What is Decision Analysis? Decision analysis consists of a set of quantitative procedures that help...

What is Decision Analysis?

Decision analysis consists of a set of quantitative procedures that help decision-makers:

• quantify the uncertainty in the processes or outcomes associated with the decision (this includes combining existing data and models with expert judgments and beliefs)

• quantify their preferences or values (this includes the values of all stakeholders)

• combine uncertainty and preferences (values) into a single model to arrive at optimal decisions

Decision analysis is a systematic process of documenting and

weighing alternative scenarios in terms of their respective costs,

probabilities of success or failure, and benefits.

• structure decision problems and develop creative decision alternatives

The decision analysis process

Identify the decision situation and objectives

Identify the alternatives

Decompose and model the problem:1. Model of problem structure2. Model of uncertainty.3. Model of preferences

Choose the best alternative

Perform sensitivity analysis

Is further analysis needed?

Implement the best alternative

NO

YES

Elements of a Decision Problem

· Values are defined simply as the things that matter most to the decision-maker(s).

· An objective is the specific thing that the decision maker wants to achieve.

· The sum of a decision maker’s objectives defines what is important and hence, constitutes his or her values.

· The decision context (or decision situation) is the setting in which the decision occurs. It determines what objectives should be considered. When a series of interrelated sequential decisions must be made, often referred to as dynamic decision situations.

· A requisite decision (Phillips 1982) considers the only the elements that are necessary to solve the problem (i.e., that are relevant within the decision context).

Decision alternatives are the options that are available to the decision-maker.

· Uncertain events are the outcomes that could happen in the future due to chance and as a result of a decision. (Only the outcomes that are meaningful to the decision-maker and that have an impact in terms of the objectives should be considered.)

· Consequences are eventual outcomes of the decision situation. Consequences are directly related to the decision-makers objectives (multiple objectives = multiple consequences).

The planning horizon is the interval from the current time and current decision to the end of the time line. It should be consistent with the decision context and objectives.

Structuring Decisions

Once the values, objectives, and decision situation have been identified they need to be put into a logical framework.

Identify and organize fundamental and means objectives.

Fundamental objectives are what the decision-maker really wants to accomplish. These are the basis by which the consequences will be measured.

Means objectives are the things that need to be accomplished to realize the fundamental objective. These are distinguished from the fundamental objectives via the WITI test – Why Is That Important?

After identifying and structuring the fundamental objectives, we can now structure the remaining elements – decisions and alternatives, uncertain events and outcomes, and consequences.

Means objectives network

Have moremoney

Make more money

Spend lessmoney

Get second job

Buy cheaperbrands

Why is that important?

How could I achieve this?

Investin stocks

Fundamentalobjectives

Meansobjectives

AtlantaWest Point Reservoir

6

8

10

12

14

16

18

20

22

24

Year1988 1990 1992 1994 1996 1998

Adu

lt La

rgem

out

h b

ass

CP

UE

Example: Typical Management Decision

The problemWastewater treatment has decreased fertilityLargemouth bass populations have declined

Angler catch rates have decreasedAnglers and marina operators are dissatisfied

Decision alternatives

12”, 14”, 16” minimum length limit

Fundamental objectivesSatisfy recreational anglers

Satisfy tournament anglers

What makes LMB anglers happy?P

erce

nt

of

resp

on

den

ts

0

5

15

25

35

Total length (in)

0

20

40

60

80

1 to 5 6 to 10 11 to 15 16 to 20 21 ormore

Creel limits

Recreational LMB angler preferences

Results of 1997 Georgia DNR Statewide Angler Study

Limit 10

Limit 6

Limit 3Limit 1

However, tournament anglers prefer large numbers of legal fish

12 14 16 18

Largemouth bass angler satisfaction

Structuring Values and Objectives

Provideconsistent

anglingopportunities

(stable population)

Maximize tournament

angler satisfaction

Maximize number of creelable

largemouth bass(number of creelable LMB)(number of large LMB)

Maximizerecreational

angler satisfaction

Maximize number

of large fish

(quantifiable objectives = outcomes)

Bait onHook

Fish Hungry

Fish caught

Recall an earlier model of fishing…..

where the probability of catching a fish is influenced by bait staying on thehook and fish being hungry

