Lecture 6: Decision Making under Risk Flashcards
When do we need to take uncertainties into account?
A rational decision process has to take uncertainties into account, as long as they affect the outcomes of our actions.
What kind of graphical representations of a decision problem exist and what are they used for?
- Influence Diagram -> support in early stages, problem structuring
- Decision Tree -> all relevant details to solve a problem
- Decision Matrix -> all relevant details to solve a problem
Components of an Influence Diagram
- Nodes:
- Objectives or values are represented by diamonds or hexagons
- Decisions are represented by squares
- Uncertainties are represented by ellipses - Arrows:
- An arrow into a value node means functional
- An arrow into a decision node means known
- An arrow into an uncertainty node means relevance
Interpretation of Arrows - Functionality
- Outcome of the node at the root is required for determining the objective at the head
- Arrow can be rooted in decision node or uncertainty node
- Arrow points to an objective
Interpretation of Arrows - Sequence
- Outcome of the node at the root will be realised before the decision at the head is made
- Arrow can be rooted in decision node or uncertainty node
- Arrow points to a decision node
- Arrow from a chance node to a decision node does not mean the decision is affected by the random event but it indicates that the outcome of the chance node is known before the decision is made!
Interpretation of Arrows - Relevance/Dependence
- Outcome of the node at the root affects the probability distribution of the uncertainty at the head
- Arrow can be rooted in decision node or uncertainty node
- Arrow points to uncertainty node
Stochastic dependence vs. causality
- An arrow between two uncertainty node reflects stochastic dependence and NOT causality.
- The arrow can be reversed if the state of knowledge available at both nodes is the same (all arrows into both nodes must be the same)
Influence Diagram - Avoid Cycles
- Make sure there are no cycles (a node cannot influence its own outcome!)
- Cycles usually indicate that events definitions need to be made more clear, especially with regard to the timing of events (e.g. disease before/after treatment)
Risk versus Uncertainty
Risk:
- DM has perfect knowledge and incomplete information but can assign probabilities to a set of possible outcomes (-> we discuss problems under risk)
Uncertainty:
- DM does not even have information about possible outcomes of a decision
Event Tree
An event tree is a decision tree without any decisions.
Plotting a decision tree
- Always plot from left to right
- Only one alternative can be chosen after each decision node
- Outcomes from a chance event should be a set of mutually exclusive (only one can occur) and collectively exhaustive (one must occur) outcomes
- Decision trees must be complete (represent all possible paths
- The order of an uncertainty node relative to a decision node is important (place before if uncertainty is resolved before)
- The order of consecutive chance nodes (that are not interrupted) is not important if there is no probabilistic dependence
Solving a Decision Tree
- Start at the rightmost end of the tree
2. At chance nodes calculate the expected value. At decision nodes select the best value path.
Scenarios (Decision Tree)
Strategies of the environment (hypothetical combination of chance events)
Strategy (Decision Tree)
Assignment of a decision to each decision node where the decision chosen depend on the yet to be determined outcomes of chance events.
Combination of Scenario & Strategy
Should yield a complete path that starts at the root of the tree and ends at one of the outcome nodes.
