identical Elements
Let’s first assume that the dams have the same p f. The probability of failure of each
dam is shown in Table 10.1 as P = 1/T single dam. T would be the historic “frequency”
10 Defining Probabilities of Events
In particular, sudden and significant changes of climatic conditions should prompt a
re-evaluation of the results of any risk assessment.
To conclude this section we need to talk again about the Bayesian inference
model. The Bayesian inference model is indeed one of the cornerstones available to
analysts among the tools for estimating probabilities and consequences. Allowing
for rational updates when new data become available (from semi-static to real-time
updates, depending on the applications and resources) will become the norm due
to social and legal requirements, social and media pressure, etc. To allow Bayesian
inference to be included (possibly at a later date of development of a risk management
approach) a few conditions are required from day one:
(1) Always start by identifying hazards using threats-to and threats-from (see
Sect. 8.2.1).
(2) All probabilities and consequences need to be expressed as ranges rather than
single values, and uncertainty needs to be recorded. For example, for every
parameter range there must be a justification recorded with the different opinions
that led to its definition recorded as well.
(3) Inter-dependencies need to be transparently implemented, i.e., the methodology
has to provide results for singe failures and domino effects.
Once these conditions are met, then on the basis of specific geotechnical (or
other) data reports, weather data, etc., a Bayesian inference model can be developed
to determine posterior probabilities. In time, as data are gathered and changes occur,
probabilities will be seamlessly updated.
At each new data entry, at discrete time intervals, as required or in real time,
depending on the application, it will be necessary to perform new probabilitymagnitude estimates for the hazards and their consequences. That will allows for
Bayesian updates of the risks.
10.2 Probability of Failure in a Portfolio
10.2.1 Independent Elements
Let’s use as an example a theoretical portfolio of independent dams. Each facility/dam
has its own probability p f of incurring Maximum Foreseeable Loss (MFL).
If the failure criteria states, very simply, that the failure of one single dam means
the portfolio fails, if the MFL events are also independent, the overall system’s
probability of failure p fS can be evaluated using the series probability Formula (4.1).
This failure criteria would be interesting, for example, for an insurer that wants to
decide whether to insure or deny insurance on a specific dam portfolio.
Independent Identical Elements
Let’s first assume that the dams have the same p f. The probability of failure of each
dam is shown in Table 10.1 as P = 1/T single dam. T would be the historic “frequency”