Théorie de la décision pour la protection des cultures · Théorie de la décision pour la protection des cultures Dr Neil M cRoberts Reader in Systems Ecology, Scottish ... [email protected]

Théorie de la décision pour la protection des cultures

Dr Neil McRoberts

Reader in Systems Ecology,

Scottish Agricultural College, Edinburgh, UK

[email protected]

Presentation topics

• Motivations for improving decision making

• Generic structure of the decision problem

• Assessing decision tool fitness for purpose

• The past and the future for decision tools?

Motivations for improving decision making

• All stakeholders in agriculture require it

– Policy makers; environmental protection

– Growers ; economic efficiency, compliance with policy

– Industry; justify use, quality assurance

Growers’ actions

Policy

Agriculture

Presentation topics





Generic structure of the decision problem

A

B

C

D

A

B

C

D

A

B

C

D

A

B

C

D

A

B

C

D

A

B

C

D

The past The present The future

A

B

C

DDM

Which action is correct?

The opportunity fordecision tools

Predicting outcomes from noisy dataAird 2005 Disease progress

0

1020

3040

50

6070

8090

100

20/05/05 03/06/05 17/06/05 01/07/05 15/07/05 29/07/05 12/08/05 26/08/05 09/09/05 23/09/05

Bed 1

Bed 2

Bed 3

Bed 4

Bed 5

Aird 2005 Environmental data

0

5

10

15

20

25

20/05/05 03/06/05 17/06/05 01/07/05 15/07/05 29/07/05 12/08/05 26/08/05 09/09/05 23/09/05

-10

10

30

50

70

90

110

Rainfall (mm)

Air Temp

RH

Ravensby 2005 Environmantal data

0

5

10

15

20

25

30

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03/06/05 17/06/05 01/07/05 15/07/05 29/07/05 12/08/05 26/08/05 09/09/05 23/09/05 07/10/05 21/10/05

-10

10

30

50

70

90

110

Rainfall (mm)

Air Temp

RH

√√√√

X

Developing & usingdecision tools

•Extract evidence-baseddiscrimination rules (EBDR)

•Use EBDR to updateknowledge & improvedecision-making

EBDR can be derived in many ways

Discriminating cases from controls

Actionneeded

Actionnot needed

Actiontaken A B

Action nottaken C D

Real state of affairs

EB

DR

res

ult

Likelihood ratios

LR+ Likelihood ratio of apositive prediction ofneed for actionsensitivity/(1-specificity)

LR- Likelihood ratio of anegative prediction of need for action(1-sensitivity)/specificity

Sensitivity (TPP) = A/(A+C)

Specificty (1-FPP) = D/(B+D)Of EBDR

Frequency distributions of “cases” and “controls” on an EBDR scale

0.0

1.4

2.8

4.2

5.6

7.0

1.4

2.8

4.2

5.6

7

Dual histogram of BERP by EP

Fre

quen

cy

EP

655 765 875 985 1095 1205 1315 1425 1535 1645 1755

10

FNPTPP

TNPFPP

EBDR value

ROC Curves for potential epidemic diagnostic

0

0.25

0.5

0.75

1

0 0.25 0.5 0.75 1

FPP

TP

P

BERP

DP3

AUROC (BERP) = 0.83

AUROC (DP3) = 0.80

No discriminatio

n

0

0.25

0.5

0.75

1

0 0.25 0.5 0.75 1

FPP

TP

PBERP

DP3

ROC Curve of BERP and DP3 againstepidemic classification

0.5926

0.0526= 11.27

LR+

0.4074

0.9474= 0.43

LR-

prior

prior

post

post

p

pLR

p

p

−×=

− + 11

Good discrimination allows effective (Bayesian) updating

Posterior odds(D+|T+) = LR + ×××× Prior odds(D+)

Updating ( we hope?) changes behaviour.

But is the balance of probabilities overwhelming?


The past The future

DM


EBDR

Prior odds(D+) ×××× LR+ = Posterior odds(D+|T+)

αααα

ββββββββ

αααα

ββββ

αααα

ββββ

αααα

ββββ

αααα

ββββ

αααα

ββββ

αααα

What forms a grower’s own EBDR?

Source of Information % Highly ImportantOwn Experience 93%Cornell Recommends 86%Extension news letters 64%Grower Meetings 43%Extension Code-a-phone 21%Chemical field rep. 14%Other 14%Ag. Chemical Handbook 7%

(1998 Survey of New York State wine grape growers)

Scottish arable growers’ evidence networks

-0.1 -0.08 -0.06 -0.04 -0.02 0 0.02 0.04-0.05

-0.03

-0.01

0.01

0.03

0.05

spousepartner

children bankman

account

advisor

rep

lawyer

employee

other

bookkeep

cropprot

contract

finance

investmarket

futures

size diversify

Correspondence analysis of decisions and decision-mak erson Scottish arable farms

CA axis 1 57% variance

CA

axi

s 2

19%

var

ianc

eState extension servicewith direct input fromSAC and other R&Dinstitutes

Presentation topics





Updating implies supplying and receiving information

“For a forecasting system to be successful, it must be adopted and implementedby growers. There must be the perception that the grower can realize specific,tangible benefits from using the forecasting system that could not be realizedin its absence.” (Campbell & Madden, 1990, p424.).

