144
10 Defining Probabilities of Events
an analyst “feels the temptation” to use a higher level of distributions, perhaps to
perform a Monte Carlo simulation, the trade-offs and potential for a misleading result
must be carefully considered.
10.1.2 Updating Probabilities
As shown in the previous section, it is possible to develop probabilistic updating
of various types of data, which may include, to mention just a few: deformation
velocity (for example cm/year); number of events of a certain magnitude (for example
number of events exceeding a certain magnitude per year); etc. The updating makes
it possible then to re-frame probabilities present in the a quantitative risk register and
to re-evaluate the risks. In what follows we present a few techniques that can be used
to update probabilities.
Exceedance Probability Updates
The exceedance probability is the probability of an event being greater than or equal
to a given value, i.e., that the event will exceed, for example, a given magnitude.
Forecasting the future exceedance of previously observed extremes is extremely
important for risk assessments. Based on repeated observations it is possible to reframe the probabilities of exceedance and thus to rationally update the risk register.
Bayesian Updates
Bayesian analyses allow to update frequencies and probabilities as new data are
generated (Ang and Tang 1975; Straub and Grêt-Regamey 2006) by space observation
or other means. Consider, for example, the case where the available information is a
set of observed n detached rocks from a slope, which are described by their volume
and the time during which they occurred. Note that the Bayesian update will be valid
only insofar as the observations are free of error (i.e., all rocks are recorded); this
is the reason why regular monitoring is a necessity. In order to allow later Bayesian
updates a quantitative risk register should include the a priori estimate of frequencies
or probabilities. If no data are available beyond a min-max range defined by models
or expert opinions, the simplest and oldest rule is to assume a uniform distribution
(Fig. 10.3), as stated earlier. However, if sufficient data were available, the risk
assessment could also be set-up with a more refined “prior” distribution and then
use Bayes to obtain the first “posterior” distribution, the second posterior, etc. The
application of Bayes shows that one single event provokes a shift of the distribution,
as shown in Fig. 10.4.
10.1.3 Summary of Elemental Probabilities
In summary, for any risk assessment and any event we can use data from various local
and external reputable sources available to us and interviews with key personnel; we
10 Defining Probabilities of Events
an analyst “feels the temptation” to use a higher level of distributions, perhaps to
perform a Monte Carlo simulation, the trade-offs and potential for a misleading result
must be carefully considered.
10.1.2 Updating Probabilities
As shown in the previous section, it is possible to develop probabilistic updating
of various types of data, which may include, to mention just a few: deformation
velocity (for example cm/year); number of events of a certain magnitude (for example
number of events exceeding a certain magnitude per year); etc. The updating makes
it possible then to re-frame probabilities present in the a quantitative risk register and
to re-evaluate the risks. In what follows we present a few techniques that can be used
to update probabilities.
Exceedance Probability Updates
The exceedance probability is the probability of an event being greater than or equal
to a given value, i.e., that the event will exceed, for example, a given magnitude.
Forecasting the future exceedance of previously observed extremes is extremely
important for risk assessments. Based on repeated observations it is possible to reframe the probabilities of exceedance and thus to rationally update the risk register.
Bayesian Updates
Bayesian analyses allow to update frequencies and probabilities as new data are
generated (Ang and Tang 1975; Straub and Grêt-Regamey 2006) by space observation
or other means. Consider, for example, the case where the available information is a
set of observed n detached rocks from a slope, which are described by their volume
and the time during which they occurred. Note that the Bayesian update will be valid
only insofar as the observations are free of error (i.e., all rocks are recorded); this
is the reason why regular monitoring is a necessity. In order to allow later Bayesian
updates a quantitative risk register should include the a priori estimate of frequencies
or probabilities. If no data are available beyond a min-max range defined by models
or expert opinions, the simplest and oldest rule is to assume a uniform distribution
(Fig. 10.3), as stated earlier. However, if sufficient data were available, the risk
assessment could also be set-up with a more refined “prior” distribution and then
use Bayes to obtain the first “posterior” distribution, the second posterior, etc. The
application of Bayes shows that one single event provokes a shift of the distribution,
as shown in Fig. 10.4.
10.1.3 Summary of Elemental Probabilities
In summary, for any risk assessment and any event we can use data from various local
and external reputable sources available to us and interviews with key personnel; we