Developing a Model of the Outcomes

Catch Fish

Fish Hungry

Bait on Hook

Yes

Yes

Yes

Yes

Yes

Yes

YesNo

No

No

No

No

No

No

0.80

0.20

0.50

0.50

0.30

0.70

0.10

0.90Probability of catching a fish on any given cast

0.50

0.50

0.50

0.50

0.50

0.50

+ 0.5*0.5*0.1 = 0.425

+ 0.5*0.5*0.9 = 0.575

Decision Tree

Yes

Yes

Yes

Yes

0.5*0.5*0.8 + 0.5*0.5*0.5 + 0.5*0.5*0.3

0.5*0.5*0.2 + 0.5*0.5*0.5 + 0.5*0.5*0.7

Probability of NOT catching a fish on any given cast

No

No

No

No

Catch Fish

Fish Hungry

Bait on Hook

Yes

Yes

Yes

Yes

Yes

Yes

YesNo

No

No

No

No

No

No

0.80

0.20

0.50

0.50

0.30

0.70

0.10

0.90

0.50

0.50

0.50

0.50

0.50

0.50

Add a Decision to the Tree

Cast?

Yes

No

Yes

No

0.00

1.00

Catch Fish

Probability of catchingfish = 0.425

Probability of catchingfish = 0

Catch Fish

YesNo

21.378.8

Bait on Hook

YesNo

50.050.0

Fish Hungry

YesNo

50.050.0

Cast bait?

YesNo

0 0

Add a Decision to the Net

Catch Fish

YesNo

42.557.5

Bait on Hook

YesNo

50.050.0

Fish Hungry

YesNo

50.050.0

Cast bait?

YesNo

0 0

Catch Fish

YesNo

0 100

Bait on Hook

YesNo

50.050.0

Fish Hungry

YesNo

50.050.0

Cast bait?

YesNo

0 0

Add Values to the TreeEnjoyment

ValueCatch Fish

Fish Hungry

Bait on Hook

Yes

Yes

Yes

Yes

Yes

Yes

YesNo

No

No

No

No

No

No

0.80

0.20

0.50

0.50

0.30

0.70

0.10

0.90

0.50

0.50

0.50

0.50

0.50

0.50

Cast?

Yes

No

Yes

No

0.00

1.00

Catch Fish

100

25

100

25

100

25

100

25

100

25

EnjoymentValue

Enjoyment value of casting Enjoyment value of NOT casting

0.5*0.5*0.8*100 + 0.5*0.5*0.2*25… = 56.87 0.00*100 + 1.00*25 = 25.00

Add Values to the Net

Bait on Hook

YesNo

50.050.0

Fish Hungry

YesNo

50.050.0

Cast bait?

YesNo

56.875025.0000

Catch Fish

YesNo

21.378.8

U

The result: an Influence Diagram

Influence Diagram, 3 basic components

Cast?

Bait onHook

FishHungry

Enjoymentvalue

CatchFish

TheDecision

Utility

KeyUncertainties

(Bayes Network)

Influence Diagram

Cast?

Bait onHook

FishHungry

Enjoymentvalue

CatchFish

NOT a flowchart

Links representdependence(causality)

ONLY type of link to representtiming (flow of information)

Where do the utility values come from???

Largemouth bass angler satisfaction

Maximize tournament

angler satisfaction

Maximizerecreational

angler satisfaction

Maximize number of creelable

largemouth bass

Maximize number

of large fish

Provideconsistent

anglingopportunities

How could I achieve this?

Meansobjectives

Why is that important?

Fundamentalobjectives

LMB decision model means objectives network

For simple (single) endpoints, it’s a simple function of estimated output e.g., animal abundance, number animals harvested.

When there are multiple endpoints, need a means to valuate each e.g., the means and objectives hierarchies

Sensitivity analysis

Like all models, Bayesian Belief Networks and Influence Diagrams should be examined via sensitivity analysis

Basic idea:

Vary the values of each parameter and examine the effect on desired outputs

Two types of sensitivity analysis

Analysis of the influence of parameters on the utility values (IDs only)“value sensitivity comparison”

Analysis of the influence of parameters on the probability of a specific outcome(IDs and BBNs)

There is no single best method of examining model sensitivity

Streambed Fine Sediment

LowModerateHigh

46.232.321.5

Watershed Slope

LowModerateHigh

33.333.333.3

Current Population Size

SmallModerateLarge

88.311.7 0 +

Fish Population

IncreasingStableDecreasing

11.049.239.8

Timber Harvest?

