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 What
do the shapes mean?
What
do the arrows mean?
Compared
to decision trees
Influence
diagrams in Analytica
Who
invented them?
Where
can I learn more?
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An influence diagram is a simple visual
representation of a decision problem. Influence diagrams offer an
intuitive way to identify and display the essential elements, including
decisions, uncertainties, and objectives, and how they influence
each other.
This simple influence diagram shows how decisions about the marketing
budget and product price influence expectations about its uncertain
market size and market share. These, in turn, influence costs and
revenues, which affect the overall profit. The product manager,
VP of marketing, and market analyst may work together to draw such
a diagram to develop a shared understanding of the key issues. The
diagram provides a high-level qualitative view under which the analyst
builds a detailed quantitative model. |
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What do the node shapes mean?
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A decision is a variable that
you, as the decision maker, have the power to control. |
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A chance variable is uncertain
and you cannot control it directly. |
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An objective variable is a quantitative
criterion that you are trying to maximize (or minimize). |
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A general variable is a deterministic
function of the quantities it depends on. |
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What do the arrows mean?
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An arrow denotes an influence.
A influences B means that knowing A would directly affect
our belief or expectation about the value of B. An influence
expresses knowledge about relevance. It does not necessarily
imply a causal relation, or a flow of material, data, or money. |
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How do influence diagrams compare
to decision trees?
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Decision trees are another common
representation for decision problems. Decision trees display the
set of alternative values for each decision and chance variable
as branches coming out of each node. |
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The influence diagram and decision
tree show different kinds of information. 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. |
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How do you create influence diagrams
in Analytica®?
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With Lumina's Analytica™ software,
you can draw an influence diagram simply by selecting new nodes,
placing them, and drawing arrows among them. When you specify a
formula for a variable to define its quantitative definition, you
can select directly from its inputs - the variables from which there
are incoming arrows. Or, if you use other variables in the definition,
the arrows will automatically redraw to keep the diagram consistent
with the underlying relationships. |
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How does Analytica extend influence
diagrams?
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Analytica extends the standard influence
diagram notation with additional types of node, to provide the power
and flexibility to handle real-world problems of greater complexity
than can be handled with conventional tools. |
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1. Hierarchy
of modules
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With module nodes, you can organize
a complex model as a hierarchy of modules. Double-click on a module
node, such as Costs, to display its details as another diagram:
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Using Analytica's modules, you can
organize a model containing hundreds, or even thousands, of variables
into a hierarchy of diagrams, each of which is small enough to be
easily comprehensible and manageable. |
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2. Variables as multidimensional arrays
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 Standard
influence diagrams assume that variables are scalar quantities.
In Analytica, a variable may be a vector, or a multidimensional
array - for example, with the market size and sales for each region,
each product, and each time period. Analytica employs index variables
to identify the dimensions.
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3. User-defined
functions
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 You
can use existing libraries of functions to extend the richness of
Analytica's modeling language for particular problem domains. Or
you can create your own functions. |
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4. Diagrams with
feedback loops
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Traditional influence diagrams don't
permit feedback loops - like, where Marketing budget -> Market
share -> Revenues -> Marketing budget. Analytica, however,
does let you create loops like this in dynamic model, provided there
is a time lag, denoted as a dashed arrow, somewhere in the loop.
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Who invented influence diagrams?
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Several people from the decision-analysis
community were involved in the creation of influence diagrams. Professor
Ronald Howard from Stanford University and his colleague, Dr. James
Matheson, refined and popularized influence diagrams as a convenient
notation for communicating about decision problems, that is complementary
to decision trees. |
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Where can I learn more?
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- Uncertainty: A Guide to Dealing with Uncertainty in Quantitative
Risk and Policy Analysis, M. Granger Morgan & Max Henrion,
Cambridge University Press, reprinted 1998. (Relevant excerpt
from Chapter 10 available as download.)
- Analytica User Guide, especially chapter 5: Building Effective
Models and Chapter 6: Creating Lucid Influence Diagrams, from
Lumina Decisions Systems, 1998. (PDF file available for free
download)
- Making Hard Decisions: An Introduction to Decision Analysis,
Second Edition, Duxbury Press, Belmont, CA, 1996.
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