An Influence Diagram for Management of Mildew in Winter Wheat

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An Influence Diagram for Management of Mildew
in Winter Wheat

• Allan Leck Jensen
• Danish Informatics
• Network in the Agricultural Sciences
• Research Center

• Finn Verner Jensen
• Department of
• Computer Science
• Aalborg University

-presented by Bingyu Zhu and Sen Xu
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Abstract

• A prototype of a decision support system for
  management of the fungal disease powdery mildew
  in winter wheat
• An influence diagram which is used to determine
  the optimal time and dose of mildew treatments
• Practical and theoretical problems during the
  construction of the influence diagram, and also
  the experience with the prototype

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Background

• In Denmark, environmental impacts of agricultural
  production must be reduced.
• Findings of pesticides and nitrogen residues in
  drinking water have induced the government to
  take actions for a significant reduction of the
  consumption of fertilizers and pesticides.

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Dilemma of farmers

• Agricultural input factors fertilizers and
  pesticidesvery expensive
• Reductions in these input factors can cause
  inadequate effects and hence economical losses
• Farmers apply excessive amounts of input factors
  to avoid inadequate effects of input factors.

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How to solve

• Reduce the consumption of input factors and save
  money if they can get the recommendations that
  when it is safe to reduce the doses.
• These recommendations could come from decision
  support systems
• Insurance farming ? Precision farming

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Decision Support System

• MIDAS Mildew Influence Diagram for Advice of
  Sprayings.
• Influence diagram Case-specific recommendations
  of timing and dosage of mildew treatments.

The Ph.D. thesis can be downloaded from
http//www.sp.dk/alj/
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The Disease-Powdery Mildew

• Weather conditiontemperature, humidity and wind
• Under favorable conditions
• Spread rapidly
• Under unfavorable conditions
• Not spread, the present disease may disappear
  with time due to the emergence of new, uninfected
  leaves and the death of old, infected leaves

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MIDAS

• Based on the field observations and the
  expectations to the future
• Determine the optimal treatment decision for the
  current disease problem
• Assumption all future decisions will be made
  optimally according to the available information
  at the time

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Decision Optimization

• Affected by uncertainty of
• Stochasticity
• Weather and disease infections with elements of
  unpredictability
• Inaccurate observations
• Field recordings of disease level are difficult
  and error prone
• Incomplete knowledge
• Interpretations of relations in domain involves
  uncertainty

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Dynamic Influence Diagram

• A sequence of time steps.
• Each time step
• Information variables
• A single treatment decision variable
• Chance variables
• Time is an important parameter

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Variable types
Static information Winter wheat variety, Soil type, Nitrogen fertilization strategy, Plant density
Dynamic information Weather, Disease incidence, Remaining time to harvest, Cost of fungicide and spraying, Label dose of fungicide, Expected price of grain and yield
Decision Dose of treatment (0 possible)
Utilities Value of yield, Cost of treatment, Value of disease induced yield loss
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Thermal Time Scale

• Three influentials
• Chronological time
• Temperature
• Crop development stage
• Thermal time scale
• Definition The expected temperature sum
  remaining to crop maturity
• Divided into thermal time periods, each
  corresponding to a time step of the decision
  model.
• Length of a time step is called a thermal week.
• Farmers give their estimates of the number of
  weeks to crop maturity

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The Initial Influence Diagram

• GDM module
• Case-specific time step modules
• Decision model

Time
Field
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The GDM module
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Dynamic Programming

• First, the final decision is considered
• For each information scenario at that time, the
  decision alternative with optimal expected
  utility is determined.
• The preceding decisions are considered in reverse
  order, and each of them is optimized under
  assumption of optimal decision making in the
  future.

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Computation Complexity Problem

• The set of information scenarios at the time of a
  decision consists of all configurations of
  observed variables which are d-connected to a
  utility node influenced by the decision.
• DiseaseLevel in initial GDM
• the current state of the disease depends on not
  only the current value of DiseaseObser, but also
  all the previous, together with all previous
  treatment decisions.

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Information Blocking Condition

• The local information of the system overwrites
  all previous information.
• P(Y Ik, Dk, X) P(Y Ik, Dk)
• for X ? U Ti (i1,,k-1),
• Y ? U Ti (ik1,,n).
• P(Y Tk, X) P(Y Tk)

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Change the structure
DiseaseObserv_1
DiseaseObserv_1
DiseaseLevelB_1
DiseaseLevelA_1
DiseaseLevelB_1
DiseaseLevelA_1
Figure3 Left The initial causal structure of
the relationships between the DiseaseObserv and
the DiseaseLevel nodes. Right The modified
structure to achieve a blocking of the past by
the observed nodes(DiseaseObserv).
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A Decision Model with 3 Time Step
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Experience--Quantitative

• Single model clique size 27388 probabilities,
  83196 for each additional time step.
• 1.6 Million for a model with 20 time steps, 14.8M
  to store.
• Performance on SUN
• Assemblage 1 sec
• Compilation 100 secs
• Loading 25 secs
• Propagation 25 secs

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Experience--Qualitative

• Evaluation of the predictions of DiseaseLevel
• True and Approximate Structures
• True structure are good.
• Approximate Structure less satisfactory
• underestimate high disease levels and
  overestimate low disease levels.
• Predicted probability distributions are too
  narrow.
• DiseaseObserv was intended to be a simple measure
  for DiseaseLevel.

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Future Work--Improvement

• Several Different Prior Distribution for P(DLB)
  in order to fit actual situation.
• Additional information node introduced, in order
  to improve the calibration of DeseaseLevel.
• Relaxation of the information blocking condition.
• Approximative for decision, true for reasoning.
• Other problems.

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Thank you!