Environmental Engineering Reference
In-Depth Information
prior probability distribution that gives a probability of 0.75 to the coin produ-
cing heads 50% of the time, and, say, a 5% probability that it produces heads all
the time, with the rest of the probability evenly distributed among other outcomes.
I am already doing better than the pure frequentist approach, despite my tiny data
set. As new data become available, these distributions can be updated, and the
credibility of each hypothesis is then reassessed. For example, after 20 goes, I
now have 13 heads and 7 tails, so I can reduce the probability of the coin only
producing heads to zero, and increase the weighting of the values in the 0.5-0.7
range.
Bayesian statistics are very useful when giving recommendations for manage-
ment action under conditions of uncertainty . This is exactly the situation we find
in the conservation of exploited resources. For example, we may wish to give a
prediction about the outcome of a particular management strategy using a model
of the dynamics of the harvested population. We can collate any data that may
inform us, in whatever form it takes, whether it be expert opinion, quantitative
data from the system itself, or data from similar systems. These data are used to
produce the prior probability distributions for the model parameters, and to
develop different candidate models for how the system works. As the models are
updated based on data, we obtain new understanding which we use to update our
priors into posterior probability distributions—this is Bayesian updating , and is
where the complicated mathematics is required. We can update both our prob-
ability distributions for parameters given a particular model structure, and our
weighting of the credibility of each model that we test (e.g. see Box 4.5). Next, we
can use these updated models to provide management advice. This advice can
be framed in probabilistic terms to reflect the underlying uncertainties—the
probability of your management producing the desired outcome, given our model
of the state of the world A, is X%, and the likelihood that model A reflects the
true state of the world is Y%. Finally we would hope that any management that is
implemented produces further new understanding, that can be used to update the
model priors next time around (Figure 5.6).
Priors
for model
parameters
Posteriors
for model
parameters
Parameter
uncertainty
Management
recommendations
Bayesian
updating
Set of
Models
Model
weighting
Competing
models
Structural
uncertainty
Sustainability
constraints
Management
objectives
Management
implementation
Data
Prior knowledge and objectives
Fig. 5.6 A schematic showing the Bayesian approach to uncertainty in
management of natural resources.
 
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