MAD revising decision trees and influence diagrams · Representing elements in a decision tree...

Basic elements about decision

trees and influence diagrams

Bibiography:P. Goodwin & G. Wright (2003) Decision Analysis for Management Judgement, John Wiley and Sons (chapter 6)

R. T. Clemen (1999) Making Hard Decisions: An Introduction to Decision Analysis, Duxbury (chapter 3)

1

Slides of Mónica Oliveira, MAD

Models and Techniques in Decision

Analysis

2

ComplexityUncertainty Problem dominated by

Choice• Decision

trees• Influence

diagrams

Choice• Decision

trees• Influence

diagrams

Evaluating options

• Multicriteria Analysis(MACBETH,EQUITY))

Resource allocation and negotiation

Revising opinion• Bayesian Nets• Event trees• Fault trees

Components decomposition

• Risk Analysis


Concepts

� Influence diagrams

� Decision trees

� Complementary concepts:

� Expected monetary value

� Risk profile and cumulative risk profile

� Other tools to model uncertainty: fault trees and event trees

3


4

We want to invest some €’s. We are uncertain about how stock markets and interest rates…

Diário Económico, 17.05.2010http://www.euribor.org/

3 months interest rates


Structuring uncertainty within

problems

• Logical and time structure between decisions

• Logical structure (dependent) between uncertain events

• Time structure of the sequence of uncertain events, related with a sequence of decisions

• Representations using key concepts:

�Influence diagrams

�Decision trees

5

Influence diagrams and decision

trees


Influence Diagrams

1. Elements are represented by:

(rectangles) represent decisions (and alternatives)

(ovals) represent uncertain events (and outcomes) (chance events)

(and calculation) nodes – represent consequences (and calculations)

Nodes are put together in a graph, connected by ARCS.Arcs represent relationships (relevance or sequence) between nodes: Predecessor node �� successor node

7


Influence Diagrams2. Logical relationships are represented by: arrows

Sequence

Relevance

8

Calculation nodes

Consequence nodes

9

Building an Influence Diagram

10

One should be ableto identify basicinfluence diagramsand modify/combinethem to matchspecific problems

Basic Influence Diagram: One decision

and one uncertain eventOutcomes

Wild Success

Flop

Alternatives

Savings

Business

Choice Business Result Return

Savings Wild Success 2200

Flop 2200

Business Wild Success 5000

Flop 0

11


A case with Imperfect Information

12

Forecast

Hits Miami

Misses Miami

Alternatives

Evacuate

Stay

Outcomes

Hits Miami

Misses Miami

Imperfect Information:• Involves one decision and two uncertain events at the time of the Decision Analysis.• One uncertain event is known at the time that the immediate decision is made.• Solving the influencediagram results in one optimaldecision for each possibleoutcome of the information source.

Choice Outcome Conseq. risk Conseq. cost

Evacuate Hits Miami Low risk High cost

Misses Miami Low risk High cost

Stay Hits Miami High risk High cost

Misses Miami Low risk Low cost

13

But if there is missing information: The

case for sequential decisions...

14

More on sequential decisions

15

Developing financial models while

accounting for uncertainty…1st version

2nd version

3rd version

16


A DECISION TREE represents all of the

possible paths that the DM might follow

through time, including all possible

decision alternatives and outcomes of

chance events

17


A simple Decision Tree

18

Decision tree and the objectives

hierarchy

Outcomes measured in multiple dimensions…

19

Representing elements in a decision

tree

Decision nodes

Represent decisions

Chance nodes

Represent chance (uncertain) events

Consequences

Consequences are specified at the ends of the branches

The options represented by branches from a decision node must be such that the DM can choose only one option.

Each chance node must havebranches that correspond to a set of mutually exclusive and collectively exhaustiveoutcomes.

When the uncertainty is

resolved, one and only one of the

outcomes occurs.

20


Reading decision trees…

• If a chance node is to the right of a decision node, the decision must be made in anticipation of the chance event.

• Conversely, placing a chanceevent before a decisionmeans that the decision is made conditional on the specific chance outcome having occurred.

• Imperfect information: DM waits for inf. before making a decision.

• The crescent shape indicates that the uncertain eventmay result in any value between two limits.

21


Decision Trees

1. Decision Trees are evaluated from left to right2. Only one alternative can be chosen after each

decision node3. Outcome from a chance event needs to be

complete, i.e. not more than one outcome can happen at the same time and one outcome will happen

4. Decision Trees represent all possible future scenarios

5. Think of nodes as occurring in time sequence6. If for chance nodes the order is not important, then

use the easiest interpretation

22

Again the hurricane example… with

imperfect information

23


Decision Trees vs. Influence

DiagramsInfluence Diagrams Decision Trees

Strenghts CompactGood for communication, in particular in the structuring phaseGood overview of large problemsGood for understanding the relevance between uncertainty nodes

Displays details, being good for in-depth understandingFlexible representationBest for assymetric decision problemsAdequate for performing sensitivity analysis

Weaknesses Details suppressed Becomes very messy for large problems

Complementary use of decision trees and influence diagrams!