NoneLowModerate

30.193831.253026.9035

Sediment Yield

LowModerateHigh

44.730.025.3

Egg-to-Fry Survival

LowModerateHigh

27.930.441.7

Net Value

Timber Harvest Example

33.172

Egg-to-Fry-Survival

Sediment Yield

Current Population Size

Watershed Slope

20 22 24 26 28 30 32 34 36 38 40Net Utility

Future Fish population

Value Sensitivity Analysis

Tornado diagram of timber harvest example

Greatestinfluence

Leastinfluence

Sed

LowMedHigh

45.929.524.6

Habitat_Condition

ComplexModerately ...Highly Simp...

33.832.933.2

Flood

NoYes

91.88.25

Mgnt_Alternatives

Alt AAlt BAlt C

0 0 0

Prior_Ripo_Cond

None LightMod High

50.050.0

Road_Disturb

LowMedHigh

38.733.028.3

Ripo_Cond

IntactMod DegradedHi Degraded

37.837.724.5

Future_Grazing

NoYes

50.050.0

Grnd_Dist_Index

LowMedHigh

33.333.333.3

Slope_Steepness

GentleMedSteep

33.333.333.3

Road_Dens

LowMedHigh

33.333.333.3

S_G

Hi MitigationMod MitigationLow Mitigation

33.333.333.3

Percent Steep Slopes

Fire

NoYes

50.050.0

Aquatic Habitat Model for Interior Columbia River Basin Model

“Probability” Sensitivity Analysis

Several measures, most common is known as “entropy reduction”or mutual information

Interior Columbia River Basin aquatic habitat modelThe summary output of the sensitivity analysis of habitat condition node is below

Sensitivity of 'Habitat_Condition' due to a finding at another node:

Node Mutual Quadratic ---- Info Score Habitat_Condition 1.58310 0.4435845 Ripo_Cond 0.16662 0.0287079 Sed 0.07749 0.0128482 S_G 0.04272 0.0067063 Flood 0.01492 0.0026125 Prior_Ripo_Cond 0.01105 0.0017047 Road_Disturb 0.00474 0.0007314 Future_Grazing 0.00143 0.0002230 Road_Dens 0.00115 0.0001767 Slope_Steepness 0.00041 0.0000635 Fire 0.00000 0.0000000 Grnd_Dist_Index 0.00000 0.0000000

Most

Least

“Probability” Sensitivity Analysis

The influence of individual nodes on habitat condition probabilities can also be examined

Sensitivity of 'Habitat_Condition' to findings at 'Ripo_Cond': Probability ranges: Min Current Max | RMS Change Complex 0.07938 0.3135 0.5415 | 0.1879 Moderately_Simplifie 0.2761 0.3316 0.3917 | 0.04826 Highly_Simplified 0.1508 0.3549 0.6446 | 0.1909

Quadratic scoring = 0.02871

Entropy reduction = 0.1666 (10.5 %)

Ground Disturbance Index

Flood

Road Density

Future Grazing

Standards & Guides

Fire-Rain

Slope Steepness

Prior Riparian Condition

Road Disturbance

Riparian Condition

Sediment

Slope 2

Probability of High Aquatic Habitat Capacity 0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70

These can also be placed in a tornado diagram:

bull trout presenceunknown, assumed 50/50

Net Value

Future Population Status

presentabsent

38.361.7

Bull trout population

presentabsent

50.050.0

Environmental impact

nonelowHigh

36.730.033.3

Management action

9.159.65

High intensity

NoneLow intensity

9.50 Expected value of management action,Best course of action but not by much

Net value is gain from resource use (low/ high) plus value or cost associatedfuture bull trout population status in a sampling frame.

Sensitivity analysis suggests that some variables have a greater influenceon the net value (utility) of a decision. Consider the following hypothetical of a natural resource management decision analysis.

