Post on 01-Jun-2020
Théorie de la décision pour la protection des cultures
Dr Neil McRoberts
Reader in Systems Ecology,
Scottish Agricultural College, Edinburgh, UK
neil.mcroberts@sac.ac.uk
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
• 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?
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
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5
10
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45
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?
Generic structure of the decision problem
The past The future
DM
Which action is correct?
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
• 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?
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
probability of event
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
probability of event
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
Generic structure of the decision problem
The past The future
DM
Which action is correct?
EBDR
Prior odds(D+) ×××× LR+ = Posterior odds(D+|T+)
αααα
ββββββββ
αααα
ββββ
αααα
ββββ
αααα
ββββ
αααα
ββββ
αααα
ββββ
αααα
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?
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
Which action is correct?
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