0 0.2 0.4 0.6 0.8 10

0.5

1

probability of event

Info

rmat

ion

requ

ired

Shannon’s (1948) entropy equation

I

i

pi

− log2

⋅∑ pi( )

Ex p

ecte

d in

f orm

a tio

n (e

ntro

py)

Changing a user’s balance of probabilities

0 0.2 0.4 0.6 0.8 10

0.5

1


Info

rmat

ion

req

uire

dE

x pec

ted

inf o

rma t

ion

(ent

ropy

)

Equal certainty

implies flipping the odds

( ) ( ))(1

)(

)(1

)(

_

_

+−+

+−+

− = DP

DP

DP

DP

req prior

prior

reqpost

reqpostLR

What does the equal uncertainty criterion imply for forecaster performance?

0 0.2 0.4 0.6 0.8 11 .10

4

1 .103

0.01

0.1

1

10

100

1 .103

1 .104

required LR for Hpost = Hpriorp = 0.5

required LR vs. p

prior or posterior probability

LR

Forecasters/toolswith LR+ ≥≥≥≥10, LR-≤≤≤≤0.1would allow equaluncertainty for mostusers

Zone of performancefor most currentforecasters

Changing a user’s balance of probabilities

0 0.2 0.4 0.6 0.8 10

0.5

1


Info

rmat

ion

req

uire

dE

x pec

ted

inf o

rma t

ion

(ent

ropy

)

Equal certainty

implies flipping the odds

( ) ( ))(1

)(

)(1

)(

_

_

+−+

+−+

− = DP

DP

DP

DP

req prior

prior

reqpost

reqpostLR


The past The future

DM


EBDR

Prior odds(D+) ×××× LR+ = Posterior odds(D+|T+)

αααα

ββββββββ

αααα

ββββ

αααα

ββββ

αααα

ββββ

αααα

ββββ

αααα

ββββ

αααα

Presentation topics





Expected utility (expected regret)

p [= P(D+)]0 1

Exp

ecte

d ut

ility

Don’t act

Acta

b

c

d

E(UA)=pb+((1-p)a)

p*

p*=(a-c)/[(a-b)-(c-d)]

The Future:Task for epidemiologyis to say what p* is

Each DM’s experience personalises p*

The past The future

DM


αααα

ββββββββ

αααα

ββββ

αααα

ββββ

αααα

ββββ

αααα

ββββ

αααα

ββββ

αααα≥≥≥≥ p*

< p*

Estimating p* requires long-term multi-site data

Data: Zwankhuizen & Zadoks 2002. Plant Path. 51: 413-423

Polyetic disease example: Dutch national late blight epidemics 1950-1996

-1

-0.5

0

0.5

1

1.5

2

1940 1950 1960 1970 1980 1990 2000

year

ln(d

isea

se in

dex)

No blight

-2.5

-2

-1.5

-1

-0.5

0

0.5

1

1.5

2

2.5

1940 1950 1960 1970 1980 1990 2000

year

ln(g

row

th r

ate)

How is system changing, and why?

var=0.163

var=0.414

Does epidemiology have the tools to answer these questions?

Polyetic disease example: Dutch national late blight epidemics 1950-1996

How is system changing, and why?

-2.5

-2

-1.5

-1

-0.5

0

0.5

1

1.5

2

2.5

1940 1950 1960 1970 1980 1990 2000

year

ln(g

row

th r

ate)

var=0.163

var=0.414

-1

-0.5

0

0.5

1

0 10 20 30 40

R_all_ACF

R_start_ACF

R_end_ACF

lag

AC

F

Even with long data series hard to distinguish between: (a) Random walk, (b) transition between 2 equilibria

Evidence of non-stationarity?

A new research agenda for epidemiology?

The new agenda addresses the same issues

p = process order (generation lag number for carry-over effects)q = polynomial coefficient

p = 1, q = 1 ⇒ Nt = f(Nt-1)

log(Nt) = a +(1+b)Nt-1 +εt

-1.5

-1

-0.5

0

0.5

1

1.5

1980 1990 2000 2010

logRs

Simulation

Motivations for improving decision making

• All stakeholders in agriculture require it

– Policy makers; environmental protection

– Growers ; economic efficiency, compliance with policy

– Industry; justify use, quality assurance

Growers’ actions

Policy

Agriculture

The managed past

Environmentalnoise

Agriculture of the future

Documents

Théorie de la décision pour la protection des cultures · Théorie de la décision pour la protection des cultures Dr Neil M cRoberts Reader in Systems Ecology, Scottish ... [email protected]