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Renaissance Risk
Changing the odds in your
favour
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
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
Smoker?
Has BronchitisHas Lung Cancer
Smoker: Yes NoYes 0.1 0.01No 0.9 0.99
Probability of Lung CancerSmoker: Yes No
Yes 0.6 0.3No 0.4 0.7
Probability of Lung Cancer
Yes 0.6No 0.4
Probability of Smoker
Renaissance Risk
Changing the odds in your
favour
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
Changing the odds in your
favour
Applying Bayes theorem to update all the probabilities when new evidence is entered
Intractable even for small BBNs
Breakthrough in late 1980s - fast algorithm
Tools like Hugin implement efficient propagation
Propagation is multi-directional
Make predictions even with missing/incomplete data
Renaissance Risk
Changing the odds in your
favour
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
Changing the odds in your
favour
System safety Faults in test/review
Operational usage Intrinsic complexity Accuracy of testing
Correctness of solution Complexity of solution
Quality of supplierSystem criticality Quality of test team
Renaissance Risk
Changing the odds in your
favour
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
Changing the odds in your
favour
BBNs offer classic solution to data-mining problem
Tools for constructing ‘optimal BBN’ from large databases
Improved predictions over classical regression-based approaches
Renaissance Risk
Changing the odds in your
favour
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
More adaptable to changes in risk characteristics
Dynamic, as new risks are rated the Network learns
Broad range of risk characteristics taken into account
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
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
Changing the odds in your
favour
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 puzzleThe false-positive puzzleThe Monty Hall puzzleThis 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
Changing the odds in your
favour
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.