Introduction to parameter optimisation Sabine Beulke, CSL, York, UK FOCUS Work Group on Degradation...
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![Page 1: Introduction to parameter optimisation Sabine Beulke, CSL, York, UK FOCUS Work Group on Degradation Kinetics Estimating Persistence and Degradation Kinetics.](https://reader036.fdocuments.in/reader036/viewer/2022082701/55152f10550346a87d8b57c2/html5/thumbnails/1.jpg)
Introduction toIntroduction toparameter optimisationparameter optimisation
Sabine Beulke, CSL, York, UK
FOCUS Work Group on Degradation Kinetics
Estimating Persistence and Degradation Kinetics
from Environmental Fate Studies in EU Registration
Brussels, 26-27 January 2005
![Page 2: Introduction to parameter optimisation Sabine Beulke, CSL, York, UK FOCUS Work Group on Degradation Kinetics Estimating Persistence and Degradation Kinetics.](https://reader036.fdocuments.in/reader036/viewer/2022082701/55152f10550346a87d8b57c2/html5/thumbnails/2.jpg)
Curve fittingCurve fitting
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![Page 3: Introduction to parameter optimisation Sabine Beulke, CSL, York, UK FOCUS Work Group on Degradation Kinetics Estimating Persistence and Degradation Kinetics.](https://reader036.fdocuments.in/reader036/viewer/2022082701/55152f10550346a87d8b57c2/html5/thumbnails/3.jpg)
OptimisationOptimisation
Least squares method:
Minimises the sum of squared residuals (RSS)
Calculated line
Residual = deviation between calculated and measured data
Measured datapoint
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![Page 4: Introduction to parameter optimisation Sabine Beulke, CSL, York, UK FOCUS Work Group on Degradation Kinetics Estimating Persistence and Degradation Kinetics.](https://reader036.fdocuments.in/reader036/viewer/2022082701/55152f10550346a87d8b57c2/html5/thumbnails/4.jpg)
OptimisationOptimisation
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Calculatecurve
Initial guess(starting value)
CalculateRSS
Modifyparameter 0
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![Page 5: Introduction to parameter optimisation Sabine Beulke, CSL, York, UK FOCUS Work Group on Degradation Kinetics Estimating Persistence and Degradation Kinetics.](https://reader036.fdocuments.in/reader036/viewer/2022082701/55152f10550346a87d8b57c2/html5/thumbnails/5.jpg)
Automatic optimisationAutomatic optimisation
Stops when:
Convergence criteria are metComparison between RSS for actual and previous runs. Convergence reached if difference is smaller than user-specified difference
Termination criteria are metFor example, when maximum number of runs has been carried out (user-specified)
Good fit not guaranteed!
![Page 6: Introduction to parameter optimisation Sabine Beulke, CSL, York, UK FOCUS Work Group on Degradation Kinetics Estimating Persistence and Degradation Kinetics.](https://reader036.fdocuments.in/reader036/viewer/2022082701/55152f10550346a87d8b57c2/html5/thumbnails/6.jpg)
Non-uniquenessNon-uniqueness
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measured FOMC
M0 92.48 DT50 7.2alpha 957.220 DT90 24.1beta 10004.3
139.277 Residual Sum of Squares
M0 92.47 DT50 7.2alpha 6696.536 DT90 24.1beta 70030.3
139.120 Residual Sum of Squares
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![Page 7: Introduction to parameter optimisation Sabine Beulke, CSL, York, UK FOCUS Work Group on Degradation Kinetics Estimating Persistence and Degradation Kinetics.](https://reader036.fdocuments.in/reader036/viewer/2022082701/55152f10550346a87d8b57c2/html5/thumbnails/7.jpg)
Non-uniquenessNon-uniqueness
Parameter correlationParameters strongly related
Effects on RSS of changes in one parameter can be compensated by changes in another parameter
Inadequate modelFor example, selection of bi-phasic model not warranted if data follow SFO
![Page 8: Introduction to parameter optimisation Sabine Beulke, CSL, York, UK FOCUS Work Group on Degradation Kinetics Estimating Persistence and Degradation Kinetics.](https://reader036.fdocuments.in/reader036/viewer/2022082701/55152f10550346a87d8b57c2/html5/thumbnails/8.jpg)
Global versus local minimumGlobal versus local minimum
The optimisation may find a local “valley” in the RSS surface, but not the absolute, global minimum.
Different parameter combinations may be returned for different starting values.
Good fit not guaranteed!
From: http://www.ssg-surfer.com/
RSS as a function ofchanges in 2 parameters
![Page 9: Introduction to parameter optimisation Sabine Beulke, CSL, York, UK FOCUS Work Group on Degradation Kinetics Estimating Persistence and Degradation Kinetics.](https://reader036.fdocuments.in/reader036/viewer/2022082701/55152f10550346a87d8b57c2/html5/thumbnails/9.jpg)
FOCUS recommendationsFOCUS recommendations
Always evaluate the visual fit
Avoid over-parameterisation
Aim at finding reasonable starting values
Always use different starting values
Constrain parameter ranges if appropriate
Plausibility checks for parameters and endpoints
Stepwise fitting where necessary
Be aware of differences between software packages
![Page 10: Introduction to parameter optimisation Sabine Beulke, CSL, York, UK FOCUS Work Group on Degradation Kinetics Estimating Persistence and Degradation Kinetics.](https://reader036.fdocuments.in/reader036/viewer/2022082701/55152f10550346a87d8b57c2/html5/thumbnails/10.jpg)
Residual plot
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Goodness of fit - visual assessmentGoodness of fit - visual assessment
Concentration vs. time plot
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![Page 11: Introduction to parameter optimisation Sabine Beulke, CSL, York, UK FOCUS Work Group on Degradation Kinetics Estimating Persistence and Degradation Kinetics.](https://reader036.fdocuments.in/reader036/viewer/2022082701/55152f10550346a87d8b57c2/html5/thumbnails/11.jpg)
Goodness of fit - statistical criteriaGoodness of fit - statistical criteria
2 test
whereC = calculated valueO = observed value = mean of all observed valueserr = measurement error percentage
If calculated 2 > tabulated 2 then the model is not appropriate at the chosen level of significance
Error percentage unknown Calculate error level at which 2 test is passed (e.g. with Excel spreadsheet provided by FOCUS)
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1100err
![Page 12: Introduction to parameter optimisation Sabine Beulke, CSL, York, UK FOCUS Work Group on Degradation Kinetics Estimating Persistence and Degradation Kinetics.](https://reader036.fdocuments.in/reader036/viewer/2022082701/55152f10550346a87d8b57c2/html5/thumbnails/12.jpg)
Confidence in parameter estimates
Calculate e.g. from ModelMaker output
A parameter is significantly different from zero if p (t) < alpha
Others (e.g. model efficiency, F-test)
iparameteroferrordardtans
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Goodness of fit - statistical criteriaGoodness of fit - statistical criteria
![Page 13: Introduction to parameter optimisation Sabine Beulke, CSL, York, UK FOCUS Work Group on Degradation Kinetics Estimating Persistence and Degradation Kinetics.](https://reader036.fdocuments.in/reader036/viewer/2022082701/55152f10550346a87d8b57c2/html5/thumbnails/13.jpg)
FOCUS optimisation procedureFOCUS optimisation procedure
Initial guess(starting values)
Enter measureddata
Evaluate:Visual fitStatistics
ParametersEndpoints
Optimise
Select kinetic model& parameters
Elim
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Ch
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ix p
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Ch
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ues