IE 2030 Lecture 7 Decision Analysis

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IE 2030 Lecture 7Decision Analysis

• Expected Value
• Utility
• Decision Trees

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Topics Today IE 2030 Lecture 7

• Introduction to PERT
• Decision tree example party planning
• Concepts
• Uncertainty
• Minimax Criterion
• Expected Value Criterion
• Risk Aversion

• Risk Neutral, Risk Averse, Risk Seeking
• Utility
• Outcome and Decision
• Decision Tree
• Value of information
• Sensitivity analysis

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Party Example (R. Howard)
900
Clear .6
Rain .4
100
OUT
IN
600
Clear .6
Rain .4
500
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Decision Trees

• Use different shapes for decisions and uncertain
  branchings
• Compute from the leaves back to the root
• Use expected values
• When you make a decision, you know the history,
  the path from the root to the decision point

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Minimax or Maximin Criterion

• Choice to make worst possible outcome as good as
  possible
• Usually gives poor decisions because excessively
  risk averse
• Fearful people use this criterion
• Are you afraid of being judged badly afterwards?
• Decisions vs. Outcomes

Probability of regret
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Maximin and other Payoff Criteria

• Who is your opponent?
• An indifferent Nature
• use probability, consider expected value
• A hostile or vengeful Fate...
• Use Maximin, consider a psychiatrist
• A self-interested person
• use game theory and economics
• A hostile person who desires your failure...
• use game theory, maximin, consider an
  intermediary or arbitrator

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Never attribute to malice, what can be adequately
explained by stupidity
Trust and Credibility
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Risk aversion

• Choice of sure thing versus lottery
• Size
• Gain or loss
• Expected value criterion
• Utility

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It is expensive to be poor

• Companies dont like to risk going out of
  business
• Wealthier people can afford to gamble
• get higher average returns
• We model this by setting very low utility values
  on outcomes below danger threshholds
• Can cause problems in environmental decisions.
  Is going bankrupt as bad as destroying the
  worlds ecology?

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Decision Analysis Value of Information (based on
R. Howards notes)
900
out
Clear .6
in
600
Rain .4
100
out
in
500
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Value of Information

• Expected value of a clairvoyant (perfect
  information) is an upper bound on the value of
  any forecast
• Analysis assumes your probabilities are correct
• Must use conditional probability to find
  probabilities of imperfect forecasts

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Forecast probabilities simple example

• Consistently 90 accurate forecast whatever the
  forecast, it is correct w.p..9
• If it rains 50 of the time, forecast rain w.p.
  .5
• If it rains 90 of time, forecast rain w.p. 1
• If it rains 100 of time, consistent 90 accuracy
  is impossible
• Many forecasts have inconsistent accuracy

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Forecast probabilities party example

• Consistently 90 accurate forecast whatever the
  forecast, it is correct w.p..9
• If it rains 40 of time, forecast rain w.p. q.
• .9q .1(1-q) 0.4
• LHS Prob(rain), calculated over event
  partition predict rain, dont predict rain
• You must decide what to do for each possible
  forecast
• What if the forecast were 0 accurate?