Influence Diagram

Influence Diagram:

Influence diagrams are a conceptual modeling tool that graphically represent the causal relationships between decisions, external factors, uncertainties and outcomes. It depicts the key elements, including decisions, uncertainties, and objectives as nodes of various shapes and colors. It shows influences among them as arrows.

This simple influence diagram depicts a variable describing the situation:
Rectangle - a decision - What do we do?
Ellipse - a chance variable - What's the outcome?
Hexagon - a final valuation - How do we like it?





Consider the simple influence diagram representing a situation where a decision-maker is planning their vacation.

• There is 1 decision node (Vacation Activity), 2 uncertainty nodes (Weather Condition, Weather Forecast), and 1 value node (Satisfaction).
• There are 2 functional arcs (ending in Satisfaction), 1 conditional arc (ending in Weather Forecast), and 1 informational arc (ending in Vacation Activity).

• Functional arcs ending in Satisfaction indicate that Satisfaction is a utility function of Weather Condition and Vacation Activity. In other words, their satisfaction can be quantified if they know what the weather is like and what their choice of activity is. (Note that they do not value Weather Forecast directly)
• Conditional arc ending in Weather Forecast indicates their belief that Weather Forecast and Weather Condition can be dependent.
• Informational arc ending in Vacation Activity indicates that they will only know Weather Forecast, not Weather Condition, when making their choice. In other words, actual weather will be known after they make their choice, and only forecast is what they can count on at this stage.

• It also follows semantically, for example, that Vacation Activity is independent on (irrelevant to) Weather Condition given Weather Forecast is known.

Influence diagrams are a conceptual modeling tool that graphically represent the causal relationships between decisions, external factors, uncertainties and outcomes. They are useful for:

• building a common understanding of “how things work”;
• facilitating communication among technical experts, decision makers and stakeholders;
• encouraging disciplined thinking about cause and effect relationships;
• defining evaluation criteria;
• complements Decision Tree diagram by showing relationships among variables.