24

25

DPL Software

Assess the Cash Flows and probabilities

using the Precision Tree software

26


27

Laboratory (next week)

Examples from PrecisionTree

28

Other concepts

Expected monetary value

Risk profile


The Risk Profile concept• A risk profile is a graph that shows the chances associated with

possible consequences.

• Each risk profile is associated with a strategy, a particular immediate alternative, as well as specific alternatives in future decisions.

0

0,1

0,2

0,3

0,4

0,5

0,6

-100000 -50000 0 50000 100000 150000 200000 250000 300000

Pro

ba

bil

ity

Value

Risk Profile For Oil Diagram of oil_infl.xls

30


The Cumulative Risk Profile concept

• In this format, the vertical axis is the chance that the payoff is less than or equal to the corresponding value on the horizontal axis.

• It results from adding up, or accumulating the chances of the individual payoffs � Along the horizontal axis we can read the chance that the payoff will be less than or equal to that specific value.

0

0,2

0,4

0,6

0,8

1

1,2

-100000 -50000 0 50000 100000 150000 200000 250000 300000

Cu

mu

lati

ve

Pro

ba

bil

ity

Value

Cumulative Probability For Oil Diagram of oil_infl.xls

31

∑≤

==≤=yii

iYyYyF:

)Pr()Pr()(


The Expected Value concept

The random variable Y has many possible outcomes!

Expected value: “BEST GUESS” for Y, what number

would you give?

Interpretation: If you were able to observe many

outcomes of Y, the calculated average of all the

outcomes would be close to E[Y].

[ ] ∑∑==

===Εn

i

ii

n

i

ii pyyYyY11

*)Pr(*

32

Other tools to model uncertainty

Event trees

Fault trees


It is simply a decision tree without any decisions!

34


What is Event Tree Analysis?

• An accidental event is defined as the first significant deviation from a normal situation that may lead to unwanted consequences (e.g., gas leak, falling object, start of fire)

• It may lead to many different consequences. The potential consequences may be illustrated by a consequence spectrum:

35

Source: System Reliability Theory: Models, Statistical Methods, and Applications, M. Rausand, A. HøylandWiley-Interscience (2003)


Example

Applications: Risk analysis of technological systems; Identification of improvements in protection systems and other safety functions

36


What is Event Tree Analysis?

• An event tree analysis (ETA) is an inductive procedure that shows all possible outcomes resulting from an accidental (initiating) event, taking into account whether installed safetybarriers are functioning or not, and additional events and factors.

• By studying all relevant accidental events (that have been identified by a preliminary hazard analysis, or some other technique), the ETA can be used to identify all potential accident scenarios and sequences in a complex system.

• Design and procedural weaknesses can be identified, and probabilities of the various outcomes from an accidental event can be determined.

37


A fault tree begins with an initial system problem, and then represent all the corrective actions or systems events that can be taken to correct the default.

38


Fault Tree Analysis

• Technique for reliability and safety analysis � The failure of an item in a system is often caused by the failure of other items, for example where a vehicle's braking failure is caused by water in the brake cylinders, which may in turn be caused by failure of the cylinder seals.

• Fault Tree Analysis provides a method of breaking down these chains of failures, with a key addition for identifying combinations of faults that cause other faults.

• Combinations of faults come in two main types: (a) where several items must fail together to cause another item to fail (an 'and'combination), and (b) where only one of a number of possible faults need happen to cause another item to fail (an 'or'' combination). These combinations work as gates by preventing the failure event to happen if specific conditions are met.

39

Fault Tree analysis in problem solving

Logical And and Or in Fault Tree analysis

Source: http://syque.com/quality_tools/toolbook/FTA/fta.htm

40


Example

A company president recognized that its personnel evaluation system was not effective at motivating its employees, and charged the personnel department with improving it. As a part of the initial analysis of

the existing system, they use FTA to identify the different ways that the evaluation system can fail

and lead to lack of motivation.Identified failure areas were investigated further, and

the new system based on a correction of these failures. As a result, motivation increased

significantly.

Source: http://syque.com/quality_tools/toolbook/FTA/fta.htm

41


Fault Trees are particularly

useful to…

• Use when the effect of a failure is known, to find how this might be caused by combinations of other failures.

• Use when designing a solution, to identify ways it may fail and consequently find ways of making the solution more robust.

• Use to identify risks in a system, and consequently identify risk reduction measures.

• Use to find failures which can cause the failure of all parts of a 'fault-tolerant' system.

43

MAD revising decision trees and influence diagrams · Representing elements in a decision tree...

Documents

Transcript of MAD revising decision trees and influence diagrams · Representing elements in a decision tree...