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**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

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Curve fitting

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**Optimization Least squares method:**

Minimizes the sum of squared residuals (RSS) Measured datapoint Calculated line Residual = deviation between calculated and measured data

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**Optimization Initial guess (starting value) Calculate curve Calculate**

RSS Modify parameter

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**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!

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Non-uniqueness

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**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

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**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!

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**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

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**Goodness of fit - visual assessment**

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**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

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**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)

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**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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