Applying Bayesian networks

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Applying Bayesian networks

• Risk forecasting examples

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The Key Problems

• 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

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Bayesian Belief Nets (BBNs)

• 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)

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A very simple BBN
Smoker?
Has Bronchitis
Has Lung Cancer
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Bayes Theorem
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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Bayesian Propagation

• 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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BBN applications - external

• 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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A BBN safety argument
System safety
Faults in test/review
Operational usage
Intrinsic complexity
Accuracy of testing
Correctness of solution
Complexity of solution
Quality of supplier
System criticality
Quality of test team
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Generic problems of building a BBN

• 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

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BBNs and data-mining

• BBNs offer classic solution to data-mining
  problem
• Tools for constructing optimal BBN from large
  databases
• Improved predictions over classical
  regression-based approaches

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Summary of BBN Benefits

• 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

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Advantages Over Classical statistics

• 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

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Never trust your guesses

• 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-(364x363xx330)/36535

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Never trust your guesses

• The birthday puzzle
• The false-positive puzzle

• You are given the followinga) 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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Never trust your guesses

• 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?

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Getting the Goat

• 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.

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Business Strategy Applications
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Business Strategy Applications