Week 9 - Decision Theory Flashcards
How do you track decisions?
Decision log
- Who
-When
- Why
Routine Decision
- small impact
- Reversible
- short term
- data available
- standard decision process
Make-or-break decision
High impact
irreversible
long term
safety or product liability is critical
no well defined decision process
Structured decision processes
- Qualitative
- Quantitative
How is risk described?
A - Future Event
C - Activity consequence
C* - Prediction of C
U - Uncertainty about what value C will take
P - probability given K
K - background information
Risk analysis methods
- Simplified (Qualitative )
- Standard (Quantitative or qualitative)
- Model-based (primarily quantitative)
simplified risk analysis
informal procedure using brainstorming and discussion
Standard Risk analysis
Formalized procedure where recognized risk analysis methods are used.
Risk matrices are often used.
Model-based risk analysis
Makes use of techniques such as event tree and fault tree analysis.
Fault Tree Analysis (FTA)
System analysis techniques used to determine the root causes and probability of occurrence of a specified undesired event.
OR gate probability
P(A U B) = P(A) + P(B) - P(A)P(B)
OR gate probability for mutually exclusive events
P(A U B) = P(A) + P(B)
OR gate with 3 inputs Probability
P(A+B+C) = P(A)+P(B)+P(C) - P(A)P(B)-P(A)P(C)-P(B)*P(C) + P(A)P(B)P(C)
AND Gate probability
P(A ∩ B) = P(A)P(B)
Cut sets
Sets of Events that together cause the top undesired event to occur.
What does a low-order cut set indicate?
High safety vulnerability
Reactive FTA
Used after an accident as an investigation method
Proactive FTA
Performed during system development to predict and prevent future problems.
Event Tree analysis (ETA)
Inductive Procedure that shows all possible outcomes resulting from an accidental initiating event.
How is ETA useful?
- identifies potential accident scenarios
- scenario frequencies
- scenario consequences
ETA Structure
initiating event
pivotal events
outcomes
probability
consequences
For ETA:
Multiply along…
Sum across…
set of branches probability must sum to…
multiply along horizontal branches
sum across vertical branches
must sum to 1
Uses of Markov Chains
- Predicting traffic flows
- communications networks load
- genetic issues
- currency exchange rates
- population dynamics
stationary matrix
Matrix converges to steady state
Called a Regular Markov Chain
How to tell if a matrix is regular?
All entries become positive
Absorbing state
If the state is impossible to leave once it is entered
Requirements for an absorbing Markov Chain
Minimum of 1 absorbing state
It is possible to go from each non-absorbing state to at-least one absorbing state
What makes a decision sensitive
- After a test the decision is different for different test results.
- The decision changes after more tests
Reasons to not do a test for a decision
- avoid costs if result is unlikely to affect decision
- If multiple tests are available a different one may be chosen.
Pre-posterior
doing a test, updating the probability distribution and deciding what to do next.
Posterior (Bayes)
Involves calculating probabilities and deciding on action given an experiment has already been done. (result is known)
Types of uncertainty
aleatory - random
Epistemic - Lack of Knowledge
Type 1 Error
Rejecting a True Hypothesis (False Positive)
Type 2 Error
Accepting a False Hypothesis (False Negative)
Utility
Defined as the state of being satisfied, useful, beneficial etc…
Ranks happiness
Marginal Utility
Additional utility gained from the consumption of one additional unit.
Total utility
Total amount of satisfaction that a person/decision maker can receive from the consumption of all units of a good or service.
Law of Diminishing Marginal Utility
As you consume more you get diminishing utility but you still consume the same number of resources.
Risk Neutral
bases all decisions on expected utility
Risk Averse
Will not be comfortable with a large probability of big loss
Not Risk averse
Will be comfortable with a small probability of a big win
Latin Hypercube sampling
Decide how many sample points to use.
Each sample point the row and column it was taken from must be recorded
Orthogonal Sampling
Sample space is divided into equal subspaces.
All points are chosen simultaneously ensuring that each subspace is sampled with the same density
