Renaissance Risk

Changing the odds in your

favour

Risk forecasting & examples

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

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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

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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

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Changing the odds in your

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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

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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

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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

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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

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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

Tools for constructing ‘optimal BBN’ from large databases

Improved predictions over classical regression-based approaches

Renaissance Risk

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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

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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

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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?

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Changing the odds in your

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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?

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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