10-12-2019 Motivation Dairy cow mastitis is a serious problem - - PDF document

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Bayesian integration of sensor information and a multivariate dynamic linear model for prediction of dairy cow mastitis

Authors: Dan B. Jensen, Henk Hogeveen, and Albert De Vries Presented by: Leonardo de Knegt IPH, KU

Motivation

• Dairy cow mastitis is a serious problem
• Financial loss
• Animal welfare issue
• Lots of data are automatically collected
• Still not optimally used
• Existing automatic mastitis alarm systems:
• Simplistic (few inputs)
• Overly sensitive (too many false alarms)

IF “everything is fine” THEN “things progress as expected” Therefore: IF “things progress UN-expectedly” THEN “Something is wrong!”

Data

• University of Florida Dairy Unit
• 550 Holstein cows
• 12-hour milking intervals
• 1,003,207 milkings: 2008 to 2014
• 2,097 milkings: mastitis
• Milk-meter sensor
• Milk yield
• Electrical conductivity
• AfiLab sensor
• Fat%
• Protein%
• Lactose%
• Blood%
• SCC

Data Level adjustment

• Multiple data sources
• Differing numerical magnitudes
• Milk yield: 16 kg
• Blood: 0.22 %
• Body weight: 600 kg
• Differing systematic and observational variances
• Problems when modelling!
• Solution: data level adjustments!
• dividing all milk yield observations by 10
• dividing all BW observations by 100
• everything else is kept as is

Methods Multivariate Dynamic Linear Model (DLM)

Structure: Observation equation System equation Usefulness:

• Monitoring of (production) systems over time

Features:

• Provides one-step-ahead forecasts,

including estimated forecast variance

• Dynamic, i.e. Adaptive

Methods Application of the DLM (1) Univariate example – Morning Milk Yield: Yield on Day 1: 0.47 kg Initial trend in morning milk yield is +0.21 kg/d Mean of first obs across all lactations in the training set

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Matrix multiplication – simple example

An element in the product is calculated as the product of a row and a column 0.47 0.21 1 1 1

0.68 0.21

G θ1

The system matrix G has a structure which produces the sum of the previous estimate with the expected trend on the yield row, when multiplied with theta.

Matrix multiplication – simple example

An element in the product is calculated as the product of a row and a column 0.68 0.21 1

0.68

F’ θ2

The design matrix F’ has a structure which separates the

• bservable

values from the unobservable trends, producing a vector of the expected

• bservation Yt

Methods Application of the DLM (1) The multi-variate case – repeat for each variable: Methods Application of the DLM (1) The multi-variate case – repeat for each variable:

F’t

• 1

2 3 4 5 6 7 F’t

• Methods

Application of the DLM (1) The multi-variate case – repeat for each variable:

Gt

• 1

2 3 4 5 6 7 Gt

• Methods

Application of the DLM (1) The multi-variate case – repeat for each variable: Co-dependencies between observable variables Co-dependencies between observable and unobservable (d) variables

1,1 … 1,7 7,1 … 7,7

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CLASS QUESTIONS

Q1: What is wrong with my milk yield model? Q2: What could be done to fix this problem?

Learning the likelihoods

• sensor example

Low Middle-Low Middle-High High Learning the likelihoods The Different variables The possible

• bservations

The probability of making that

• bservation, given

that the cow has mastitis The probability of making that

• bservation, given

that the cow does not have mastitis

Applying the likelihoods Mast. MY CE F% P% L% B% BW SSC Prev. M Parity Seas. WIM Applying the likelihoods

Prior probability of Mastitis: 5 % 16 % ariable Observed category p(Observed |Pos) p(Observed |Neg) Milk Yield Low 0.38 0.15 Middle-Low 0.25 0.34 Middle-High 0.23 0.36 High 0.14 0.15 Season Cold 0.53 0.66 Warm 0.47 0.34

Prior(pos) = 0.5  p(Pos|Yield,Season) = 0.78 Prior(pos) = 0.05  p(Pos|Yield,Season) = 0.16

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Output examples

Performances Morning vs. Evening vs. Both

AUC = 0.89 SE = 0.80 SP = 0.81

Concluding remarks Advantages:

• Good way of combining sensor and non-sensor data
• Missing data can be easily handled

Needed improvements:

• Biologically meaningful trend functions
• Better performance in the first two weeks of lactation

Perspectives:

• Alternatives to naive Bayesian classifyer