Management action

13.7517.25

High intensity

NoneLow intensity

18.25

Net Value


presentabsent

65.734.3


presentabsent

100 0


nonelowHigh

36.730.033.3

Best course of action

Same decision, but presence known

Value of information

Best course of action

Management action

5.452.05

High intensity

NoneLow intensity

0.75

Net Value


presentabsent

11.089.0


presentabsent

0 100


nonelowHigh

36.730.033.3

Same decision, but absence known


Management action

5.452.05

High intensity

NoneLow intensity

0.75

Net Value


presentabsent

11.089.0


presentabsent

0 100


nonelowHigh

36.730.033.3

Draw an arc between the decision and bull trout population:

Value of Information

This representsthe flow of information.In this instance, knowledgeof the presence of bull trout

Bull trout present

None [18.25]

Low_intensity [17.25]

High_intensity [13.75]

Bull Trout Absent

None [0.75]

Low_intensity [2.05]

High_intensity [5.45]

Expected value of management action when…

Optimal value in green

Environmental_inpact None [18.25]

Environmental_inpact Low_intensity [17.25]

Environmental_inpact High_intensity [13.75]

Management_action Present

.500

[18.25]

Environmental_inpact None [0.75]

Environmental_inpact Low_intensity [2.05]

Environmental_inpact High_intensity [5.45]

Management_action Absent

.500

[5.45]

Current_Population_Status

18.25*0.500 + 5.45*0.500 = 11.85

The value of PERFECT information

Calculate Value of information

11.85 – 9.65 = 2.20


But… not all information is perfect (it almost never is)

Sampling error

Some sources of imperfection

Incomplete understanding of process

Random error

Others???

Therefore, we need to consider these when evaluating information

Let’s say that we want to harvest a watershed that could contain bull trout. We don’t know if it does contain trout and want to know if it’s worth sampling

Assume 100 samples are needed to detect bull trout 80% of the time. TheCost of sampling = 0.5

Assume 80% probability of detection:

P(detected| present) = 0.80

Assume 50% probability of bull trout present:

P(present) = 0.50 P(not present) = 0.50

P(detected| not present) = 0

The probability of detecting bull trout = 0.8*0.5 + 0*0.5 = 0.40

First we estimate the probability of detecting bull trout if we sampled

Value of imperfect information, step 1

Net Value

Management action

NoneLow inte...High inte...

9.500009.650009.59999


presentabsent

38.361.7


nonelowHigh

36.730.033.3


presentabsent

50.050.0

Sampling Results

PresentAbsent

40.060.0


P(not detected| present)*P(present)

P(not detected| present)*P(present) + P(not detected| not present)*P(not present)

However, we want to know the (posterior) probability that bull trout are present if not detected (Bayes formula)

Assume 80% probability of detection:

P(not detected| present) = 1- 0.80 = 0.20

Assume 50% probability of bull trout present:

P(present) = 0.50 P(not present) = 0.50

P(not detected| not present) = 1

0.20*0.50

0.20*0.50 + 1*0.50= 0.167 or 16.7%

Now calculate:

The posteriorprobability thatbull trout are present

Net Value

Management action


9.500009.650009.59999


presentabsent

38.361.7


nonelowHigh

36.730.033.3


presentabsent

50.050.0

Sampling Results

PresentAbsent

40.060.0

Notice arrow is reversedrepresenting posterior prob.


none [9.50]

low_intensity

[9.15] high_intensity

[9.65]

Management activity

[9.65]

none

[13.75]

low_intensity

[18.25]

high_intensity

[17.25] Bull trout present

0.400 [18.25]

none [0.75]

low_intensity [2.05]

high_intensity [5.45]

Bull trout absent 0.600

[5.45]

[10.57]

Posterior probability given 50/50 prior and 80% detection probability

Sampling decision

10.57 – 9.65 = 0.92

Value of sampling information

Sample

Not sample

[10.57]

Value

0.92 minus the cost of collecting samples to get 80% detection probability (0.5)

Assuming a 50% probability of presence

Net = 0.92 – 0.5= 0.42

Information value is calculated similar to perfect information

Net Value

Management action



presentabsent

50.050.0


nonelowHigh

33.333.333.3


presentabsent

50.050.0

Sampling Results

PresentAbsent

50.050.0

Sample?

YesNo

Value of imperfect information

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