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Introduction to parameter optimization

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Presentation on theme: "Introduction to parameter optimization"— Presentation transcript:

1 Introduction to parameter optimization
Soils & Environmental Exposure Assessment Introduction to parameter optimization Sabine Beulke, Central Science Laboratory, York, UK Kinetic Evaluation according to Recommendations by the FOCUS Work Group on Degradation Kinetics Washington, January 2006 PSD, 6-7 March 2003

2 Curve fitting

3 Optimization Least squares method:
Minimizes the sum of squared residuals (RSS) Measured datapoint Calculated line Residual = deviation between calculated and measured data

4 Optimization Initial guess (starting value) Calculate curve Calculate
RSS Modify parameter

5 Automatic optimization
Stops when: Convergence criteria are met Comparison between RSS for actual and previous runs. Convergence reached if difference is smaller than user-specified difference Termination criteria are met For example, when maximum number of runs has been carried out (user-specified) Good fit not guaranteed!

6 Non-uniqueness

7 Non-uniqueness Parameter correlation Inadequate model
Parameters strongly related Effects on RSS of changes in one parameter can be compensated by changes in another parameter Inadequate model For example, selection of bi-phasic model not warranted if data follow SFO

8 Global versus local minimum
RSS as a function of changes in 2 parameters From: 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!

9 FOCUS 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

10 Goodness of fit - visual assessment

11 Goodness of fit - statistical criteria
2 test where C = calculated value O = observed value = mean of all observed values err = 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

12 Goodness of fit - statistical criteria
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)

13 FOCUS optimization procedure
Enter measured data Select kinetic model & parameters Initial guess (starting values) Change model, fix parameters? Eliminate outliers, weighting? Change starting values Evaluate: Visual fit Statistics Parameters Endpoints Optimize

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