1. Influence Diagrams, Decision
Trees and Probability
Reference: Clemen & Reilly. Making Hard Decisions, 2nd ed. Chapter 3. Duxbury, 2001
NOTE: Some materials for this presentation courtesy of Dr. Dan Maxwell

2. } Influence Diagrams Another way to structure decision problems
Graphical representation
Considers:
Decisions to make
Uncertain events
Value of outcomes }
Nodes in network
Chance Node
Deterministic Node
Decision Node
Value Node
– Relations between nodes

3. Influence Diagrams Decision Chance Relevance Value Probabilistic
Information
Arc
Deterministic
Chance
Functional
Relevance

4. Representing Influence with ArrowsB E
The outcome of event A is
relevant for assessing the
chances associated with event B.
The decision maker has information on the outcome of event E when
making decision F. C D G H
Decision C is relevant for
assessing the chances
associated with event D.
Information from Decision G is used to make decision H.

5. Basic Risky Decision Outcomes: Market Up Market Down Market Activity
Investment
choice
Payoff
Market
Choice Outcome Payoff
Choices:
Stocks
Savings Up
Down
200
500
-400
Savings
Stocks

6. } Evacuation Decision Possible Forecasts Will Hit Miami
Won’t Hit Miami
Outcomes:
Hits Miami
Misses Miami
Hurricane
Path
Forecast
Evacuation
Decision
Payoff
Choice Outcome Payoff
Choices:
Evacuate
Stay
Hit
Miss
Safety
High Cost
Danger
Low cost
Low Cost }
Evacuate
Stay
Note: Decision made after forecast
– Forecast is imperfect
– Is forecast correct?

7. Strategy for Building Influence Diagrams
• No Recipe
• Start with very simple diagram
– Iteratively add detail
– Stop when enough to capture essence of problem
– There is art involved
• Common Mistakes
– Interpret as flowchart
- No sequential nature
- No cycles
– Influence not causation

8. Deterministic Nodes
• Additional nodes to aggregate intermediate results
• Emphasizes and simplifies structure of the ID
ex. New Product Introduction
(1)
• Very simple
representation
• Value is the profit
– derived from
revenue and cost
• Might not capture all
relevant aspects of
problem
Revenue
Cost
Introduce
Product
Profit

9. Deterministic Nodes ex. New Product Introduction (2)
Units
Sold
Fixed
Cost
Variable
Cost
Price
Profit
Introduce
Product
• More complex – captures more detail
• Harder to understand and evaluate

10. Deterministic Nodes ex. New Product Introduction (3)
Units
Sold
Fixed
Cost
Variable
Cost
Price
Introduce
Product
Revenue
Cost
• Uses Deterministic Nodes
• Sometimes denoted with
double circle or as value node
• Easier to understand and evaluate
Profit

11. Deterministic Nodes ex. New Product Introduction (3)
Units
Sold
Fixed
Cost
Variable
Cost
Price
Introduce
Product
Revenue
Cost
• Uses Deterministic Nodes
• Sometimes denoted with
double circle or as value node
• Easier to understand and evaluate
Profit

12. Multiple Objectives
• Value of outcome depends on tradeoffs of competing objectives
• Can be represented in Influence Diagrams as follows:
ex. FAA decision on Bomb Detection System
Bomb Detection
System Choice
Detection
Effectiveness
Time to
Implement
Passenger
Acceptance
Cost
• Build Additive
Value Function
Overall
Satisfaction

13. Multiple Objectives
• Value of outcome depends on tradeoffs of competing objectives
• Can be represented in Influence Diagrams as follows:
ex. FAA decision on Bomb Detection System
Bomb Detection
System Choice
Detection
Effectiveness
Time to
Implement
Passenger
Acceptance
Cost
Overall
Satisfaction
Measure

14. Multiple Objectives
• Value of outcome depends on tradeoffs of competing objectives
• Can be represented in Influence Diagrams as follows:
ex. FAA decision on Bomb Detection System
Bomb Detection
System Choice
Detection
Effectiveness
Time to
Implement
Passenger
Acceptance
Values
Cost
Overall
Satisfaction
Measure

15. Sequential Decisions • Simplest is 2 decision sequence
• No cycles allowed in Influence Diagrams
• Sequential decisions are “strung together”
ex. Orchard owner decision to protect trees from bad weather
Weather
Day 1
Weather
Day 2
Weather
Day n
Forecast
Day 1
Forecast
Day 2
Forecast
Day n
Different than one in the book
Day 1 weather does not affect Forecast for Day 1
How much of this is an affinity diagram?
Protect?
Day 1
Protect?
Day 2
Protect?
Day n
Payoff
Day 1
Payoff
Day 1
Payoff
Day n
Total Payoff

16. Sequential Decisions • Simplest is 2 decision sequence
• No cycles allowed in Influence Diagrams
• Sequential decisions are “strung together”
ex. Orchard owner decision to protect trees from bad weather
Weather
Day 1
Weather
Day 2
Weather
Day n
Forecast
Day 1
Forecast
Day 2
Forecast
Day n
Different than one in the book
Day 1 weather does not affect Forecast for Day 1
Protect?
Day 1
Protect?
Day 2
Protect?
Day n
Payoff
Day 1
Payoff
Day 1
Payoff
Day n
Total Payoff

17. Strategy for Building Influence Diagrams
• No Recipe
• Start with very simple diagram
– Iteratively add detail
– Stop when enough to capture essence of problem
– There is art involved
• Common Mistakes
– Interpret as flowchart
- No sequential nature
- No cycles
– Influence not causation

18. Solving Influence Diagrams
Step 1: Clean up Influence Diagram
No “Barren Nodes”
Only one Value Node (or one Super Value Node into which all the other value node feed)
No cycles
Step 2: Look for any Chance Nodes that:
Directly precedes the Value Node (only node)
Do not directly precede any other type node
Reduce these nodes by taking expected values
Value node inherits their predecessors

19. Algorithm (continued)
Step 3: Look for Decision node that:
Directly precedes the Value Node, and
Has as predecessors all other direct predecessors of the Value Node
If none, go to Step 5.
Else, reduce the node by choosing the optimum [expected] value.
Step 4: Go to Step 2 and continue until the Influence Diagram is completely solved
Step 5: You are here because you couldn’t reduce any chance nodes.
Reverse the arc between 2 chance nodes using Bayes Theorem and go to Step 2.

20. Solving Influence Diagrams
Influence Diagrams are usually solved using software
Freeware and Commercial software exists
In this class, we will use the Decision Tools software provided with the text
WARNING! Register software < 30 days
For exam, I won’t ask you to solve directly from a influence diagram