Simple influence diagram

Influence diagrams


This simple influence diagram depicts a variable describing the situation, a decision "What do we do?", a chance variable "What's the outcome?", and our final valuation "How do we like it?". These four node types are the building blocks of decision problems.  The influence diagram gives a high-level conceptual view on which  you may build a detailed quantitative model.

What do the nodes mean?

A decision is a variable that you (or your organization) as the decision maker have the power to modify directly. It could be whether to invest in a new project, how much to invest, how much to bid, where to locate a new site, or, in this example, what budget to allocate for marketing.

A chance variable is an uncertain quantity, whose value you don't (yet) know, because you don't have complete information -- maybe it's in the future -- and which (unlike a decision) you cannot control directly.

An objective is a measure of your satisfaction with possible outcomes. It might be net present value, lives saved, or EBITDA, or more generally, "utility". Usually, the decision maker is trying to find decisions to maximize (or minimize) the objective.  Often an objective combines multiple subobjectives or attributes, which may be in conflict -- such as energy costs, and environmental and health risks. Usually, when the objective is uncertain, decision analysts suggest maximizing the expected value, or more generally expected utility, based on risk preference.


What do the arrows mean?

An arrow denotes an influence. An arrow from A to B means that that knowing A would directly affect our belief or expectation about the value of B. An influence expresses knowledge about relevance. It may, but need not, imply a causal relation, or a flow of material, information, or money.

Decision trees and influence diagrams



Influence diagram for R&D decision makingDecision trees and the influence diagrams are complementary views of a decision problem: Decision trees display the set of alternative values for each decision and chance variable as branches coming out of each node. The influence diagram shows the dependencies among the variables more clearly than the decision tree. The decision tree shows more details of possible paths or scenarios as sequences of branches from left to right. But, this detail comes at a steep price: First, you must treat all variables as discrete (a small number of alternatives) even if they are actually continuous. Second, the number of nodes in a decision tree increases exponentially with the number of decision and chance variables. We would need 121 nodes to display the decision tree corresponding to the simple market-analysis influence diagram at the top of this page, even if we assume only three branches for each of the two decisions and two chance variables. The tree would be too complicated to display on this Web page. The influence diagram is a much more compact representation. 

How do you create influence diagrams in Analytica®?


How does Analytica extend influence diagrams?


1. Hierarchy of modules


2. Variables as multidimensional arrays

3. User-defined functions

4. Diagrams with feedback loops
Traditional influence diagrams don't permit feedback loops - for instance Marketing budget -> Market share -> Revenues -> Marketing budget. Analytica, however, does let you create loops like this in a dynamic model, provided there is a time lag, denoted as a dashed arrow, somewhere in the loop.

Who invented influence diagrams?


Where can I learn more?
