Transcript Risk forecasting & examples Renaissance Risk Changing the odds in your favour

Risk forecasting & examples
Renaissance Risk
Changing the odds in your favour
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Rule Based decision-support systems cannot handle uncertainty
Regression-based prediction systems cannot handle complex
cause-effect relationships
How to combine different types of evidence
How to combine both qualitative and quantitative information to
arrive at a quantitative risk assessment
How to make visible and auditable the assumptions of the
assessor
How to achieve more confidence in quantitative arguments
Renaissance Risk
Changing the odds in your favour
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Powerful graphical framework in which to reason about
uncertainty using diverse forms of evidence
Nodes of graph represent uncertain variables
Arcs of graph represent casual or influential relationships between
the variables
Associated with each node is a probability table (CPT)
Renaissance Risk
Changing the odds in your favour
Probability of Smoker
Yes
0.6
No
0.4
Smoker?
Has Lung Cancer
Probability of Lung Cancer
Smoker: Yes
No
Yes
0.1
0.01
No
0.9
0.99
Has Bronchitis
Probability of Lung Cancer
Smoker: Yes
No
Yes
0.6
0.3
No
0.4
0.7
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A: ‘Person has cancer’ p(A) = 0.1 (prior)
B: ‘Person is smoker’ p(B) = 0.5
What is p(A\B)? (posterior)
p(B\A) = 0.8 (likelihood)
P(A\B).P(B) = P(B\A).P(A)
P(A\B) = P(B\A).P(A)/P(B)
So p(A\B) = 0.16
Renaissance Risk
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Applying Bayes theorem to update all the probabilities when new
evidence is entered
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Intractable even for small BBNs
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Breakthrough in late 1980s - fast algorithm
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Tools like Hugin implement efficient propagation
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Propagation is multi-directional
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Make predictions even with missing/incomplete data
Renaissance Risk
Changing the odds in your favour
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Microsoft automated decision support:
 Office 95 (and later) help wizards
 Customer support/diagnostics
Hewlett Packard - fault diagnosis
NASA space shuttle VISTA system (display relevant telemetry
data)
MUNIN system for medical diagnosis
Renaissance Risk
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System safety
Faults in test/review
Operational usage
Intrinsic complexity
Correctness of solution
System criticality
Accuracy of testing
Complexity of solution
Quality of supplier
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Quality of test team
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Defining the BBN topology
 What is the ‘right’ collection of nodes and arcs?
 Use ‘idioms’ and join operations
Defining the Node Probability Table (CPTs)
 Benefit of BBNs is that we can use empirical AND subjective
data, but how to deal with combinatorial explosion and
continuous variables?
 Elicitation process that extrapolates a complete NPT based
on a small number of inputs
 Incorporating probabilistic and deterministic functions
 Building BBN from database
Renaissance Risk
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BBNs offer classic solution to data-mining problem
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Tools for constructing ‘optimal BBN’ from large databases
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Improved predictions over classical regression-based approaches
Renaissance Risk
Changing the odds in your favour
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Best Method for reasoning under uncertainty
Computational tractability issues have largely been solved (unlike,
e.g. neural nets) so BBNs can be used NOW on real, large-scale
problems
Can combine diverse data, including subjective beliefs and
empirical data
Can enter incomplete evidence and still obtain prediction
Perform powerful ‘what-if’ analysis to test sensitivity of
conclusions
Visual reasoning tool and a major documentation aid
Renaissance Risk
Changing the odds in your favour
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More adaptable to changes in risk characteristics
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Dynamic, as new risks are rated the Network learns
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Broad range of risk characteristics taken into account
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Allows investigations of risk characteristics to ultimate premium
rates
Avoids predetermined relationships as these are determined
directly from experience
Adds value to the Risk Management process
Renaissance Risk
Changing the odds in your favour
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The birthday puzzle
What is the chance that in a group
of 36 randomly selected people,
two or more will be found to
share the same birthday?
The neatest way to work out the
exact solution is to calculate 1
minus the probability that all 36
people will have different
birthdays:
1-[(364x363x…x330)/36535]
Renaissance Risk
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The birthday puzzle
The false-positive puzzle
You are given the following:
a) in random testing, you test
positive for a disease,
b) in 5% of cases, this test shows
positive even when the subject
does not have the disease,
c) in the population at large, one
person in 1000 has the disease.
What is the probability that you
have the disease?
Renaissance Risk
Changing the odds in your favour
The
birthday puzzle
The false-positive puzzle
The Monty Hall puzzle
This is based on an old American
game show in which contestants
were offered a choice of three
boxes. Open the correct one and
you won a car; open either of the
others and you won a goat.
There was a twist, after the
contestant had chosen, but before
the box was opened, the host
opened one of the other boxes to
reveal a goat. Then he asked of
the contestant wanted to stick
with his first choice, or change his
mind and open the third box
instead.
Question: is it a good idea to
change your mind, a bad idea, or
does it make no difference?
Renaissance Risk
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The door containing the prize is
known to Monty and thus “Prize”
has an impact on “Monty Opens”.
Monty will never choose to open
the door of your first selection so
also “First Selection “has impact
on “Monty Opens”.
This give us the BBN shown in
the figure opposite.
Renaissance Risk
Changing the odds in your favour
Renaissance Risk
Changing the odds in your favour
Renaissance Risk
Changing the odds in your favour